idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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36,801 | Permutation testing for machine learning: permute entire set or only training set? | I just met that question and found that there is a simulation study (Valente et al., 2021) proved to permutation all data before CV is correct.
And, here is reason.
A theoretical insight into why the other resampling schemes result in an inflation of false positives can be gained from (Bengio and Grandvalet, 2004), wh... | Permutation testing for machine learning: permute entire set or only training set? | I just met that question and found that there is a simulation study (Valente et al., 2021) proved to permutation all data before CV is correct.
And, here is reason.
A theoretical insight into why the | Permutation testing for machine learning: permute entire set or only training set?
I just met that question and found that there is a simulation study (Valente et al., 2021) proved to permutation all data before CV is correct.
And, here is reason.
A theoretical insight into why the other resampling schemes result in a... | Permutation testing for machine learning: permute entire set or only training set?
I just met that question and found that there is a simulation study (Valente et al., 2021) proved to permutation all data before CV is correct.
And, here is reason.
A theoretical insight into why the |
36,802 | Why are most epidemic models continuous-time? | This is a really interesting question and I doubt that there is any one 'correct' answer to it, but here are my thoughts on the reasons, which can be split into three categories.
History
I suggest you have a look at Section 2.7 Discrete-Time Models in the book Modeling Infectious Diseases in Humans and Animals by Keeli... | Why are most epidemic models continuous-time? | This is a really interesting question and I doubt that there is any one 'correct' answer to it, but here are my thoughts on the reasons, which can be split into three categories.
History
I suggest you | Why are most epidemic models continuous-time?
This is a really interesting question and I doubt that there is any one 'correct' answer to it, but here are my thoughts on the reasons, which can be split into three categories.
History
I suggest you have a look at Section 2.7 Discrete-Time Models in the book Modeling Infe... | Why are most epidemic models continuous-time?
This is a really interesting question and I doubt that there is any one 'correct' answer to it, but here are my thoughts on the reasons, which can be split into three categories.
History
I suggest you |
36,803 | Why are most epidemic models continuous-time? | This is an interesting question.
I mean, I guess you could ask the same thing about derivatives. What does it really mean to be going 60 kms per hour instantaneously if speed is distance travelled per unit time? It seems inherently discrete (measuring distance over a specific interval of time, even if that interval ... | Why are most epidemic models continuous-time? | This is an interesting question.
I mean, I guess you could ask the same thing about derivatives. What does it really mean to be going 60 kms per hour instantaneously if speed is distance travelled p | Why are most epidemic models continuous-time?
This is an interesting question.
I mean, I guess you could ask the same thing about derivatives. What does it really mean to be going 60 kms per hour instantaneously if speed is distance travelled per unit time? It seems inherently discrete (measuring distance over a spe... | Why are most epidemic models continuous-time?
This is an interesting question.
I mean, I guess you could ask the same thing about derivatives. What does it really mean to be going 60 kms per hour instantaneously if speed is distance travelled p |
36,804 | What is the sample space in a statistical model? | To begin with, the statistical model is a triple $(\Omega,\mathcal{F},P)$, where $\Omega$ is the sample space, $\mathcal{F}$ is a sigma-algebra of subsets of $\Omega$ and $P$ is a family of probability distributions that can be indexed by a parameter $\theta$.
To make things clear, let's understand why we need all of t... | What is the sample space in a statistical model? | To begin with, the statistical model is a triple $(\Omega,\mathcal{F},P)$, where $\Omega$ is the sample space, $\mathcal{F}$ is a sigma-algebra of subsets of $\Omega$ and $P$ is a family of probabilit | What is the sample space in a statistical model?
To begin with, the statistical model is a triple $(\Omega,\mathcal{F},P)$, where $\Omega$ is the sample space, $\mathcal{F}$ is a sigma-algebra of subsets of $\Omega$ and $P$ is a family of probability distributions that can be indexed by a parameter $\theta$.
To make th... | What is the sample space in a statistical model?
To begin with, the statistical model is a triple $(\Omega,\mathcal{F},P)$, where $\Omega$ is the sample space, $\mathcal{F}$ is a sigma-algebra of subsets of $\Omega$ and $P$ is a family of probabilit |
36,805 | What is the sample space in a statistical model? | I'll keep it as simple as I can. The sample space depends on your sampling method, but in your case, it is probably $\mathbb R^n$. Let's see how else could it be:
Let's say you decide to sample $n$ trees (it's not really relevant where and how) and measure their age and height. In that case, the sample you gather rang... | What is the sample space in a statistical model? | I'll keep it as simple as I can. The sample space depends on your sampling method, but in your case, it is probably $\mathbb R^n$. Let's see how else could it be:
Let's say you decide to sample $n$ t | What is the sample space in a statistical model?
I'll keep it as simple as I can. The sample space depends on your sampling method, but in your case, it is probably $\mathbb R^n$. Let's see how else could it be:
Let's say you decide to sample $n$ trees (it's not really relevant where and how) and measure their age and... | What is the sample space in a statistical model?
I'll keep it as simple as I can. The sample space depends on your sampling method, but in your case, it is probably $\mathbb R^n$. Let's see how else could it be:
Let's say you decide to sample $n$ t |
36,806 | What is the sample space in a statistical model? | A sample space is a set of all possible outcomes of a random experiment. An event is a subset of the sample space. A probability function takes an event as input, and outputs a real number between 0 and 1 (probability).
A stochastic model captures our understanding of the random experiment. In order to summarize all po... | What is the sample space in a statistical model? | A sample space is a set of all possible outcomes of a random experiment. An event is a subset of the sample space. A probability function takes an event as input, and outputs a real number between 0 a | What is the sample space in a statistical model?
A sample space is a set of all possible outcomes of a random experiment. An event is a subset of the sample space. A probability function takes an event as input, and outputs a real number between 0 and 1 (probability).
A stochastic model captures our understanding of th... | What is the sample space in a statistical model?
A sample space is a set of all possible outcomes of a random experiment. An event is a subset of the sample space. A probability function takes an event as input, and outputs a real number between 0 a |
36,807 | How to correctly analyze fatality rate and daily deaths of Chinese and Italian COVID-19 outbreak? | Reason 1 something technical about the computation.
Dying occurs with some delay to getting sick. As a consequence the ratio of people that got sick and the people that have died, is not equal to the ratio of people that will die.
(Still, if the number of sick cases and death cases both grow exponentially with the same... | How to correctly analyze fatality rate and daily deaths of Chinese and Italian COVID-19 outbreak? | Reason 1 something technical about the computation.
Dying occurs with some delay to getting sick. As a consequence the ratio of people that got sick and the people that have died, is not equal to the | How to correctly analyze fatality rate and daily deaths of Chinese and Italian COVID-19 outbreak?
Reason 1 something technical about the computation.
Dying occurs with some delay to getting sick. As a consequence the ratio of people that got sick and the people that have died, is not equal to the ratio of people that w... | How to correctly analyze fatality rate and daily deaths of Chinese and Italian COVID-19 outbreak?
Reason 1 something technical about the computation.
Dying occurs with some delay to getting sick. As a consequence the ratio of people that got sick and the people that have died, is not equal to the |
36,808 | How to correctly analyze fatality rate and daily deaths of Chinese and Italian COVID-19 outbreak? | Note in your wikipedia definition of case fatality rate, you NEED to know the eventual outcome of all individuals infected with disease. As they note, of the 100, 9 die, and 91 recover, they do not live with infection. Your data do not show the number who recovered from disease. If the lag between confirmed case and de... | How to correctly analyze fatality rate and daily deaths of Chinese and Italian COVID-19 outbreak? | Note in your wikipedia definition of case fatality rate, you NEED to know the eventual outcome of all individuals infected with disease. As they note, of the 100, 9 die, and 91 recover, they do not li | How to correctly analyze fatality rate and daily deaths of Chinese and Italian COVID-19 outbreak?
Note in your wikipedia definition of case fatality rate, you NEED to know the eventual outcome of all individuals infected with disease. As they note, of the 100, 9 die, and 91 recover, they do not live with infection. You... | How to correctly analyze fatality rate and daily deaths of Chinese and Italian COVID-19 outbreak?
Note in your wikipedia definition of case fatality rate, you NEED to know the eventual outcome of all individuals infected with disease. As they note, of the 100, 9 die, and 91 recover, they do not li |
36,809 | How to correctly analyze fatality rate and daily deaths of Chinese and Italian COVID-19 outbreak? | recently something occurred to us when we also perform test. The fatality rate does not quite describe number of death by certain disease to start with. We performed test against Covid-19 patient who have/not have chronic disease. it turns out patient who have chronic disease would have more chance to develop Pneumonia... | How to correctly analyze fatality rate and daily deaths of Chinese and Italian COVID-19 outbreak? | recently something occurred to us when we also perform test. The fatality rate does not quite describe number of death by certain disease to start with. We performed test against Covid-19 patient who | How to correctly analyze fatality rate and daily deaths of Chinese and Italian COVID-19 outbreak?
recently something occurred to us when we also perform test. The fatality rate does not quite describe number of death by certain disease to start with. We performed test against Covid-19 patient who have/not have chronic ... | How to correctly analyze fatality rate and daily deaths of Chinese and Italian COVID-19 outbreak?
recently something occurred to us when we also perform test. The fatality rate does not quite describe number of death by certain disease to start with. We performed test against Covid-19 patient who |
36,810 | Support Vector Machine with Perceptron Loss | Maximizing the margin is not just "rhetoric". It is the essential feature of support vector machines and ensures that the trained classifier has the optimal generalization properties. More precisely, making the margin large maximizes the probability that the classification error on new data will be small. The theory be... | Support Vector Machine with Perceptron Loss | Maximizing the margin is not just "rhetoric". It is the essential feature of support vector machines and ensures that the trained classifier has the optimal generalization properties. More precisely, | Support Vector Machine with Perceptron Loss
Maximizing the margin is not just "rhetoric". It is the essential feature of support vector machines and ensures that the trained classifier has the optimal generalization properties. More precisely, making the margin large maximizes the probability that the classification er... | Support Vector Machine with Perceptron Loss
Maximizing the margin is not just "rhetoric". It is the essential feature of support vector machines and ensures that the trained classifier has the optimal generalization properties. More precisely, |
36,811 | Is it always possible to find the feature map from a given kernel? | Short answer: It depends on what you mean by find and the precise kind of kernel you are looking at. In many cases you can prove the abstract existence of such a feature map but in practice it is always hard and generally impossible to "write it down". Furthermore, the constructions are mathematically subtle. You need ... | Is it always possible to find the feature map from a given kernel? | Short answer: It depends on what you mean by find and the precise kind of kernel you are looking at. In many cases you can prove the abstract existence of such a feature map but in practice it is alwa | Is it always possible to find the feature map from a given kernel?
Short answer: It depends on what you mean by find and the precise kind of kernel you are looking at. In many cases you can prove the abstract existence of such a feature map but in practice it is always hard and generally impossible to "write it down". ... | Is it always possible to find the feature map from a given kernel?
Short answer: It depends on what you mean by find and the precise kind of kernel you are looking at. In many cases you can prove the abstract existence of such a feature map but in practice it is alwa |
36,812 | Is there such a thing as a "good/bad" seed in pseudo-random number generation? | You might want to look at Matsumoto et al.'s "Common Defects in Initialization of Pseudorandom Number Generators".
In one sense shouldn't matter what seed you use, in that with a good PRNG, weird results should be rare, just as low-probability outcomes in nature should be rare. Whether you can use the same seed all of... | Is there such a thing as a "good/bad" seed in pseudo-random number generation? | You might want to look at Matsumoto et al.'s "Common Defects in Initialization of Pseudorandom Number Generators".
In one sense shouldn't matter what seed you use, in that with a good PRNG, weird resu | Is there such a thing as a "good/bad" seed in pseudo-random number generation?
You might want to look at Matsumoto et al.'s "Common Defects in Initialization of Pseudorandom Number Generators".
In one sense shouldn't matter what seed you use, in that with a good PRNG, weird results should be rare, just as low-probabili... | Is there such a thing as a "good/bad" seed in pseudo-random number generation?
You might want to look at Matsumoto et al.'s "Common Defects in Initialization of Pseudorandom Number Generators".
In one sense shouldn't matter what seed you use, in that with a good PRNG, weird resu |
36,813 | How to explain random forest ML algorithm doesn't learn at all, while logistic regression learns very well? | RF does very poorly when the data is highly sparse, because there's a high probability that the feature it selects to split on will be all 0s. See: When to avoid Random Forest?
Something as simple as svd or non-negative-matrix-factorization can improve RF when it recovers a useful dense representation of the sparse da... | How to explain random forest ML algorithm doesn't learn at all, while logistic regression learns ver | RF does very poorly when the data is highly sparse, because there's a high probability that the feature it selects to split on will be all 0s. See: When to avoid Random Forest?
Something as simple as | How to explain random forest ML algorithm doesn't learn at all, while logistic regression learns very well?
RF does very poorly when the data is highly sparse, because there's a high probability that the feature it selects to split on will be all 0s. See: When to avoid Random Forest?
Something as simple as svd or non-... | How to explain random forest ML algorithm doesn't learn at all, while logistic regression learns ver
RF does very poorly when the data is highly sparse, because there's a high probability that the feature it selects to split on will be all 0s. See: When to avoid Random Forest?
Something as simple as |
36,814 | How to explain random forest ML algorithm doesn't learn at all, while logistic regression learns very well? | You've left the default value for n_iter, 10, in the search. That's way too low for most uses with more than a couple important hyperparameters, and especially if your search space contains large regions of poorly performing hyperparameter combinations.
In particular, I think your tree complexity controls are too often... | How to explain random forest ML algorithm doesn't learn at all, while logistic regression learns ver | You've left the default value for n_iter, 10, in the search. That's way too low for most uses with more than a couple important hyperparameters, and especially if your search space contains large regi | How to explain random forest ML algorithm doesn't learn at all, while logistic regression learns very well?
You've left the default value for n_iter, 10, in the search. That's way too low for most uses with more than a couple important hyperparameters, and especially if your search space contains large regions of poorl... | How to explain random forest ML algorithm doesn't learn at all, while logistic regression learns ver
You've left the default value for n_iter, 10, in the search. That's way too low for most uses with more than a couple important hyperparameters, and especially if your search space contains large regi |
36,815 | Sign of Covariance and of Spearman's Rho | There are many counterexamples. But let's address the underlying question:
What I am eventually after is a proof that if $h$ is an increasing monotonic transformation, then $\operatorname{Sign}\{\operatorname{Cov}(X,Y)\}=\operatorname{Sign}\{\operatorname{Cov}(X,h(Y))\}$.
This is false.
The first counterexample is ... | Sign of Covariance and of Spearman's Rho | There are many counterexamples. But let's address the underlying question:
What I am eventually after is a proof that if $h$ is an increasing monotonic transformation, then $\operatorname{Sign}\{\op | Sign of Covariance and of Spearman's Rho
There are many counterexamples. But let's address the underlying question:
What I am eventually after is a proof that if $h$ is an increasing monotonic transformation, then $\operatorname{Sign}\{\operatorname{Cov}(X,Y)\}=\operatorname{Sign}\{\operatorname{Cov}(X,h(Y))\}$.
Thi... | Sign of Covariance and of Spearman's Rho
There are many counterexamples. But let's address the underlying question:
What I am eventually after is a proof that if $h$ is an increasing monotonic transformation, then $\operatorname{Sign}\{\op |
36,816 | Sign of Covariance and of Spearman's Rho | I say they can have opposite signs.
Let's look at the following simulation.
# Set a random seed so that everyone can get the same results
#
set.seed(1)
# Import the library that simulates correlated bivariate data
#
library(MASS)
# Simulate bivariate normal data with standard normal
# marginals and 0.9 Pears... | Sign of Covariance and of Spearman's Rho | I say they can have opposite signs.
Let's look at the following simulation.
# Set a random seed so that everyone can get the same results
#
set.seed(1)
# Import the library that simulates correl | Sign of Covariance and of Spearman's Rho
I say they can have opposite signs.
Let's look at the following simulation.
# Set a random seed so that everyone can get the same results
#
set.seed(1)
# Import the library that simulates correlated bivariate data
#
library(MASS)
# Simulate bivariate normal data with s... | Sign of Covariance and of Spearman's Rho
I say they can have opposite signs.
Let's look at the following simulation.
# Set a random seed so that everyone can get the same results
#
set.seed(1)
# Import the library that simulates correl |
36,817 | Sign of Covariance and of Spearman's Rho | To enhance the value of this thread I will lay out why Quadrant Dependence implies that
a) Covariance will have the same sign as Spearman's Rho if both are not zero
b) The sign of covariance is not affected by strictly increasing monotonic transformations, if it remains non-zero.
I will show it for continuous distribut... | Sign of Covariance and of Spearman's Rho | To enhance the value of this thread I will lay out why Quadrant Dependence implies that
a) Covariance will have the same sign as Spearman's Rho if both are not zero
b) The sign of covariance is not af | Sign of Covariance and of Spearman's Rho
To enhance the value of this thread I will lay out why Quadrant Dependence implies that
a) Covariance will have the same sign as Spearman's Rho if both are not zero
b) The sign of covariance is not affected by strictly increasing monotonic transformations, if it remains non-zero... | Sign of Covariance and of Spearman's Rho
To enhance the value of this thread I will lay out why Quadrant Dependence implies that
a) Covariance will have the same sign as Spearman's Rho if both are not zero
b) The sign of covariance is not af |
36,818 | How can I compare models without fitting? | In this situation you are essentially comparing the distributions of the $\epsilon_i$ among the 3 models. So you need to examine issues like:
Are the mean values of the $\epsilon_i$ different among the 3 models, and is any of these mean values different from 0? (That is, is there a bias in any of the models and do the... | How can I compare models without fitting? | In this situation you are essentially comparing the distributions of the $\epsilon_i$ among the 3 models. So you need to examine issues like:
Are the mean values of the $\epsilon_i$ different among t | How can I compare models without fitting?
In this situation you are essentially comparing the distributions of the $\epsilon_i$ among the 3 models. So you need to examine issues like:
Are the mean values of the $\epsilon_i$ different among the 3 models, and is any of these mean values different from 0? (That is, is th... | How can I compare models without fitting?
In this situation you are essentially comparing the distributions of the $\epsilon_i$ among the 3 models. So you need to examine issues like:
Are the mean values of the $\epsilon_i$ different among t |
36,819 | How can I compare models without fitting? | A probabilistic comparison of the models, e.g. involving some likelihood computed from the $\epsilon$ with some data (and derived from this AIC or ratio test), makes little sense.
This is because
You already know for certain that the model is gonna be wrong.
The residuals that you end up with have no relation with t... | How can I compare models without fitting? | A probabilistic comparison of the models, e.g. involving some likelihood computed from the $\epsilon$ with some data (and derived from this AIC or ratio test), makes little sense.
This is because
Y | How can I compare models without fitting?
A probabilistic comparison of the models, e.g. involving some likelihood computed from the $\epsilon$ with some data (and derived from this AIC or ratio test), makes little sense.
This is because
You already know for certain that the model is gonna be wrong.
The residuals th... | How can I compare models without fitting?
A probabilistic comparison of the models, e.g. involving some likelihood computed from the $\epsilon$ with some data (and derived from this AIC or ratio test), makes little sense.
This is because
Y |
36,820 | Using regression weights when $Y$ might be measured with nonzero-mean measurement error | I would use the 'probability of biased' as a dummy variable in the regression; it can possibly 'sop up' the bias present in the biased case. Using your example, (but calling set.seed(1234) before the call to get_df), I tried
summary(lm(y_observed ~ x1 + x2 + I(1-pr_unbiased), data=df_unrated))
and got:
Call:
lm(formul... | Using regression weights when $Y$ might be measured with nonzero-mean measurement error | I would use the 'probability of biased' as a dummy variable in the regression; it can possibly 'sop up' the bias present in the biased case. Using your example, (but calling set.seed(1234) before the | Using regression weights when $Y$ might be measured with nonzero-mean measurement error
I would use the 'probability of biased' as a dummy variable in the regression; it can possibly 'sop up' the bias present in the biased case. Using your example, (but calling set.seed(1234) before the call to get_df), I tried
summary... | Using regression weights when $Y$ might be measured with nonzero-mean measurement error
I would use the 'probability of biased' as a dummy variable in the regression; it can possibly 'sop up' the bias present in the biased case. Using your example, (but calling set.seed(1234) before the |
36,821 | Using regression weights when $Y$ might be measured with nonzero-mean measurement error | This is an omitted-variable problem where you have an indicator variable $Z$ that is unobserved, but which has a relationship with the response variable. Since "bias" is a property of an estimator, not a regression variable, I am going to reframe your question as one where you want to find the true regression function... | Using regression weights when $Y$ might be measured with nonzero-mean measurement error | This is an omitted-variable problem where you have an indicator variable $Z$ that is unobserved, but which has a relationship with the response variable. Since "bias" is a property of an estimator, n | Using regression weights when $Y$ might be measured with nonzero-mean measurement error
This is an omitted-variable problem where you have an indicator variable $Z$ that is unobserved, but which has a relationship with the response variable. Since "bias" is a property of an estimator, not a regression variable, I am g... | Using regression weights when $Y$ might be measured with nonzero-mean measurement error
This is an omitted-variable problem where you have an indicator variable $Z$ that is unobserved, but which has a relationship with the response variable. Since "bias" is a property of an estimator, n |
36,822 | Using regression weights when $Y$ might be measured with nonzero-mean measurement error | Your idea will not give an unbiased estimate, unless you can always be 100% sure whether it is biased or not. As soon as one biased example can be part of your training set with nonzero probability, there will be bias, as you have nothing to cancel out that bias. In practice, your bias will simply be multiplied by a fa... | Using regression weights when $Y$ might be measured with nonzero-mean measurement error | Your idea will not give an unbiased estimate, unless you can always be 100% sure whether it is biased or not. As soon as one biased example can be part of your training set with nonzero probability, t | Using regression weights when $Y$ might be measured with nonzero-mean measurement error
Your idea will not give an unbiased estimate, unless you can always be 100% sure whether it is biased or not. As soon as one biased example can be part of your training set with nonzero probability, there will be bias, as you have n... | Using regression weights when $Y$ might be measured with nonzero-mean measurement error
Your idea will not give an unbiased estimate, unless you can always be 100% sure whether it is biased or not. As soon as one biased example can be part of your training set with nonzero probability, t |
36,823 | Convergence of the Matérn covariance function to the squared exponential | The Matérn function can be written in terms of
$$f_{\nu}(x) = C_\nu |x|^{\nu} K_{\nu}\left(|x|\right)\tag{*}$$
where $C_\nu$ is a normalizing constant (to make the value of $f_\nu(0)$ equal to $1$) and $x = \sqrt{2\nu}\, d/\rho.$
(This agrees with the Wikipedia notation where $x$ represents $\sqrt{2\nu} d/\rho.$)
As sh... | Convergence of the Matérn covariance function to the squared exponential | The Matérn function can be written in terms of
$$f_{\nu}(x) = C_\nu |x|^{\nu} K_{\nu}\left(|x|\right)\tag{*}$$
where $C_\nu$ is a normalizing constant (to make the value of $f_\nu(0)$ equal to $1$) an | Convergence of the Matérn covariance function to the squared exponential
The Matérn function can be written in terms of
$$f_{\nu}(x) = C_\nu |x|^{\nu} K_{\nu}\left(|x|\right)\tag{*}$$
where $C_\nu$ is a normalizing constant (to make the value of $f_\nu(0)$ equal to $1$) and $x = \sqrt{2\nu}\, d/\rho.$
(This agrees with... | Convergence of the Matérn covariance function to the squared exponential
The Matérn function can be written in terms of
$$f_{\nu}(x) = C_\nu |x|^{\nu} K_{\nu}\left(|x|\right)\tag{*}$$
where $C_\nu$ is a normalizing constant (to make the value of $f_\nu(0)$ equal to $1$) an |
36,824 | $\min(x)$ as a quantile estimator for the 1% quantile of $x$ | Min of 100 observations long sample is used as an estimator of 1% quantile in practice. I've seen it called "empirical percentile."
Known distribution family
If you want a different estimate AND have an idea about the distribution of the data, then I suggest to look at order statistics medians. For instance, this R pa... | $\min(x)$ as a quantile estimator for the 1% quantile of $x$ | Min of 100 observations long sample is used as an estimator of 1% quantile in practice. I've seen it called "empirical percentile."
Known distribution family
If you want a different estimate AND have | $\min(x)$ as a quantile estimator for the 1% quantile of $x$
Min of 100 observations long sample is used as an estimator of 1% quantile in practice. I've seen it called "empirical percentile."
Known distribution family
If you want a different estimate AND have an idea about the distribution of the data, then I suggest... | $\min(x)$ as a quantile estimator for the 1% quantile of $x$
Min of 100 observations long sample is used as an estimator of 1% quantile in practice. I've seen it called "empirical percentile."
Known distribution family
If you want a different estimate AND have |
36,825 | What does decay_steps mean in Tensorflow tf.train.exponential_decay? | As mentioned in the code of the function the relation of decay_steps with decayed_learning_rate is the following:
decayed_learning_rate = learning_rate *
decay_rate ^ (global_step / decay_steps)
Hence, you should set the decay_steps proportional to the global_step of the algorithm. | What does decay_steps mean in Tensorflow tf.train.exponential_decay? | As mentioned in the code of the function the relation of decay_steps with decayed_learning_rate is the following:
decayed_learning_rate = learning_rate *
decay_rate ^ (global_ste | What does decay_steps mean in Tensorflow tf.train.exponential_decay?
As mentioned in the code of the function the relation of decay_steps with decayed_learning_rate is the following:
decayed_learning_rate = learning_rate *
decay_rate ^ (global_step / decay_steps)
Hence, you should set the decay_s... | What does decay_steps mean in Tensorflow tf.train.exponential_decay?
As mentioned in the code of the function the relation of decay_steps with decayed_learning_rate is the following:
decayed_learning_rate = learning_rate *
decay_rate ^ (global_ste |
36,826 | Calculate the variance of $\sum\limits_{i=1}^{n-1} \sum\limits_{j=i+1}^n S(X_i - X_j)$ for $X_1,\ldots,X_n$ i.i.d. random variables | For the covariance term $\operatorname{Cov}\{S(X_i-X_j),S(X_l-X_w)\}, j>i, w>l$ the only zero cases occur when both $l$ and $w$ are different from $i$ and $j$.
Tedious decomposition of the summations gives
\begin{align}
4^{-1}n^4 \operatorname{Var}(U) = {} & \sum_{i=1}^{n-1} \sum_{j>i}^n \operatorname{Var} \{S(X_i-X_j)... | Calculate the variance of $\sum\limits_{i=1}^{n-1} \sum\limits_{j=i+1}^n S(X_i - X_j)$ for $X_1,\ldo | For the covariance term $\operatorname{Cov}\{S(X_i-X_j),S(X_l-X_w)\}, j>i, w>l$ the only zero cases occur when both $l$ and $w$ are different from $i$ and $j$.
Tedious decomposition of the summations | Calculate the variance of $\sum\limits_{i=1}^{n-1} \sum\limits_{j=i+1}^n S(X_i - X_j)$ for $X_1,\ldots,X_n$ i.i.d. random variables
For the covariance term $\operatorname{Cov}\{S(X_i-X_j),S(X_l-X_w)\}, j>i, w>l$ the only zero cases occur when both $l$ and $w$ are different from $i$ and $j$.
Tedious decomposition of the... | Calculate the variance of $\sum\limits_{i=1}^{n-1} \sum\limits_{j=i+1}^n S(X_i - X_j)$ for $X_1,\ldo
For the covariance term $\operatorname{Cov}\{S(X_i-X_j),S(X_l-X_w)\}, j>i, w>l$ the only zero cases occur when both $l$ and $w$ are different from $i$ and $j$.
Tedious decomposition of the summations |
36,827 | Calculate the variance of $\sum\limits_{i=1}^{n-1} \sum\limits_{j=i+1}^n S(X_i - X_j)$ for $X_1,\ldots,X_n$ i.i.d. random variables | You have the right idea writing the variance as a sum of many covariances. Using iid-ness, you just need to separate that into two or three different kinds of sums that all have equal summands. Once you know all the summands are equal, you just need to count the number of times they show up.
If you look at the answer y... | Calculate the variance of $\sum\limits_{i=1}^{n-1} \sum\limits_{j=i+1}^n S(X_i - X_j)$ for $X_1,\ldo | You have the right idea writing the variance as a sum of many covariances. Using iid-ness, you just need to separate that into two or three different kinds of sums that all have equal summands. Once y | Calculate the variance of $\sum\limits_{i=1}^{n-1} \sum\limits_{j=i+1}^n S(X_i - X_j)$ for $X_1,\ldots,X_n$ i.i.d. random variables
You have the right idea writing the variance as a sum of many covariances. Using iid-ness, you just need to separate that into two or three different kinds of sums that all have equal summ... | Calculate the variance of $\sum\limits_{i=1}^{n-1} \sum\limits_{j=i+1}^n S(X_i - X_j)$ for $X_1,\ldo
You have the right idea writing the variance as a sum of many covariances. Using iid-ness, you just need to separate that into two or three different kinds of sums that all have equal summands. Once y |
36,828 | Calculate the variance of $\sum\limits_{i=1}^{n-1} \sum\limits_{j=i+1}^n S(X_i - X_j)$ for $X_1,\ldots,X_n$ i.i.d. random variables | You wrote: "since $\operatorname{Cov}\{S(X_i-X_j),S(X_\ell-X_w)\}=0,\forall i\neq \ell,j \neq w$."
That's wrong. In some terms you have $i\ne\ell$ and $j\ne w$ but $\ell=j.$ What happens then?
Suppose $n=5$ and $(i,j)=(1,2)$ and we forbid $1=\ell$ and $2=j.$ Then cases of nonzero covariance include:
\begin{align}
(\ell... | Calculate the variance of $\sum\limits_{i=1}^{n-1} \sum\limits_{j=i+1}^n S(X_i - X_j)$ for $X_1,\ldo | You wrote: "since $\operatorname{Cov}\{S(X_i-X_j),S(X_\ell-X_w)\}=0,\forall i\neq \ell,j \neq w$."
That's wrong. In some terms you have $i\ne\ell$ and $j\ne w$ but $\ell=j.$ What happens then?
Suppose | Calculate the variance of $\sum\limits_{i=1}^{n-1} \sum\limits_{j=i+1}^n S(X_i - X_j)$ for $X_1,\ldots,X_n$ i.i.d. random variables
You wrote: "since $\operatorname{Cov}\{S(X_i-X_j),S(X_\ell-X_w)\}=0,\forall i\neq \ell,j \neq w$."
That's wrong. In some terms you have $i\ne\ell$ and $j\ne w$ but $\ell=j.$ What happens t... | Calculate the variance of $\sum\limits_{i=1}^{n-1} \sum\limits_{j=i+1}^n S(X_i - X_j)$ for $X_1,\ldo
You wrote: "since $\operatorname{Cov}\{S(X_i-X_j),S(X_\ell-X_w)\}=0,\forall i\neq \ell,j \neq w$."
That's wrong. In some terms you have $i\ne\ell$ and $j\ne w$ but $\ell=j.$ What happens then?
Suppose |
36,829 | When are correlated Normal random variables multivariate Normal? [duplicate] | Say I observe n univariate random variables $X_1, \dots, X_n$ that are each $N(\mu, \sigma^2)$ with common correlation $\rho$. Is it possible that these are jointly normal? If so, what are the conditions and how would I know if they are jointly normal.
There are no conditions based only on the marginal pdfs that can ... | When are correlated Normal random variables multivariate Normal? [duplicate] | Say I observe n univariate random variables $X_1, \dots, X_n$ that are each $N(\mu, \sigma^2)$ with common correlation $\rho$. Is it possible that these are jointly normal? If so, what are the condit | When are correlated Normal random variables multivariate Normal? [duplicate]
Say I observe n univariate random variables $X_1, \dots, X_n$ that are each $N(\mu, \sigma^2)$ with common correlation $\rho$. Is it possible that these are jointly normal? If so, what are the conditions and how would I know if they are joint... | When are correlated Normal random variables multivariate Normal? [duplicate]
Say I observe n univariate random variables $X_1, \dots, X_n$ that are each $N(\mu, \sigma^2)$ with common correlation $\rho$. Is it possible that these are jointly normal? If so, what are the condit |
36,830 | When are correlated Normal random variables multivariate Normal? [duplicate] | It certainly is possible.
From a theoretical perspective, there are many different ways to "characterize" the Multivariate Normal distribution, see for example Hamedani, G. G. (1992). Bivariate and multivariate normal characterizations: a brief survey. Communications in Statistics-Theory and Methods, 21(9), 2665-2688.... | When are correlated Normal random variables multivariate Normal? [duplicate] | It certainly is possible.
From a theoretical perspective, there are many different ways to "characterize" the Multivariate Normal distribution, see for example Hamedani, G. G. (1992). Bivariate and m | When are correlated Normal random variables multivariate Normal? [duplicate]
It certainly is possible.
From a theoretical perspective, there are many different ways to "characterize" the Multivariate Normal distribution, see for example Hamedani, G. G. (1992). Bivariate and multivariate normal characterizations: a bri... | When are correlated Normal random variables multivariate Normal? [duplicate]
It certainly is possible.
From a theoretical perspective, there are many different ways to "characterize" the Multivariate Normal distribution, see for example Hamedani, G. G. (1992). Bivariate and m |
36,831 | When are correlated Normal random variables multivariate Normal? [duplicate] | This is an interesting question. I will look at it from another viewpoint: When should you expect that a joint distribution with normal marginals, not is multinormal?
Certain phenomena occurring in data cannot be described by a multinormal distribution, and some examples (even a list) of such phenomena is interesting.... | When are correlated Normal random variables multivariate Normal? [duplicate] | This is an interesting question. I will look at it from another viewpoint: When should you expect that a joint distribution with normal marginals, not is multinormal?
Certain phenomena occurring in d | When are correlated Normal random variables multivariate Normal? [duplicate]
This is an interesting question. I will look at it from another viewpoint: When should you expect that a joint distribution with normal marginals, not is multinormal?
Certain phenomena occurring in data cannot be described by a multinormal di... | When are correlated Normal random variables multivariate Normal? [duplicate]
This is an interesting question. I will look at it from another viewpoint: When should you expect that a joint distribution with normal marginals, not is multinormal?
Certain phenomena occurring in d |
36,832 | Examples of variables on interval scale (besides temperature) | I will consider a variable on an interval scale to be one which has an order of their elements, with a meaningful and comparable difference, but with a zero which is not meaningful. This is in contrast with ratio scales which have all the qualities of interval scales and also a meaningful zero, where zero means the qu... | Examples of variables on interval scale (besides temperature) | I will consider a variable on an interval scale to be one which has an order of their elements, with a meaningful and comparable difference, but with a zero which is not meaningful. This is in contra | Examples of variables on interval scale (besides temperature)
I will consider a variable on an interval scale to be one which has an order of their elements, with a meaningful and comparable difference, but with a zero which is not meaningful. This is in contrast with ratio scales which have all the qualities of inter... | Examples of variables on interval scale (besides temperature)
I will consider a variable on an interval scale to be one which has an order of their elements, with a meaningful and comparable difference, but with a zero which is not meaningful. This is in contra |
36,833 | Examples of variables on interval scale (besides temperature) | In economics, utility can be considered to be on interval scale. There is some disagreement whether utility should be ordinal or cardinal, but in the case of cardinal utility, it is measured on the interval scale.
The following is a quote from Wikipedia's article on Cardinal utility, section Measurability:
It is help... | Examples of variables on interval scale (besides temperature) | In economics, utility can be considered to be on interval scale. There is some disagreement whether utility should be ordinal or cardinal, but in the case of cardinal utility, it is measured on the i | Examples of variables on interval scale (besides temperature)
In economics, utility can be considered to be on interval scale. There is some disagreement whether utility should be ordinal or cardinal, but in the case of cardinal utility, it is measured on the interval scale.
The following is a quote from Wikipedia's a... | Examples of variables on interval scale (besides temperature)
In economics, utility can be considered to be on interval scale. There is some disagreement whether utility should be ordinal or cardinal, but in the case of cardinal utility, it is measured on the i |
36,834 | Calculate probability of disease appearance | I personally feel this lends itself well to a survival analysis.
You have people without moles in a certain hand at the start of the period (your at risk population); you can select these, and you have time points for follow-up and whether or not they were censored (developed a mole). This gives you a hazard for whatev... | Calculate probability of disease appearance | I personally feel this lends itself well to a survival analysis.
You have people without moles in a certain hand at the start of the period (your at risk population); you can select these, and you hav | Calculate probability of disease appearance
I personally feel this lends itself well to a survival analysis.
You have people without moles in a certain hand at the start of the period (your at risk population); you can select these, and you have time points for follow-up and whether or not they were censored (developed... | Calculate probability of disease appearance
I personally feel this lends itself well to a survival analysis.
You have people without moles in a certain hand at the start of the period (your at risk population); you can select these, and you hav |
36,835 | Calculate probability of disease appearance | There is no modeling to be done here, all of your questions are simple conditional probabilities.
Alright, since people did not appreciate that answer, you need to clarify a couple of things.
I am interested in finding the probability of a hand developing a mole among only the patients that developed a mole in one h... | Calculate probability of disease appearance | There is no modeling to be done here, all of your questions are simple conditional probabilities.
Alright, since people did not appreciate that answer, you need to clarify a couple of things.
I am | Calculate probability of disease appearance
There is no modeling to be done here, all of your questions are simple conditional probabilities.
Alright, since people did not appreciate that answer, you need to clarify a couple of things.
I am interested in finding the probability of a hand developing a mole among only... | Calculate probability of disease appearance
There is no modeling to be done here, all of your questions are simple conditional probabilities.
Alright, since people did not appreciate that answer, you need to clarify a couple of things.
I am |
36,836 | Calculate probability of disease appearance | Personally, I think you can start by studying the multicovariance
generalized linear models: https://cran.r-project.org/web/packages/mcglm/index.html
https://cran.r-project.org/web/packages/mcglm/vignettes/GLMExamples.html
http://cursos.leg.ufpr.br/mcglm4aed/slides/2-mcglm.html#(1)
Those models are apropriated for wh... | Calculate probability of disease appearance | Personally, I think you can start by studying the multicovariance
generalized linear models: https://cran.r-project.org/web/packages/mcglm/index.html
https://cran.r-project.org/web/packages/mcglm/vig | Calculate probability of disease appearance
Personally, I think you can start by studying the multicovariance
generalized linear models: https://cran.r-project.org/web/packages/mcglm/index.html
https://cran.r-project.org/web/packages/mcglm/vignettes/GLMExamples.html
http://cursos.leg.ufpr.br/mcglm4aed/slides/2-mcglm.... | Calculate probability of disease appearance
Personally, I think you can start by studying the multicovariance
generalized linear models: https://cran.r-project.org/web/packages/mcglm/index.html
https://cran.r-project.org/web/packages/mcglm/vig |
36,837 | What is the difference between invariance to translation, covariance to translation and equivariance to translation? | There are two schools of thought when it comes to definitin of equivariance, covariance, invariance, and same-equivariance.
Covariance is a concept often used in physics and is the same term as equivariance. Both are used when applying the transformation $\pi$ on the input of the function $f$ can be achieved by appyin... | What is the difference between invariance to translation, covariance to translation and equivariance | There are two schools of thought when it comes to definitin of equivariance, covariance, invariance, and same-equivariance.
Covariance is a concept often used in physics and is the same term as equiv | What is the difference between invariance to translation, covariance to translation and equivariance to translation?
There are two schools of thought when it comes to definitin of equivariance, covariance, invariance, and same-equivariance.
Covariance is a concept often used in physics and is the same term as equivari... | What is the difference between invariance to translation, covariance to translation and equivariance
There are two schools of thought when it comes to definitin of equivariance, covariance, invariance, and same-equivariance.
Covariance is a concept often used in physics and is the same term as equiv |
36,838 | Transfer learning: How and why retrain only final layers of a network? | Why would one want to avoid retaining all the layers of a transfer learning network if the fine-tuning dataset was small? Ie, (if I understand it correctly), why would one not want to apply normal back-propagation through to the input layer?
If the new dataset is small, the reason to restrict training to the new layer... | Transfer learning: How and why retrain only final layers of a network? | Why would one want to avoid retaining all the layers of a transfer learning network if the fine-tuning dataset was small? Ie, (if I understand it correctly), why would one not want to apply normal bac | Transfer learning: How and why retrain only final layers of a network?
Why would one want to avoid retaining all the layers of a transfer learning network if the fine-tuning dataset was small? Ie, (if I understand it correctly), why would one not want to apply normal back-propagation through to the input layer?
If the... | Transfer learning: How and why retrain only final layers of a network?
Why would one want to avoid retaining all the layers of a transfer learning network if the fine-tuning dataset was small? Ie, (if I understand it correctly), why would one not want to apply normal bac |
36,839 | Transfer learning: How and why retrain only final layers of a network? | This answer applies to finetuning pretrained transformer models in NLP, but not computer vision.
Contrary to Ng's advice, and somewhat contrary to the currently accepted answer, it's standard practice to fine-tune the entire transformer, more-or-less regardless of the amount of training data. See the standard text clas... | Transfer learning: How and why retrain only final layers of a network? | This answer applies to finetuning pretrained transformer models in NLP, but not computer vision.
Contrary to Ng's advice, and somewhat contrary to the currently accepted answer, it's standard practice | Transfer learning: How and why retrain only final layers of a network?
This answer applies to finetuning pretrained transformer models in NLP, but not computer vision.
Contrary to Ng's advice, and somewhat contrary to the currently accepted answer, it's standard practice to fine-tune the entire transformer, more-or-les... | Transfer learning: How and why retrain only final layers of a network?
This answer applies to finetuning pretrained transformer models in NLP, but not computer vision.
Contrary to Ng's advice, and somewhat contrary to the currently accepted answer, it's standard practice |
36,840 | Finite sum of beta prime iid random variables | Let $\{X_i\}_{i=1}^n$ with $X_i\overset{\text{i.i.d}}{\sim}\beta^\prime(\alpha,\beta)$ and $Z=X_1+\dots+X_n$. It follows from linearity of the expected value that
$$
\mathsf EZ=\sum_{i=1}^n\mathsf EX_i=n\mathsf EX=\frac{n\alpha}{\beta-1},\quad\beta>1.
$$
Furthermore, by mutual independence of the $X_i$'s we have
$$
\ma... | Finite sum of beta prime iid random variables | Let $\{X_i\}_{i=1}^n$ with $X_i\overset{\text{i.i.d}}{\sim}\beta^\prime(\alpha,\beta)$ and $Z=X_1+\dots+X_n$. It follows from linearity of the expected value that
$$
\mathsf EZ=\sum_{i=1}^n\mathsf EX_ | Finite sum of beta prime iid random variables
Let $\{X_i\}_{i=1}^n$ with $X_i\overset{\text{i.i.d}}{\sim}\beta^\prime(\alpha,\beta)$ and $Z=X_1+\dots+X_n$. It follows from linearity of the expected value that
$$
\mathsf EZ=\sum_{i=1}^n\mathsf EX_i=n\mathsf EX=\frac{n\alpha}{\beta-1},\quad\beta>1.
$$
Furthermore, by mut... | Finite sum of beta prime iid random variables
Let $\{X_i\}_{i=1}^n$ with $X_i\overset{\text{i.i.d}}{\sim}\beta^\prime(\alpha,\beta)$ and $Z=X_1+\dots+X_n$. It follows from linearity of the expected value that
$$
\mathsf EZ=\sum_{i=1}^n\mathsf EX_ |
36,841 | Interpretation of the Pearson Correlation with respect to Z-Scores | The Pearson sample correlation coefficient can be written as:
$$r = \frac{1}{n-1} \sum_{i=1}^n z_{1,i} \cdot z_{2,i} \quad \quad \quad z_{k,i} = \frac{x_{k,i} - \bar{x}_k}{s_k}.$$
This result means that the sample correlation of two vectors $\boldsymbol{x}_1$ and $\boldsymbol{x}_2$ is equivalent to the sample correlati... | Interpretation of the Pearson Correlation with respect to Z-Scores | The Pearson sample correlation coefficient can be written as:
$$r = \frac{1}{n-1} \sum_{i=1}^n z_{1,i} \cdot z_{2,i} \quad \quad \quad z_{k,i} = \frac{x_{k,i} - \bar{x}_k}{s_k}.$$
This result means th | Interpretation of the Pearson Correlation with respect to Z-Scores
The Pearson sample correlation coefficient can be written as:
$$r = \frac{1}{n-1} \sum_{i=1}^n z_{1,i} \cdot z_{2,i} \quad \quad \quad z_{k,i} = \frac{x_{k,i} - \bar{x}_k}{s_k}.$$
This result means that the sample correlation of two vectors $\boldsymbol... | Interpretation of the Pearson Correlation with respect to Z-Scores
The Pearson sample correlation coefficient can be written as:
$$r = \frac{1}{n-1} \sum_{i=1}^n z_{1,i} \cdot z_{2,i} \quad \quad \quad z_{k,i} = \frac{x_{k,i} - \bar{x}_k}{s_k}.$$
This result means th |
36,842 | Interpretation of the Pearson Correlation with respect to Z-Scores | Consider a simple linear regression on ($y_i$, $x_i$), $i=1,..,n: y_i = \alpha + \beta*x_i + e_i$, where $e_i$ is error (and the usual regression assumptions) and take a look at the regression coefficient: $\hat{\beta} = S_{xy}/S_{xx}$, which can be written as a function of the correlation coefficient r. Specificially,... | Interpretation of the Pearson Correlation with respect to Z-Scores | Consider a simple linear regression on ($y_i$, $x_i$), $i=1,..,n: y_i = \alpha + \beta*x_i + e_i$, where $e_i$ is error (and the usual regression assumptions) and take a look at the regression coeffic | Interpretation of the Pearson Correlation with respect to Z-Scores
Consider a simple linear regression on ($y_i$, $x_i$), $i=1,..,n: y_i = \alpha + \beta*x_i + e_i$, where $e_i$ is error (and the usual regression assumptions) and take a look at the regression coefficient: $\hat{\beta} = S_{xy}/S_{xx}$, which can be wri... | Interpretation of the Pearson Correlation with respect to Z-Scores
Consider a simple linear regression on ($y_i$, $x_i$), $i=1,..,n: y_i = \alpha + \beta*x_i + e_i$, where $e_i$ is error (and the usual regression assumptions) and take a look at the regression coeffic |
36,843 | Seasonal Data with GAMMs | Depends how you want nest the autocorrelation, within days?
modar2 <- gamm(apparentTemperature ~ s(year) + s(month, bs = "cc", k = 12) +
s(time, k = 20), data = timetemp,
correlation = corARMA(form = ~ 1|day, p = 2),
control = ctrl)
would have smooth long term trend, smooth... | Seasonal Data with GAMMs | Depends how you want nest the autocorrelation, within days?
modar2 <- gamm(apparentTemperature ~ s(year) + s(month, bs = "cc", k = 12) +
s(time, k = 20), data = timetemp,
| Seasonal Data with GAMMs
Depends how you want nest the autocorrelation, within days?
modar2 <- gamm(apparentTemperature ~ s(year) + s(month, bs = "cc", k = 12) +
s(time, k = 20), data = timetemp,
correlation = corARMA(form = ~ 1|day, p = 2),
control = ctrl)
would have smoot... | Seasonal Data with GAMMs
Depends how you want nest the autocorrelation, within days?
modar2 <- gamm(apparentTemperature ~ s(year) + s(month, bs = "cc", k = 12) +
s(time, k = 20), data = timetemp,
|
36,844 | Support vector machines (SVMs) are the zero temperature limit of logistic regression? | In the case of hard-margin SVM and linearly separable data, this is true.
An intuitive sketch: The loss for each datapoint in logistic regression dies out almost as an exponential decay curve as you get farther from the decision boundary (in the correct direction of course). This exponential decay means that the points... | Support vector machines (SVMs) are the zero temperature limit of logistic regression? | In the case of hard-margin SVM and linearly separable data, this is true.
An intuitive sketch: The loss for each datapoint in logistic regression dies out almost as an exponential decay curve as you g | Support vector machines (SVMs) are the zero temperature limit of logistic regression?
In the case of hard-margin SVM and linearly separable data, this is true.
An intuitive sketch: The loss for each datapoint in logistic regression dies out almost as an exponential decay curve as you get farther from the decision bound... | Support vector machines (SVMs) are the zero temperature limit of logistic regression?
In the case of hard-margin SVM and linearly separable data, this is true.
An intuitive sketch: The loss for each datapoint in logistic regression dies out almost as an exponential decay curve as you g |
36,845 | random forest for imbalanced data? | There are usually two methods to deal with imbalanced data while using the random forest model. One approach is cost-sensitive learning and the other is sampling. For extremely imbalanced data, random forest generally tends to be biased towards the majority class.
The cost-sensitive approach would be to assign differe... | random forest for imbalanced data? | There are usually two methods to deal with imbalanced data while using the random forest model. One approach is cost-sensitive learning and the other is sampling. For extremely imbalanced data, random | random forest for imbalanced data?
There are usually two methods to deal with imbalanced data while using the random forest model. One approach is cost-sensitive learning and the other is sampling. For extremely imbalanced data, random forest generally tends to be biased towards the majority class.
The cost-sensitive ... | random forest for imbalanced data?
There are usually two methods to deal with imbalanced data while using the random forest model. One approach is cost-sensitive learning and the other is sampling. For extremely imbalanced data, random |
36,846 | Distribution of $X+Y$ when $X$ and $Y$ are i.i.d with pdf $f(x)=\alpha\beta^{-\alpha}x^{\alpha-1}\mathbf1_{0<x<\beta}$ | Since
\begin{align}
\int_{\max(t-\beta,0)}^{\min(t,\beta)}(y(t-y))^{\alpha-1}\,\mathrm{d}y\,\mathbf1_{0<t<2\beta}&=\begin{cases}
\int_{0}^{t}(y(t-y))^{\alpha-1}\,\mathrm{d}y&\text{when }0\le t\le \beta\\
\int_{t-\beta}^{\beta}(y(t-y))^{\alpha-1}\,\mathrm{d}y&\text{when }\beta\le t\le 2\beta\\
\end{cases}\\
\end{align}
... | Distribution of $X+Y$ when $X$ and $Y$ are i.i.d with pdf $f(x)=\alpha\beta^{-\alpha}x^{\alpha-1}\ma | Since
\begin{align}
\int_{\max(t-\beta,0)}^{\min(t,\beta)}(y(t-y))^{\alpha-1}\,\mathrm{d}y\,\mathbf1_{0<t<2\beta}&=\begin{cases}
\int_{0}^{t}(y(t-y))^{\alpha-1}\,\mathrm{d}y&\text{when }0\le t\le \bet | Distribution of $X+Y$ when $X$ and $Y$ are i.i.d with pdf $f(x)=\alpha\beta^{-\alpha}x^{\alpha-1}\mathbf1_{0<x<\beta}$
Since
\begin{align}
\int_{\max(t-\beta,0)}^{\min(t,\beta)}(y(t-y))^{\alpha-1}\,\mathrm{d}y\,\mathbf1_{0<t<2\beta}&=\begin{cases}
\int_{0}^{t}(y(t-y))^{\alpha-1}\,\mathrm{d}y&\text{when }0\le t\le \beta... | Distribution of $X+Y$ when $X$ and $Y$ are i.i.d with pdf $f(x)=\alpha\beta^{-\alpha}x^{\alpha-1}\ma
Since
\begin{align}
\int_{\max(t-\beta,0)}^{\min(t,\beta)}(y(t-y))^{\alpha-1}\,\mathrm{d}y\,\mathbf1_{0<t<2\beta}&=\begin{cases}
\int_{0}^{t}(y(t-y))^{\alpha-1}\,\mathrm{d}y&\text{when }0\le t\le \bet |
36,847 | What is the relationship between Cox regression and Tobit regression? | Abbreviated Model Descriptions
The Cox model is a survival model that cleverly models the hazard ratios through the observed ranks of the data, without needing to make an assumption of the underlying baseline distribution, but still requires the proportional hazards assumption.
The Tobit model is essentially standard ... | What is the relationship between Cox regression and Tobit regression? | Abbreviated Model Descriptions
The Cox model is a survival model that cleverly models the hazard ratios through the observed ranks of the data, without needing to make an assumption of the underlying | What is the relationship between Cox regression and Tobit regression?
Abbreviated Model Descriptions
The Cox model is a survival model that cleverly models the hazard ratios through the observed ranks of the data, without needing to make an assumption of the underlying baseline distribution, but still requires the prop... | What is the relationship between Cox regression and Tobit regression?
Abbreviated Model Descriptions
The Cox model is a survival model that cleverly models the hazard ratios through the observed ranks of the data, without needing to make an assumption of the underlying |
36,848 | What is the relationship between Cox regression and Tobit regression? | Neither a normally distributed error term nor a linear link would be an adequate choice for modeling time-to-event outcomes in most circumstances. The distribution of failure times tend to skew right by a large degree.
For models with no censoring, most of the books on failure time analyses discuss parametric models. ... | What is the relationship between Cox regression and Tobit regression? | Neither a normally distributed error term nor a linear link would be an adequate choice for modeling time-to-event outcomes in most circumstances. The distribution of failure times tend to skew right | What is the relationship between Cox regression and Tobit regression?
Neither a normally distributed error term nor a linear link would be an adequate choice for modeling time-to-event outcomes in most circumstances. The distribution of failure times tend to skew right by a large degree.
For models with no censoring, ... | What is the relationship between Cox regression and Tobit regression?
Neither a normally distributed error term nor a linear link would be an adequate choice for modeling time-to-event outcomes in most circumstances. The distribution of failure times tend to skew right |
36,849 | Are XGBoost probabilities well-calibrated? | No, they are not well-calibrated. The predicted probabilities are likely not outright horrible as we would expect from an SVM classifier but they are not usually very well-calibrated. For that matter the estimated probability deciles are not even guaranteed to be monotonic. In Caruana et al. (2004) "Ensemble Selection ... | Are XGBoost probabilities well-calibrated? | No, they are not well-calibrated. The predicted probabilities are likely not outright horrible as we would expect from an SVM classifier but they are not usually very well-calibrated. For that matter | Are XGBoost probabilities well-calibrated?
No, they are not well-calibrated. The predicted probabilities are likely not outright horrible as we would expect from an SVM classifier but they are not usually very well-calibrated. For that matter the estimated probability deciles are not even guaranteed to be monotonic. In... | Are XGBoost probabilities well-calibrated?
No, they are not well-calibrated. The predicted probabilities are likely not outright horrible as we would expect from an SVM classifier but they are not usually very well-calibrated. For that matter |
36,850 | Deep Learning approaches for Record Linkage | One classic method for linking text documents uses cosine similarity on TF-IDF features. A simple way to extend this would be to use Doc2Vec or similar document embeddings instead of TF-IDF - cosine similarity of word/document embeddings captures semantic similarity (some people might point out that word embeddings are... | Deep Learning approaches for Record Linkage | One classic method for linking text documents uses cosine similarity on TF-IDF features. A simple way to extend this would be to use Doc2Vec or similar document embeddings instead of TF-IDF - cosine s | Deep Learning approaches for Record Linkage
One classic method for linking text documents uses cosine similarity on TF-IDF features. A simple way to extend this would be to use Doc2Vec or similar document embeddings instead of TF-IDF - cosine similarity of word/document embeddings captures semantic similarity (some peo... | Deep Learning approaches for Record Linkage
One classic method for linking text documents uses cosine similarity on TF-IDF features. A simple way to extend this would be to use Doc2Vec or similar document embeddings instead of TF-IDF - cosine s |
36,851 | The Myth of Long-Horizon Predictability | I think a simple answer is that one doesn't want to measure R^2 on original scale of the timeseries. If one's forecast is purely a copy of the last seen timeseries value, the R^2 would be huge. Example:
This could be called a spurious case. I am getting the value 0.96, while this forecast is totally bullshit-ish.
R^2 ... | The Myth of Long-Horizon Predictability | I think a simple answer is that one doesn't want to measure R^2 on original scale of the timeseries. If one's forecast is purely a copy of the last seen timeseries value, the R^2 would be huge. Exampl | The Myth of Long-Horizon Predictability
I think a simple answer is that one doesn't want to measure R^2 on original scale of the timeseries. If one's forecast is purely a copy of the last seen timeseries value, the R^2 would be huge. Example:
This could be called a spurious case. I am getting the value 0.96, while thi... | The Myth of Long-Horizon Predictability
I think a simple answer is that one doesn't want to measure R^2 on original scale of the timeseries. If one's forecast is purely a copy of the last seen timeseries value, the R^2 would be huge. Exampl |
36,852 | The Myth of Long-Horizon Predictability | The problem does not arise because we are using the same dataset for training and validation. It arises because of the effect of the persistence of the variables on magnifying sampling errors and small effects at longer time horizons. As stated in the article, even if you cannot predict future stock market returns from... | The Myth of Long-Horizon Predictability | The problem does not arise because we are using the same dataset for training and validation. It arises because of the effect of the persistence of the variables on magnifying sampling errors and smal | The Myth of Long-Horizon Predictability
The problem does not arise because we are using the same dataset for training and validation. It arises because of the effect of the persistence of the variables on magnifying sampling errors and small effects at longer time horizons. As stated in the article, even if you cannot ... | The Myth of Long-Horizon Predictability
The problem does not arise because we are using the same dataset for training and validation. It arises because of the effect of the persistence of the variables on magnifying sampling errors and smal |
36,853 | What is exponential family criterion to test the sufficiency and completeness of an estimator? | The significance of that line is that if you can verify that the parameter space contains an open set in $R^k$, you know, without any further work, that the sufficient statistics $T(X)$ are also complete. That is usually a lot easier to do than trying to apply the definition of completeness directly.
Completeness is a... | What is exponential family criterion to test the sufficiency and completeness of an estimator? | The significance of that line is that if you can verify that the parameter space contains an open set in $R^k$, you know, without any further work, that the sufficient statistics $T(X)$ are also compl | What is exponential family criterion to test the sufficiency and completeness of an estimator?
The significance of that line is that if you can verify that the parameter space contains an open set in $R^k$, you know, without any further work, that the sufficient statistics $T(X)$ are also complete. That is usually a l... | What is exponential family criterion to test the sufficiency and completeness of an estimator?
The significance of that line is that if you can verify that the parameter space contains an open set in $R^k$, you know, without any further work, that the sufficient statistics $T(X)$ are also compl |
36,854 | Hard probability problem: How to calculate the the probability of having selected only < 70% of all marbles in a bag, given the following draw rules? | Let's solve this generalized Coupon Collector's problem generally, drawing $m=9$ out of $n=100$ balls for $r=50$ times.
If $E(i;r)$ is the event that exactly $i$ distinct balls have been seen after $r$ draws, then--conditional on this--the chance in the next draw of obtaining $k$ balls that haven't yet been seen is fou... | Hard probability problem: How to calculate the the probability of having selected only < 70% of all | Let's solve this generalized Coupon Collector's problem generally, drawing $m=9$ out of $n=100$ balls for $r=50$ times.
If $E(i;r)$ is the event that exactly $i$ distinct balls have been seen after $r | Hard probability problem: How to calculate the the probability of having selected only < 70% of all marbles in a bag, given the following draw rules?
Let's solve this generalized Coupon Collector's problem generally, drawing $m=9$ out of $n=100$ balls for $r=50$ times.
If $E(i;r)$ is the event that exactly $i$ distinct... | Hard probability problem: How to calculate the the probability of having selected only < 70% of all
Let's solve this generalized Coupon Collector's problem generally, drawing $m=9$ out of $n=100$ balls for $r=50$ times.
If $E(i;r)$ is the event that exactly $i$ distinct balls have been seen after $r |
36,855 | Bias initialization in convolutional neural network | Just noting that the answer to this question suggests setting CNN biases to 0, quoting CS231n Stanford course:
Initializing the biases. It is possible and common to initialize the
biases to be zero, since the asymmetry breaking is provided by the
small random numbers in the weights. For ReLU non-linearities, some
... | Bias initialization in convolutional neural network | Just noting that the answer to this question suggests setting CNN biases to 0, quoting CS231n Stanford course:
Initializing the biases. It is possible and common to initialize the
biases to be zero | Bias initialization in convolutional neural network
Just noting that the answer to this question suggests setting CNN biases to 0, quoting CS231n Stanford course:
Initializing the biases. It is possible and common to initialize the
biases to be zero, since the asymmetry breaking is provided by the
small random num... | Bias initialization in convolutional neural network
Just noting that the answer to this question suggests setting CNN biases to 0, quoting CS231n Stanford course:
Initializing the biases. It is possible and common to initialize the
biases to be zero |
36,856 | Bias initialization in convolutional neural network | Usually you initialise them to 1.0
Biases should be trainable variables not constant, their value must be allowed to change during training. Biases are necessary in every deep network architecture I know of, without them your network will most likely be unable to learn anything.
I don't know what a siamese neural netwo... | Bias initialization in convolutional neural network | Usually you initialise them to 1.0
Biases should be trainable variables not constant, their value must be allowed to change during training. Biases are necessary in every deep network architecture I k | Bias initialization in convolutional neural network
Usually you initialise them to 1.0
Biases should be trainable variables not constant, their value must be allowed to change during training. Biases are necessary in every deep network architecture I know of, without them your network will most likely be unable to lear... | Bias initialization in convolutional neural network
Usually you initialise them to 1.0
Biases should be trainable variables not constant, their value must be allowed to change during training. Biases are necessary in every deep network architecture I k |
36,857 | Input layer batch normalization | It is unlikely they will be the same, since batch normalization has a gamma and beta variable on top of the normalization process. In the paper, it is mentioned that this gamma and beta is used for scaling and shifting the activations to an appropriate degree in order to correct represent the data. Here is from the pap... | Input layer batch normalization | It is unlikely they will be the same, since batch normalization has a gamma and beta variable on top of the normalization process. In the paper, it is mentioned that this gamma and beta is used for sc | Input layer batch normalization
It is unlikely they will be the same, since batch normalization has a gamma and beta variable on top of the normalization process. In the paper, it is mentioned that this gamma and beta is used for scaling and shifting the activations to an appropriate degree in order to correct represen... | Input layer batch normalization
It is unlikely they will be the same, since batch normalization has a gamma and beta variable on top of the normalization process. In the paper, it is mentioned that this gamma and beta is used for sc |
36,858 | Difference between the Fisherian and Neymanian methods for causal inference? | In short, your intuition is correct.
Fisher's approach is based on randomization tests: using the randomization procedure of the treatment assignment, you assume a sharp null hypothesis of no effect and then compute the exact p-value, that is, the probability of seeing an effect as big as the one observed assuming no e... | Difference between the Fisherian and Neymanian methods for causal inference? | In short, your intuition is correct.
Fisher's approach is based on randomization tests: using the randomization procedure of the treatment assignment, you assume a sharp null hypothesis of no effect a | Difference between the Fisherian and Neymanian methods for causal inference?
In short, your intuition is correct.
Fisher's approach is based on randomization tests: using the randomization procedure of the treatment assignment, you assume a sharp null hypothesis of no effect and then compute the exact p-value, that is,... | Difference between the Fisherian and Neymanian methods for causal inference?
In short, your intuition is correct.
Fisher's approach is based on randomization tests: using the randomization procedure of the treatment assignment, you assume a sharp null hypothesis of no effect a |
36,859 | In PCA, is there a systematic way of dropping variables to maximise the segregation of two populations? | Principal Components (PCs) are based on the variances of the predictor variables/features. There is no assurance that the most highly variable features will be those that are most highly related to your classification. That is one possible explanation for your results. Also, when you limit yourself to projections onto ... | In PCA, is there a systematic way of dropping variables to maximise the segregation of two populatio | Principal Components (PCs) are based on the variances of the predictor variables/features. There is no assurance that the most highly variable features will be those that are most highly related to yo | In PCA, is there a systematic way of dropping variables to maximise the segregation of two populations?
Principal Components (PCs) are based on the variances of the predictor variables/features. There is no assurance that the most highly variable features will be those that are most highly related to your classificatio... | In PCA, is there a systematic way of dropping variables to maximise the segregation of two populatio
Principal Components (PCs) are based on the variances of the predictor variables/features. There is no assurance that the most highly variable features will be those that are most highly related to yo |
36,860 | Similarity measures for more than 2 variables | This answer will draw heavily on the ecological literature, where Jaccard and other (dis)similarity measures are commonly used to quantify the compositional (dis)similarity between species assemblages at different sites. The single best reference is Baselga (2013) Multiple site dissimilarity quantifies compositional h... | Similarity measures for more than 2 variables | This answer will draw heavily on the ecological literature, where Jaccard and other (dis)similarity measures are commonly used to quantify the compositional (dis)similarity between species assemblages | Similarity measures for more than 2 variables
This answer will draw heavily on the ecological literature, where Jaccard and other (dis)similarity measures are commonly used to quantify the compositional (dis)similarity between species assemblages at different sites. The single best reference is Baselga (2013) Multiple... | Similarity measures for more than 2 variables
This answer will draw heavily on the ecological literature, where Jaccard and other (dis)similarity measures are commonly used to quantify the compositional (dis)similarity between species assemblages |
36,861 | Similarity measures for more than 2 variables | A possible direction is to represent the problem as a graph.
The variables will be the nodes and the edges will be strong enough pair wise correlation.
You can define many correlation measures based on the graph, and you should find the one that suites you most. In most common graph correlations, the denser the graph, ... | Similarity measures for more than 2 variables | A possible direction is to represent the problem as a graph.
The variables will be the nodes and the edges will be strong enough pair wise correlation.
You can define many correlation measures based o | Similarity measures for more than 2 variables
A possible direction is to represent the problem as a graph.
The variables will be the nodes and the edges will be strong enough pair wise correlation.
You can define many correlation measures based on the graph, and you should find the one that suites you most. In most com... | Similarity measures for more than 2 variables
A possible direction is to represent the problem as a graph.
The variables will be the nodes and the edges will be strong enough pair wise correlation.
You can define many correlation measures based o |
36,862 | Similarity measures for more than 2 variables | Similarity is always between two items. It can then be extended to more (say three) items by first creating single representation for two items and then finding its similarity with the third item. So, when you have 1000 items you can ask the question how similar or far is any given vector from the representation of the... | Similarity measures for more than 2 variables | Similarity is always between two items. It can then be extended to more (say three) items by first creating single representation for two items and then finding its similarity with the third item. So, | Similarity measures for more than 2 variables
Similarity is always between two items. It can then be extended to more (say three) items by first creating single representation for two items and then finding its similarity with the third item. So, when you have 1000 items you can ask the question how similar or far is a... | Similarity measures for more than 2 variables
Similarity is always between two items. It can then be extended to more (say three) items by first creating single representation for two items and then finding its similarity with the third item. So, |
36,863 | Suspiciously high shrinkage in random effects logistic regression | I suspect that the answer here has to do with the definition of "effective sample size". A rule of thumb (from Harrell's Regression Modeling Strategies book) is that effective sample size for a Bernoulli variable is the minimum of the number of successes and failures; e.g. a sample of size 10,000 with only 4 successes ... | Suspiciously high shrinkage in random effects logistic regression | I suspect that the answer here has to do with the definition of "effective sample size". A rule of thumb (from Harrell's Regression Modeling Strategies book) is that effective sample size for a Bernou | Suspiciously high shrinkage in random effects logistic regression
I suspect that the answer here has to do with the definition of "effective sample size". A rule of thumb (from Harrell's Regression Modeling Strategies book) is that effective sample size for a Bernoulli variable is the minimum of the number of successes... | Suspiciously high shrinkage in random effects logistic regression
I suspect that the answer here has to do with the definition of "effective sample size". A rule of thumb (from Harrell's Regression Modeling Strategies book) is that effective sample size for a Bernou |
36,864 | Is feature selection with dummy coding of categorical variables problematic? [duplicate] | (I'm writing this here just to be sure the question isn't left "unanswered".)
Yes, it can be a problem if we run lasso on a design matrix with dummy variable coding. Perhaps only some levels will be selected by the model. Like you mention, this makes the coding we choose a "tuning parameter" of the model, something tha... | Is feature selection with dummy coding of categorical variables problematic? [duplicate] | (I'm writing this here just to be sure the question isn't left "unanswered".)
Yes, it can be a problem if we run lasso on a design matrix with dummy variable coding. Perhaps only some levels will be s | Is feature selection with dummy coding of categorical variables problematic? [duplicate]
(I'm writing this here just to be sure the question isn't left "unanswered".)
Yes, it can be a problem if we run lasso on a design matrix with dummy variable coding. Perhaps only some levels will be selected by the model. Like you ... | Is feature selection with dummy coding of categorical variables problematic? [duplicate]
(I'm writing this here just to be sure the question isn't left "unanswered".)
Yes, it can be a problem if we run lasso on a design matrix with dummy variable coding. Perhaps only some levels will be s |
36,865 | Is there a symbol for the median of a population? | I have seen a number of symbols used to denote the population median.
One I have seen quite a few times is $\tilde\mu$, but as whuber suggests in comments, you should define whatever you do use. So if you were to use this suggestion, you could say something like:
$H_0: \ \tilde{\mu}_{a} = \tilde{\mu}_{b}$
$H_a: \ \t... | Is there a symbol for the median of a population? | I have seen a number of symbols used to denote the population median.
One I have seen quite a few times is $\tilde\mu$, but as whuber suggests in comments, you should define whatever you do use. So if | Is there a symbol for the median of a population?
I have seen a number of symbols used to denote the population median.
One I have seen quite a few times is $\tilde\mu$, but as whuber suggests in comments, you should define whatever you do use. So if you were to use this suggestion, you could say something like:
$H_0:... | Is there a symbol for the median of a population?
I have seen a number of symbols used to denote the population median.
One I have seen quite a few times is $\tilde\mu$, but as whuber suggests in comments, you should define whatever you do use. So if |
36,866 | Is there a symbol for the median of a population? | I am currently in an introduction to statistics class and the textbook says that the median of a statistic can be represented with an "M" (a capital m). And the median of a parameter can be represented with a "θ" (a theta). This is as straightforward of an answer as you are going to get, though I am sure the way you ha... | Is there a symbol for the median of a population? | I am currently in an introduction to statistics class and the textbook says that the median of a statistic can be represented with an "M" (a capital m). And the median of a parameter can be represente | Is there a symbol for the median of a population?
I am currently in an introduction to statistics class and the textbook says that the median of a statistic can be represented with an "M" (a capital m). And the median of a parameter can be represented with a "θ" (a theta). This is as straightforward of an answer as you... | Is there a symbol for the median of a population?
I am currently in an introduction to statistics class and the textbook says that the median of a statistic can be represented with an "M" (a capital m). And the median of a parameter can be represente |
36,867 | Is there a symbol for the median of a population? | The Greek letter Eta (η) can also be used to represent the population median. Check this from Wikipedia: In Statistics, η2 is the "partial regression coefficient". η is the symbol for the linear predictor of a generalized linear model, and can also be used to denote the median of a population, or thresholding parameter... | Is there a symbol for the median of a population? | The Greek letter Eta (η) can also be used to represent the population median. Check this from Wikipedia: In Statistics, η2 is the "partial regression coefficient". η is the symbol for the linear predi | Is there a symbol for the median of a population?
The Greek letter Eta (η) can also be used to represent the population median. Check this from Wikipedia: In Statistics, η2 is the "partial regression coefficient". η is the symbol for the linear predictor of a generalized linear model, and can also be used to denote the... | Is there a symbol for the median of a population?
The Greek letter Eta (η) can also be used to represent the population median. Check this from Wikipedia: In Statistics, η2 is the "partial regression coefficient". η is the symbol for the linear predi |
36,868 | Is there a symbol for the median of a population? | You can refer to the median as $Q(a,50\%)$, i.e. the 50th percentile, and write the null hypothesis as:
$$H_0: Q(a,50\%)=Q(b,50\%)$$
This notation is longer than the other notations here, but its meaning is probably more obvious. So you probably would want to clarify that $Q$ is the quantile function, but readers might... | Is there a symbol for the median of a population? | You can refer to the median as $Q(a,50\%)$, i.e. the 50th percentile, and write the null hypothesis as:
$$H_0: Q(a,50\%)=Q(b,50\%)$$
This notation is longer than the other notations here, but its mean | Is there a symbol for the median of a population?
You can refer to the median as $Q(a,50\%)$, i.e. the 50th percentile, and write the null hypothesis as:
$$H_0: Q(a,50\%)=Q(b,50\%)$$
This notation is longer than the other notations here, but its meaning is probably more obvious. So you probably would want to clarify th... | Is there a symbol for the median of a population?
You can refer to the median as $Q(a,50\%)$, i.e. the 50th percentile, and write the null hypothesis as:
$$H_0: Q(a,50\%)=Q(b,50\%)$$
This notation is longer than the other notations here, but its mean |
36,869 | As sample size increases, why does the standard deviation of results get smaller? Can someone please provide a laymen example and explain why | As sample size increases (for example, a trading strategy with an 80%
edge), why does the standard deviation of results get smaller?
The key concept here is "results." What are these results? The results are the variances of estimators of population parameters such as mean $\mu$.
For instance, if you're measuring th... | As sample size increases, why does the standard deviation of results get smaller? Can someone please | As sample size increases (for example, a trading strategy with an 80%
edge), why does the standard deviation of results get smaller?
The key concept here is "results." What are these results? The r | As sample size increases, why does the standard deviation of results get smaller? Can someone please provide a laymen example and explain why
As sample size increases (for example, a trading strategy with an 80%
edge), why does the standard deviation of results get smaller?
The key concept here is "results." What ar... | As sample size increases, why does the standard deviation of results get smaller? Can someone please
As sample size increases (for example, a trading strategy with an 80%
edge), why does the standard deviation of results get smaller?
The key concept here is "results." What are these results? The r |
36,870 | As sample size increases, why does the standard deviation of results get smaller? Can someone please provide a laymen example and explain why | Maybe the easiest way to think about it is with regards to the difference between a population and a sample. If I ask you what the mean of a variable is in your sample, you don't give me an estimate, do you? You just calculate it and tell me, because, by definition, you have all the data that comprises the sample and c... | As sample size increases, why does the standard deviation of results get smaller? Can someone please | Maybe the easiest way to think about it is with regards to the difference between a population and a sample. If I ask you what the mean of a variable is in your sample, you don't give me an estimate, | As sample size increases, why does the standard deviation of results get smaller? Can someone please provide a laymen example and explain why
Maybe the easiest way to think about it is with regards to the difference between a population and a sample. If I ask you what the mean of a variable is in your sample, you don't... | As sample size increases, why does the standard deviation of results get smaller? Can someone please
Maybe the easiest way to think about it is with regards to the difference between a population and a sample. If I ask you what the mean of a variable is in your sample, you don't give me an estimate, |
36,871 | Total Sum of Squares, Covariance between residuals and the predicted values | I'm going to assume this is all in the context of a linear model $Y = X\beta + \varepsilon$. Letting $H = X(X^T X)^{-1}X^T$, we have fitted values $\hat Y = H Y$ and residuals $e = Y - \hat Y = (I - H)Y$. For the second term in your expression,
$$
\sum_i (y_i - \hat y_i)(\hat y_i - \bar y) = \langle e, HY - \bar y \mat... | Total Sum of Squares, Covariance between residuals and the predicted values | I'm going to assume this is all in the context of a linear model $Y = X\beta + \varepsilon$. Letting $H = X(X^T X)^{-1}X^T$, we have fitted values $\hat Y = H Y$ and residuals $e = Y - \hat Y = (I - H | Total Sum of Squares, Covariance between residuals and the predicted values
I'm going to assume this is all in the context of a linear model $Y = X\beta + \varepsilon$. Letting $H = X(X^T X)^{-1}X^T$, we have fitted values $\hat Y = H Y$ and residuals $e = Y - \hat Y = (I - H)Y$. For the second term in your expression,... | Total Sum of Squares, Covariance between residuals and the predicted values
I'm going to assume this is all in the context of a linear model $Y = X\beta + \varepsilon$. Letting $H = X(X^T X)^{-1}X^T$, we have fitted values $\hat Y = H Y$ and residuals $e = Y - \hat Y = (I - H |
36,872 | What is Bayesian melding? | This question certainly deserves an answer, so I will do my best and hope that others will improve this answer. I have been reading the paper by Raftery and Poole which introduced the technique. A variety of applications can be found by searching for "Bayesian melding" but most of them just seem to repeat the notation ... | What is Bayesian melding? | This question certainly deserves an answer, so I will do my best and hope that others will improve this answer. I have been reading the paper by Raftery and Poole which introduced the technique. A var | What is Bayesian melding?
This question certainly deserves an answer, so I will do my best and hope that others will improve this answer. I have been reading the paper by Raftery and Poole which introduced the technique. A variety of applications can be found by searching for "Bayesian melding" but most of them just se... | What is Bayesian melding?
This question certainly deserves an answer, so I will do my best and hope that others will improve this answer. I have been reading the paper by Raftery and Poole which introduced the technique. A var |
36,873 | Is there a parametric joint distribution such that $X$ and $Y$ are both uniform and $\mathbb{E}[Y \;|\; X]$ is linear? | We can develop rich parametric families from the trivial solution with copula $F(x,y) = \min(x,y)$, the case of perfect (positive) correlation, and its counterpart for perfect negative correlation. Concentrating the probability instead along the line segment connecting $(0,\alpha)$ to $(1,\beta)$ with $\beta\gt \alpha... | Is there a parametric joint distribution such that $X$ and $Y$ are both uniform and $\mathbb{E}[Y \; | We can develop rich parametric families from the trivial solution with copula $F(x,y) = \min(x,y)$, the case of perfect (positive) correlation, and its counterpart for perfect negative correlation. C | Is there a parametric joint distribution such that $X$ and $Y$ are both uniform and $\mathbb{E}[Y \;|\; X]$ is linear?
We can develop rich parametric families from the trivial solution with copula $F(x,y) = \min(x,y)$, the case of perfect (positive) correlation, and its counterpart for perfect negative correlation. Co... | Is there a parametric joint distribution such that $X$ and $Y$ are both uniform and $\mathbb{E}[Y \;
We can develop rich parametric families from the trivial solution with copula $F(x,y) = \min(x,y)$, the case of perfect (positive) correlation, and its counterpart for perfect negative correlation. C |
36,874 | Relating $f(\mathrm{Var}[X])$ to $\mathrm{Var}[f(X)]$ for Positive, Increasing, and Concave $f(X)$ | There is no relation between the two quantities $f(\text{Var}[X])$ and $\text{Var}[f(X)]$ for concave $f$. Here are the examples to demonstrate this:
Ex 1: Suppose random variable $X$ has the pmf: $p_X(0) = \frac{1}{2}$ and $p_X(4) = \frac{1}{2}$, and $f(x) = \sqrt{x}$. We get $\text{Var}[f(X)] = 1$ and $f(\text{Var}[... | Relating $f(\mathrm{Var}[X])$ to $\mathrm{Var}[f(X)]$ for Positive, Increasing, and Concave $f(X)$ | There is no relation between the two quantities $f(\text{Var}[X])$ and $\text{Var}[f(X)]$ for concave $f$. Here are the examples to demonstrate this:
Ex 1: Suppose random variable $X$ has the pmf: $p | Relating $f(\mathrm{Var}[X])$ to $\mathrm{Var}[f(X)]$ for Positive, Increasing, and Concave $f(X)$
There is no relation between the two quantities $f(\text{Var}[X])$ and $\text{Var}[f(X)]$ for concave $f$. Here are the examples to demonstrate this:
Ex 1: Suppose random variable $X$ has the pmf: $p_X(0) = \frac{1}{2}$ ... | Relating $f(\mathrm{Var}[X])$ to $\mathrm{Var}[f(X)]$ for Positive, Increasing, and Concave $f(X)$
There is no relation between the two quantities $f(\text{Var}[X])$ and $\text{Var}[f(X)]$ for concave $f$. Here are the examples to demonstrate this:
Ex 1: Suppose random variable $X$ has the pmf: $p |
36,875 | How to use cross validation for model comparison | Are the previously mentioned steps follow any standard procedure?
Yes! You are using hold-out validation set for final classifier comparison and k-fold cross-validation for the parameter (model) selection.
If not, how can I use Repeated/Nested CV in my case?
Since you are considering different models, one way to improv... | How to use cross validation for model comparison | Are the previously mentioned steps follow any standard procedure?
Yes! You are using hold-out validation set for final classifier comparison and k-fold cross-validation for the parameter (model) selec | How to use cross validation for model comparison
Are the previously mentioned steps follow any standard procedure?
Yes! You are using hold-out validation set for final classifier comparison and k-fold cross-validation for the parameter (model) selection.
If not, how can I use Repeated/Nested CV in my case?
Since you ar... | How to use cross validation for model comparison
Are the previously mentioned steps follow any standard procedure?
Yes! You are using hold-out validation set for final classifier comparison and k-fold cross-validation for the parameter (model) selec |
36,876 | How to use cross validation for model comparison | I'd like to propose an argument, that @discipulus answer is not entirely correct.
What is the standard procedure?
Normally, the setup looks like this:
Split the dataset (for example, training 60%, cross-validation 20%, test 20%).
[Cross-validation set] Find the best model (comparing different models and/or different h... | How to use cross validation for model comparison | I'd like to propose an argument, that @discipulus answer is not entirely correct.
What is the standard procedure?
Normally, the setup looks like this:
Split the dataset (for example, training 60%, cr | How to use cross validation for model comparison
I'd like to propose an argument, that @discipulus answer is not entirely correct.
What is the standard procedure?
Normally, the setup looks like this:
Split the dataset (for example, training 60%, cross-validation 20%, test 20%).
[Cross-validation set] Find the best mod... | How to use cross validation for model comparison
I'd like to propose an argument, that @discipulus answer is not entirely correct.
What is the standard procedure?
Normally, the setup looks like this:
Split the dataset (for example, training 60%, cr |
36,877 | How to derive the asymptotic distribution of the test statistic of a large sample test for equality of two binomial populations? | The OP is correct that you just cannot "add" convergence in distribution, for this you have to be aware of the covariance structure, which is fortunately enough trivial in this case.
update: Thanks for pointing out the earlier, crucial (and pretty bad) mistake. Hopefully the following answer is more or less correct...
... | How to derive the asymptotic distribution of the test statistic of a large sample test for equality | The OP is correct that you just cannot "add" convergence in distribution, for this you have to be aware of the covariance structure, which is fortunately enough trivial in this case.
update: Thanks fo | How to derive the asymptotic distribution of the test statistic of a large sample test for equality of two binomial populations?
The OP is correct that you just cannot "add" convergence in distribution, for this you have to be aware of the covariance structure, which is fortunately enough trivial in this case.
update: ... | How to derive the asymptotic distribution of the test statistic of a large sample test for equality
The OP is correct that you just cannot "add" convergence in distribution, for this you have to be aware of the covariance structure, which is fortunately enough trivial in this case.
update: Thanks fo |
36,878 | In propensity score analysis, what are options to deal with very small or large propensities? | This is a good detect. You are referring to positivity assumption. It requires that there be both exposed and unexposed participants at every combination of the values of the observed confounder(s) in the population under study. Positivity violations occur when certain subgroups in a sample rarely or never receive some... | In propensity score analysis, what are options to deal with very small or large propensities? | This is a good detect. You are referring to positivity assumption. It requires that there be both exposed and unexposed participants at every combination of the values of the observed confounder(s) in | In propensity score analysis, what are options to deal with very small or large propensities?
This is a good detect. You are referring to positivity assumption. It requires that there be both exposed and unexposed participants at every combination of the values of the observed confounder(s) in the population under stud... | In propensity score analysis, what are options to deal with very small or large propensities?
This is a good detect. You are referring to positivity assumption. It requires that there be both exposed and unexposed participants at every combination of the values of the observed confounder(s) in |
36,879 | Are predictions from Bayesian Gaussian Process Regression normally distributed? | GPR does not make any statistical assumptions about the predictors. They don't even have to be numbers! All you need is a prior mean function and a covariance function, which can also be defined for non-numeric data (discrete joint unions, strings, sets, etc.).
This is sort of true or assumed when people talk about G... | Are predictions from Bayesian Gaussian Process Regression normally distributed? | GPR does not make any statistical assumptions about the predictors. They don't even have to be numbers! All you need is a prior mean function and a covariance function, which can also be defined for | Are predictions from Bayesian Gaussian Process Regression normally distributed?
GPR does not make any statistical assumptions about the predictors. They don't even have to be numbers! All you need is a prior mean function and a covariance function, which can also be defined for non-numeric data (discrete joint unions... | Are predictions from Bayesian Gaussian Process Regression normally distributed?
GPR does not make any statistical assumptions about the predictors. They don't even have to be numbers! All you need is a prior mean function and a covariance function, which can also be defined for |
36,880 | In three-way ANOVA, how to interpret the three-way interaction? | A three way interaction means that the interaction among the two factors (A * B) is different across the levels of the third factor (C). If the interaction of A * B differs a lot among the levels of C then it sounds reasonable that the two way interaction A * B should not appear as significant. This could be the case o... | In three-way ANOVA, how to interpret the three-way interaction? | A three way interaction means that the interaction among the two factors (A * B) is different across the levels of the third factor (C). If the interaction of A * B differs a lot among the levels of C | In three-way ANOVA, how to interpret the three-way interaction?
A three way interaction means that the interaction among the two factors (A * B) is different across the levels of the third factor (C). If the interaction of A * B differs a lot among the levels of C then it sounds reasonable that the two way interaction ... | In three-way ANOVA, how to interpret the three-way interaction?
A three way interaction means that the interaction among the two factors (A * B) is different across the levels of the third factor (C). If the interaction of A * B differs a lot among the levels of C |
36,881 | In three-way ANOVA, how to interpret the three-way interaction? | The three-way ANOVA is used to determine if there is an interaction effect (independent variables interact if the effect of one of the variables differs depending on the level of the other variable) between three independent variables on a continuous dependent variable.
Therefore you would only be interested in the sig... | In three-way ANOVA, how to interpret the three-way interaction? | The three-way ANOVA is used to determine if there is an interaction effect (independent variables interact if the effect of one of the variables differs depending on the level of the other variable) b | In three-way ANOVA, how to interpret the three-way interaction?
The three-way ANOVA is used to determine if there is an interaction effect (independent variables interact if the effect of one of the variables differs depending on the level of the other variable) between three independent variables on a continuous depen... | In three-way ANOVA, how to interpret the three-way interaction?
The three-way ANOVA is used to determine if there is an interaction effect (independent variables interact if the effect of one of the variables differs depending on the level of the other variable) b |
36,882 | can you explicitly show me the first iteration of newton-raphson and fisher scoring? | For Newton-Raphson, yes, we have
$$ \pi_1 = \pi_0 - u(\pi_0)/J(\pi_0).$$
For Fisher scoring, as you mentioned, there is unknown parameter ($\pi$) in the expected information $I(\pi)$. Given $I(\pi)=-E(J(\pi))=E[u(\pi)u^{'}(\pi)]$, we use the sample first derivative to approximate the expected second derivative
$$\hat I... | can you explicitly show me the first iteration of newton-raphson and fisher scoring? | For Newton-Raphson, yes, we have
$$ \pi_1 = \pi_0 - u(\pi_0)/J(\pi_0).$$
For Fisher scoring, as you mentioned, there is unknown parameter ($\pi$) in the expected information $I(\pi)$. Given $I(\pi)=-E | can you explicitly show me the first iteration of newton-raphson and fisher scoring?
For Newton-Raphson, yes, we have
$$ \pi_1 = \pi_0 - u(\pi_0)/J(\pi_0).$$
For Fisher scoring, as you mentioned, there is unknown parameter ($\pi$) in the expected information $I(\pi)$. Given $I(\pi)=-E(J(\pi))=E[u(\pi)u^{'}(\pi)]$, we u... | can you explicitly show me the first iteration of newton-raphson and fisher scoring?
For Newton-Raphson, yes, we have
$$ \pi_1 = \pi_0 - u(\pi_0)/J(\pi_0).$$
For Fisher scoring, as you mentioned, there is unknown parameter ($\pi$) in the expected information $I(\pi)$. Given $I(\pi)=-E |
36,883 | What is the reason behind major difference in selection of mtry in RandomForest for Classification & regression? | The only useful source I found for this is the original paper of RF itself: http://machinelearning202.pbworks.com/w/file/fetch/60606349/breiman_randomforests.pdf
To quote "An interesting difference between regression and classification is that the
correlation increases quite slowly as the number of features used increa... | What is the reason behind major difference in selection of mtry in RandomForest for Classification & | The only useful source I found for this is the original paper of RF itself: http://machinelearning202.pbworks.com/w/file/fetch/60606349/breiman_randomforests.pdf
To quote "An interesting difference be | What is the reason behind major difference in selection of mtry in RandomForest for Classification & regression?
The only useful source I found for this is the original paper of RF itself: http://machinelearning202.pbworks.com/w/file/fetch/60606349/breiman_randomforests.pdf
To quote "An interesting difference between r... | What is the reason behind major difference in selection of mtry in RandomForest for Classification &
The only useful source I found for this is the original paper of RF itself: http://machinelearning202.pbworks.com/w/file/fetch/60606349/breiman_randomforests.pdf
To quote "An interesting difference be |
36,884 | What is the reason behind major difference in selection of mtry in RandomForest for Classification & regression? | Good defaults of hyperparameters in machine learning algorithms have to be found empirically on datasets (if there would be a good theory for setting them, they would not be a hyperparameter anymore).
Probably it has shown good performances for the creator of the specific package on some datasets, so he has chosen thi... | What is the reason behind major difference in selection of mtry in RandomForest for Classification & | Good defaults of hyperparameters in machine learning algorithms have to be found empirically on datasets (if there would be a good theory for setting them, they would not be a hyperparameter anymore). | What is the reason behind major difference in selection of mtry in RandomForest for Classification & regression?
Good defaults of hyperparameters in machine learning algorithms have to be found empirically on datasets (if there would be a good theory for setting them, they would not be a hyperparameter anymore).
Proba... | What is the reason behind major difference in selection of mtry in RandomForest for Classification &
Good defaults of hyperparameters in machine learning algorithms have to be found empirically on datasets (if there would be a good theory for setting them, they would not be a hyperparameter anymore). |
36,885 | Bias-Variance decomposition derivation | Here is a hint: consider $Y - \hat f = (Y - f) + (f - \hat f)$, and remember that $E(Y-f)=0$ and that $f$ is not random. Also, as @GeoMatt22 pointed out, you'll need $Cov(\varepsilon_0, \hat f) = 0$, which we get by virtue of iid errors.
(Basically I think you're probably making this more complicated than it needs to b... | Bias-Variance decomposition derivation | Here is a hint: consider $Y - \hat f = (Y - f) + (f - \hat f)$, and remember that $E(Y-f)=0$ and that $f$ is not random. Also, as @GeoMatt22 pointed out, you'll need $Cov(\varepsilon_0, \hat f) = 0$, | Bias-Variance decomposition derivation
Here is a hint: consider $Y - \hat f = (Y - f) + (f - \hat f)$, and remember that $E(Y-f)=0$ and that $f$ is not random. Also, as @GeoMatt22 pointed out, you'll need $Cov(\varepsilon_0, \hat f) = 0$, which we get by virtue of iid errors.
(Basically I think you're probably making t... | Bias-Variance decomposition derivation
Here is a hint: consider $Y - \hat f = (Y - f) + (f - \hat f)$, and remember that $E(Y-f)=0$ and that $f$ is not random. Also, as @GeoMatt22 pointed out, you'll need $Cov(\varepsilon_0, \hat f) = 0$, |
36,886 | What is the correct analysis for this type of question? (Conditional Logistic Regression?) | First:
"Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful."
Box, G. E. P.; Draper, N. R. (1987), Empirical Model-Building and Response Surfaces, John Wiley & Sons.
Thus there is no one and only correct way to model your data.
The research question is broadly i... | What is the correct analysis for this type of question? (Conditional Logistic Regression?) | First:
"Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful."
Box, G. E. P.; Draper, N. R. (1987), Empirical Model-Building and Response Surfac | What is the correct analysis for this type of question? (Conditional Logistic Regression?)
First:
"Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful."
Box, G. E. P.; Draper, N. R. (1987), Empirical Model-Building and Response Surfaces, John Wiley & Sons.
Thus ... | What is the correct analysis for this type of question? (Conditional Logistic Regression?)
First:
"Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful."
Box, G. E. P.; Draper, N. R. (1987), Empirical Model-Building and Response Surfac |
36,887 | What is the correct analysis for this type of question? (Conditional Logistic Regression?) | I believe that conditional logistic regression will give you the desired results.
You correctly identify the need to use a repeated measures convention when analyzing this data. You have 5 respondents evaluated for the binary outcome of correct/incorrect face/object recognition over multiple conditions. The numerous r... | What is the correct analysis for this type of question? (Conditional Logistic Regression?) | I believe that conditional logistic regression will give you the desired results.
You correctly identify the need to use a repeated measures convention when analyzing this data. You have 5 respondent | What is the correct analysis for this type of question? (Conditional Logistic Regression?)
I believe that conditional logistic regression will give you the desired results.
You correctly identify the need to use a repeated measures convention when analyzing this data. You have 5 respondents evaluated for the binary ou... | What is the correct analysis for this type of question? (Conditional Logistic Regression?)
I believe that conditional logistic regression will give you the desired results.
You correctly identify the need to use a repeated measures convention when analyzing this data. You have 5 respondent |
36,888 | Multiplication, addition, and concatenation in deep neural networks | Addition and concatenation are special cases of multiplication, where the weights are equal to 0 or 1. As a result, one can view using addition and concatenation as assumptions of what the network should be doing.
E.g., in https://arxiv.org/abs/1606.03475, figure 1, we used concatenation to create the token emdeddings... | Multiplication, addition, and concatenation in deep neural networks | Addition and concatenation are special cases of multiplication, where the weights are equal to 0 or 1. As a result, one can view using addition and concatenation as assumptions of what the network sh | Multiplication, addition, and concatenation in deep neural networks
Addition and concatenation are special cases of multiplication, where the weights are equal to 0 or 1. As a result, one can view using addition and concatenation as assumptions of what the network should be doing.
E.g., in https://arxiv.org/abs/1606.0... | Multiplication, addition, and concatenation in deep neural networks
Addition and concatenation are special cases of multiplication, where the weights are equal to 0 or 1. As a result, one can view using addition and concatenation as assumptions of what the network sh |
36,889 | Why do we want an objective function to be a convex function? | First of all as @whuber mentioned many people are involved in non-convex optimisation. Having said, your definition of "as long as the local minimum is the global minimum" is rather... lax. See for instance the Easom function ($f(x,y) = -\cos(x)\cos(y)\exp(-(x-\pi)^2 - (y-\pi)^2)$. It has a single minimum if that is yo... | Why do we want an objective function to be a convex function? | First of all as @whuber mentioned many people are involved in non-convex optimisation. Having said, your definition of "as long as the local minimum is the global minimum" is rather... lax. See for in | Why do we want an objective function to be a convex function?
First of all as @whuber mentioned many people are involved in non-convex optimisation. Having said, your definition of "as long as the local minimum is the global minimum" is rather... lax. See for instance the Easom function ($f(x,y) = -\cos(x)\cos(y)\exp(-... | Why do we want an objective function to be a convex function?
First of all as @whuber mentioned many people are involved in non-convex optimisation. Having said, your definition of "as long as the local minimum is the global minimum" is rather... lax. See for in |
36,890 | Strange likelihood trace from MCMC chain | Log-likelihood is a sum of log-densities over some datapoints, given some parameter values. Recall that densities are relative measures of "probability per foot". This means that they can be arbitrary low, or high, as in this example of uniform density. Since you sum density estimates for different points they will be ... | Strange likelihood trace from MCMC chain | Log-likelihood is a sum of log-densities over some datapoints, given some parameter values. Recall that densities are relative measures of "probability per foot". This means that they can be arbitrary | Strange likelihood trace from MCMC chain
Log-likelihood is a sum of log-densities over some datapoints, given some parameter values. Recall that densities are relative measures of "probability per foot". This means that they can be arbitrary low, or high, as in this example of uniform density. Since you sum density est... | Strange likelihood trace from MCMC chain
Log-likelihood is a sum of log-densities over some datapoints, given some parameter values. Recall that densities are relative measures of "probability per foot". This means that they can be arbitrary |
36,891 | Hidden Markov Model and Naive Bayes similarity | Hidden Markov Model assumes a relationship between $y_n$ and $y_{n+1}$.
For example say we are doing natural language processing, and $y_n$ denotes the $n$-th world in a sentence. If we know $y_n$ is "stack" then the probability of $y_{n+1}$ being "overflow" might be higher than knowing $y_n$ being something else say "... | Hidden Markov Model and Naive Bayes similarity | Hidden Markov Model assumes a relationship between $y_n$ and $y_{n+1}$.
For example say we are doing natural language processing, and $y_n$ denotes the $n$-th world in a sentence. If we know $y_n$ is | Hidden Markov Model and Naive Bayes similarity
Hidden Markov Model assumes a relationship between $y_n$ and $y_{n+1}$.
For example say we are doing natural language processing, and $y_n$ denotes the $n$-th world in a sentence. If we know $y_n$ is "stack" then the probability of $y_{n+1}$ being "overflow" might be highe... | Hidden Markov Model and Naive Bayes similarity
Hidden Markov Model assumes a relationship between $y_n$ and $y_{n+1}$.
For example say we are doing natural language processing, and $y_n$ denotes the $n$-th world in a sentence. If we know $y_n$ is |
36,892 | Compare MLR model to model $Y_i = (\beta_0 + \beta_1x_{1i} + \beta_2x_{2i} + \epsilon_i)^{\beta_3}$? | No (at least not with nls)
From its documentation, nls fits functions of the form $Y_i| \theta, X_i = f(\theta, X_i) + \epsilon$ (and is the MLE in the case that $\epsilon$ is iid Normal), so your relationship is not in the non-linear least squares class.
Let's see if we can describe the distribution $Y$ might follow. ... | Compare MLR model to model $Y_i = (\beta_0 + \beta_1x_{1i} + \beta_2x_{2i} + \epsilon_i)^{\beta_3}$? | No (at least not with nls)
From its documentation, nls fits functions of the form $Y_i| \theta, X_i = f(\theta, X_i) + \epsilon$ (and is the MLE in the case that $\epsilon$ is iid Normal), so your rel | Compare MLR model to model $Y_i = (\beta_0 + \beta_1x_{1i} + \beta_2x_{2i} + \epsilon_i)^{\beta_3}$?
No (at least not with nls)
From its documentation, nls fits functions of the form $Y_i| \theta, X_i = f(\theta, X_i) + \epsilon$ (and is the MLE in the case that $\epsilon$ is iid Normal), so your relationship is not in... | Compare MLR model to model $Y_i = (\beta_0 + \beta_1x_{1i} + \beta_2x_{2i} + \epsilon_i)^{\beta_3}$?
No (at least not with nls)
From its documentation, nls fits functions of the form $Y_i| \theta, X_i = f(\theta, X_i) + \epsilon$ (and is the MLE in the case that $\epsilon$ is iid Normal), so your rel |
36,893 | Compare MLR model to model $Y_i = (\beta_0 + \beta_1x_{1i} + \beta_2x_{2i} + \epsilon_i)^{\beta_3}$? | I think Andrew M have given a good answer; I just want to make a few related points.
As Andrew M indicates you can't do the model as is directly with nonlinear least squares; however, you can fit this closely related model with nonlinear LS:
$Y_i = (\beta_0 + \beta_1x_{1i} + \beta_2x_{2i})^{\beta_3} + \epsilon_i$
Th... | Compare MLR model to model $Y_i = (\beta_0 + \beta_1x_{1i} + \beta_2x_{2i} + \epsilon_i)^{\beta_3}$? | I think Andrew M have given a good answer; I just want to make a few related points.
As Andrew M indicates you can't do the model as is directly with nonlinear least squares; however, you can fit this | Compare MLR model to model $Y_i = (\beta_0 + \beta_1x_{1i} + \beta_2x_{2i} + \epsilon_i)^{\beta_3}$?
I think Andrew M have given a good answer; I just want to make a few related points.
As Andrew M indicates you can't do the model as is directly with nonlinear least squares; however, you can fit this closely related mo... | Compare MLR model to model $Y_i = (\beta_0 + \beta_1x_{1i} + \beta_2x_{2i} + \epsilon_i)^{\beta_3}$?
I think Andrew M have given a good answer; I just want to make a few related points.
As Andrew M indicates you can't do the model as is directly with nonlinear least squares; however, you can fit this |
36,894 | What is the meaning of the notation $P_\theta()$, where a probability has a subscript Greek letter? | It means under the distribution $\theta$, the probability of that statistic $T(x)$ being equal to $t$ is zero. Another way you can write it is:
$Pr(T(x) = t | \Theta = \theta) = 0$. | What is the meaning of the notation $P_\theta()$, where a probability has a subscript Greek letter? | It means under the distribution $\theta$, the probability of that statistic $T(x)$ being equal to $t$ is zero. Another way you can write it is:
$Pr(T(x) = t | \Theta = \theta) = 0$. | What is the meaning of the notation $P_\theta()$, where a probability has a subscript Greek letter?
It means under the distribution $\theta$, the probability of that statistic $T(x)$ being equal to $t$ is zero. Another way you can write it is:
$Pr(T(x) = t | \Theta = \theta) = 0$. | What is the meaning of the notation $P_\theta()$, where a probability has a subscript Greek letter?
It means under the distribution $\theta$, the probability of that statistic $T(x)$ being equal to $t$ is zero. Another way you can write it is:
$Pr(T(x) = t | \Theta = \theta) = 0$. |
36,895 | Cook's distance in detecting outliers | Like you said Cook’s Distance measures the change in the regression by removing each individual point. If things change quite a bit by the omission of a single point, than that point was having a lot of influence on your model. Define $\hat{Y}_{j(i)}$ to be the fitted value for the jth observation when the ith observat... | Cook's distance in detecting outliers | Like you said Cook’s Distance measures the change in the regression by removing each individual point. If things change quite a bit by the omission of a single point, than that point was having a lot | Cook's distance in detecting outliers
Like you said Cook’s Distance measures the change in the regression by removing each individual point. If things change quite a bit by the omission of a single point, than that point was having a lot of influence on your model. Define $\hat{Y}_{j(i)}$ to be the fitted value for the... | Cook's distance in detecting outliers
Like you said Cook’s Distance measures the change in the regression by removing each individual point. If things change quite a bit by the omission of a single point, than that point was having a lot |
36,896 | Cook's distance in detecting outliers | Cook's D is ineffective in detecting cluster of outliers because removing one of those will not affect the model too much (there're still other outliers).
You could use the residual as a measure, which is sensitive to clusters. A simple implementation of k-means is also effective. | Cook's distance in detecting outliers | Cook's D is ineffective in detecting cluster of outliers because removing one of those will not affect the model too much (there're still other outliers).
You could use the residual as a measure, whic | Cook's distance in detecting outliers
Cook's D is ineffective in detecting cluster of outliers because removing one of those will not affect the model too much (there're still other outliers).
You could use the residual as a measure, which is sensitive to clusters. A simple implementation of k-means is also effective. | Cook's distance in detecting outliers
Cook's D is ineffective in detecting cluster of outliers because removing one of those will not affect the model too much (there're still other outliers).
You could use the residual as a measure, whic |
36,897 | FDR correction when tests are correlated | You're looking for the Benjamini-Yekutieli procedure:
Benjamini, Yoav; Yekutieli, Daniel. The control of the false discovery rate in multiple testing under dependency. Ann. Statist. 29 (2001), no. 4, 1165--1188. doi:10.1214/aos/1013699998. http://projecteuclid.org/euclid.aos/1013699998
The procedure is available in R u... | FDR correction when tests are correlated | You're looking for the Benjamini-Yekutieli procedure:
Benjamini, Yoav; Yekutieli, Daniel. The control of the false discovery rate in multiple testing under dependency. Ann. Statist. 29 (2001), no. 4, | FDR correction when tests are correlated
You're looking for the Benjamini-Yekutieli procedure:
Benjamini, Yoav; Yekutieli, Daniel. The control of the false discovery rate in multiple testing under dependency. Ann. Statist. 29 (2001), no. 4, 1165--1188. doi:10.1214/aos/1013699998. http://projecteuclid.org/euclid.aos/101... | FDR correction when tests are correlated
You're looking for the Benjamini-Yekutieli procedure:
Benjamini, Yoav; Yekutieli, Daniel. The control of the false discovery rate in multiple testing under dependency. Ann. Statist. 29 (2001), no. 4, |
36,898 | Different ways to understand neural networks | Neural networks are a generalization of regression. http://briandolhansky.com/blog/artificial-neural-networks-linear-regression-part-1
neural networks are universal function approximators (Wikipedia)
Turing Machines are Recurrent Neural Networks (http://lipas.uwasa.fi/stes/step96/step96/hyotyniemi1/) | Different ways to understand neural networks | Neural networks are a generalization of regression. http://briandolhansky.com/blog/artificial-neural-networks-linear-regression-part-1
neural networks are universal function approximators (Wikipedia)
| Different ways to understand neural networks
Neural networks are a generalization of regression. http://briandolhansky.com/blog/artificial-neural-networks-linear-regression-part-1
neural networks are universal function approximators (Wikipedia)
Turing Machines are Recurrent Neural Networks (http://lipas.uwasa.fi/stes/s... | Different ways to understand neural networks
Neural networks are a generalization of regression. http://briandolhansky.com/blog/artificial-neural-networks-linear-regression-part-1
neural networks are universal function approximators (Wikipedia)
|
36,899 | Different ways to understand neural networks | Neural networks as finite approximations of continuous functions:
https://en.wikipedia.org/wiki/Universal_approximation_theorem
In short, neural networks can approximate continuous functions with arbitrary accuracy (that depends on the number of neurons) and consequently form a dense set in the space of continuous func... | Different ways to understand neural networks | Neural networks as finite approximations of continuous functions:
https://en.wikipedia.org/wiki/Universal_approximation_theorem
In short, neural networks can approximate continuous functions with arbi | Different ways to understand neural networks
Neural networks as finite approximations of continuous functions:
https://en.wikipedia.org/wiki/Universal_approximation_theorem
In short, neural networks can approximate continuous functions with arbitrary accuracy (that depends on the number of neurons) and consequently for... | Different ways to understand neural networks
Neural networks as finite approximations of continuous functions:
https://en.wikipedia.org/wiki/Universal_approximation_theorem
In short, neural networks can approximate continuous functions with arbi |
36,900 | Are there two definitions of the word bias? | The term "bias" has a specific definition in the statistical literature (the difference between the expected value of an estimator and the thing being estimated), but that isn't to say it loses its original, more general meaning. Which one is intended will depend on context, and oftentimes you will have a mixture of t... | Are there two definitions of the word bias? | The term "bias" has a specific definition in the statistical literature (the difference between the expected value of an estimator and the thing being estimated), but that isn't to say it loses its or | Are there two definitions of the word bias?
The term "bias" has a specific definition in the statistical literature (the difference between the expected value of an estimator and the thing being estimated), but that isn't to say it loses its original, more general meaning. Which one is intended will depend on context,... | Are there two definitions of the word bias?
The term "bias" has a specific definition in the statistical literature (the difference between the expected value of an estimator and the thing being estimated), but that isn't to say it loses its or |
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