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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40,201 | How can I use Propensity Scores to adjust for survey non-response bias? | The answer to this depends on whether you have a probability sample versus a nonprobability sample, where a probability sample refers to a sample selected using random sampling from the population.
If you have a probability sample
For probability samples, you know each sample member's sampling selection probability (i.... | How can I use Propensity Scores to adjust for survey non-response bias? | The answer to this depends on whether you have a probability sample versus a nonprobability sample, where a probability sample refers to a sample selected using random sampling from the population.
If | How can I use Propensity Scores to adjust for survey non-response bias?
The answer to this depends on whether you have a probability sample versus a nonprobability sample, where a probability sample refers to a sample selected using random sampling from the population.
If you have a probability sample
For probability s... | How can I use Propensity Scores to adjust for survey non-response bias?
The answer to this depends on whether you have a probability sample versus a nonprobability sample, where a probability sample refers to a sample selected using random sampling from the population.
If |
40,202 | Is a time series which is a deterministic linear trend + white noise considered an ARIMA model? | No, $X_t$ is not considered an ARIMA model.
Walter Enders writes here in his textbook (3rd edition, p. 191)
We have shown that differencing can sometimes be used to transform a nonstationary model into a stationary model with an ARMA representation. This does not mean that all nonstationary models can be transformed i... | Is a time series which is a deterministic linear trend + white noise considered an ARIMA model? | No, $X_t$ is not considered an ARIMA model.
Walter Enders writes here in his textbook (3rd edition, p. 191)
We have shown that differencing can sometimes be used to transform a nonstationary model in | Is a time series which is a deterministic linear trend + white noise considered an ARIMA model?
No, $X_t$ is not considered an ARIMA model.
Walter Enders writes here in his textbook (3rd edition, p. 191)
We have shown that differencing can sometimes be used to transform a nonstationary model into a stationary model wi... | Is a time series which is a deterministic linear trend + white noise considered an ARIMA model?
No, $X_t$ is not considered an ARIMA model.
Walter Enders writes here in his textbook (3rd edition, p. 191)
We have shown that differencing can sometimes be used to transform a nonstationary model in |
40,203 | Is a time series which is a deterministic linear trend + white noise considered an ARIMA model? | I personally consider Rob Hyndman's forecast package for R the gold standard in ARIMA modeling and forecasting. And this package will quite happily deal with time series of the form of your differenced series and call them "ARIMA with non-zero mean".
> set.seed(4); forecast::auto.arima(rnorm(100,5,1))
Series: rnorm(100... | Is a time series which is a deterministic linear trend + white noise considered an ARIMA model? | I personally consider Rob Hyndman's forecast package for R the gold standard in ARIMA modeling and forecasting. And this package will quite happily deal with time series of the form of your difference | Is a time series which is a deterministic linear trend + white noise considered an ARIMA model?
I personally consider Rob Hyndman's forecast package for R the gold standard in ARIMA modeling and forecasting. And this package will quite happily deal with time series of the form of your differenced series and call them "... | Is a time series which is a deterministic linear trend + white noise considered an ARIMA model?
I personally consider Rob Hyndman's forecast package for R the gold standard in ARIMA modeling and forecasting. And this package will quite happily deal with time series of the form of your difference |
40,204 | F1 score, PR or ROC curve for regression | F1 score, PR or ROC curve are not specific to classification models only.
I have never seen the F1 score or ROC used to evaluate a numerical prediction. I am unfamiliar with "PR".
The definition of the F1 score crucially relies on precision and recall, or positive/negative predictive value, and I do not see how it can... | F1 score, PR or ROC curve for regression | F1 score, PR or ROC curve are not specific to classification models only.
I have never seen the F1 score or ROC used to evaluate a numerical prediction. I am unfamiliar with "PR".
The definition of t | F1 score, PR or ROC curve for regression
F1 score, PR or ROC curve are not specific to classification models only.
I have never seen the F1 score or ROC used to evaluate a numerical prediction. I am unfamiliar with "PR".
The definition of the F1 score crucially relies on precision and recall, or positive/negative pred... | F1 score, PR or ROC curve for regression
F1 score, PR or ROC curve are not specific to classification models only.
I have never seen the F1 score or ROC used to evaluate a numerical prediction. I am unfamiliar with "PR".
The definition of t |
40,205 | A theoretical question on fractional factorials | You can read off the additional assumptions from the alias structure. For your example a $\mathbf{2}^{15}$ design needs, as you said, $32768$ experimental runs, but with that you can estimate even the 15-factor full interaction. Such many-factor interactions are seldom interpretable, and if you restrict yourself to mai... | A theoretical question on fractional factorials | You can read off the additional assumptions from the alias structure. For your example a $\mathbf{2}^{15}$ design needs, as you said, $32768$ experimental runs, but with that you can estimate even the | A theoretical question on fractional factorials
You can read off the additional assumptions from the alias structure. For your example a $\mathbf{2}^{15}$ design needs, as you said, $32768$ experimental runs, but with that you can estimate even the 15-factor full interaction. Such many-factor interactions are seldom in... | A theoretical question on fractional factorials
You can read off the additional assumptions from the alias structure. For your example a $\mathbf{2}^{15}$ design needs, as you said, $32768$ experimental runs, but with that you can estimate even the |
40,206 | Is there a parametric equivalent to the chi-squared test? | Poisson regression.
Here is an example of a potential table you may be describing.
category
method 1 2 3 4
hand 101 210 590 99
machine 97 401 403 99
A poisson regression with additive effects should yield the same expected cell count as the chi-square procedure.
Here is how we would fit t... | Is there a parametric equivalent to the chi-squared test? | Poisson regression.
Here is an example of a potential table you may be describing.
category
method 1 2 3 4
hand 101 210 590 99
machine 97 401 403 99
A poisson regression | Is there a parametric equivalent to the chi-squared test?
Poisson regression.
Here is an example of a potential table you may be describing.
category
method 1 2 3 4
hand 101 210 590 99
machine 97 401 403 99
A poisson regression with additive effects should yield the same expected cell cou... | Is there a parametric equivalent to the chi-squared test?
Poisson regression.
Here is an example of a potential table you may be describing.
category
method 1 2 3 4
hand 101 210 590 99
machine 97 401 403 99
A poisson regression |
40,207 | If $X_n \sim \text{Beta}(n, n)$ Show that $[X_n - \text{E}(X_n)]/\sqrt{\text{Var}(X_n)} \stackrel{D}{\longrightarrow} N(0,1)$ | I was pondering how to formulate the simplest possible elementary solution to this problem and it occurred to me we can avoid any consideration of Beta functions (no Stirling's approximation needed; indeed, even information about the moments of Beta distributions is unnecessary). The result is extremely general and, I... | If $X_n \sim \text{Beta}(n, n)$ Show that $[X_n - \text{E}(X_n)]/\sqrt{\text{Var}(X_n)} \stackrel{D} | I was pondering how to formulate the simplest possible elementary solution to this problem and it occurred to me we can avoid any consideration of Beta functions (no Stirling's approximation needed; i | If $X_n \sim \text{Beta}(n, n)$ Show that $[X_n - \text{E}(X_n)]/\sqrt{\text{Var}(X_n)} \stackrel{D}{\longrightarrow} N(0,1)$
I was pondering how to formulate the simplest possible elementary solution to this problem and it occurred to me we can avoid any consideration of Beta functions (no Stirling's approximation nee... | If $X_n \sim \text{Beta}(n, n)$ Show that $[X_n - \text{E}(X_n)]/\sqrt{\text{Var}(X_n)} \stackrel{D}
I was pondering how to formulate the simplest possible elementary solution to this problem and it occurred to me we can avoid any consideration of Beta functions (no Stirling's approximation needed; i |
40,208 | Expressing a marginal probability using copulas | The issue of notation seems crucial. I propose, therefore, to disambiguate the ubiquitous and overloaded "$f$" by means of subscripts. Thus, $f_{XYZ}$ will be the full density function and (therefore) the marginal density for $(X,Y)$ is
$$f_{XY}(x,y) = \int_{-\infty}^{\infty} f_{XYZ}(x,y,z)\,\mathrm{d}z.$$
If, for a ... | Expressing a marginal probability using copulas | The issue of notation seems crucial. I propose, therefore, to disambiguate the ubiquitous and overloaded "$f$" by means of subscripts. Thus, $f_{XYZ}$ will be the full density function and (therefor | Expressing a marginal probability using copulas
The issue of notation seems crucial. I propose, therefore, to disambiguate the ubiquitous and overloaded "$f$" by means of subscripts. Thus, $f_{XYZ}$ will be the full density function and (therefore) the marginal density for $(X,Y)$ is
$$f_{XY}(x,y) = \int_{-\infty}^{\... | Expressing a marginal probability using copulas
The issue of notation seems crucial. I propose, therefore, to disambiguate the ubiquitous and overloaded "$f$" by means of subscripts. Thus, $f_{XYZ}$ will be the full density function and (therefor |
40,209 | Simple example of the $\sigma$-field generated by a random variable (Concept check) | You're right, but you might appreciate knowing how to find this sigma field using the definition:
The sigma-field generated by a random variable $X:\Omega\to\mathbb{R}$ consists of all the inverse images $X^{-1}(B)$ of the Borel sets $B\subset \mathbb{R}.$
Because $y$ has only two possible values $b_1$ and $b_2,$ the... | Simple example of the $\sigma$-field generated by a random variable (Concept check) | You're right, but you might appreciate knowing how to find this sigma field using the definition:
The sigma-field generated by a random variable $X:\Omega\to\mathbb{R}$ consists of all the inverse im | Simple example of the $\sigma$-field generated by a random variable (Concept check)
You're right, but you might appreciate knowing how to find this sigma field using the definition:
The sigma-field generated by a random variable $X:\Omega\to\mathbb{R}$ consists of all the inverse images $X^{-1}(B)$ of the Borel sets $... | Simple example of the $\sigma$-field generated by a random variable (Concept check)
You're right, but you might appreciate knowing how to find this sigma field using the definition:
The sigma-field generated by a random variable $X:\Omega\to\mathbb{R}$ consists of all the inverse im |
40,210 | Difference between Repeated measures ANOVA, ANCOVA and Linear mixed effects model | First there is the question of whether it is OK to use percent change as the outcome. In a regression model with baseline as a regressor this is a very bad idea because the outcome is mathematically coupled to the regressor which will induce correlation (ie statistically significant associations) where none is actually... | Difference between Repeated measures ANOVA, ANCOVA and Linear mixed effects model | First there is the question of whether it is OK to use percent change as the outcome. In a regression model with baseline as a regressor this is a very bad idea because the outcome is mathematically c | Difference between Repeated measures ANOVA, ANCOVA and Linear mixed effects model
First there is the question of whether it is OK to use percent change as the outcome. In a regression model with baseline as a regressor this is a very bad idea because the outcome is mathematically coupled to the regressor which will ind... | Difference between Repeated measures ANOVA, ANCOVA and Linear mixed effects model
First there is the question of whether it is OK to use percent change as the outcome. In a regression model with baseline as a regressor this is a very bad idea because the outcome is mathematically c |
40,211 | Analyzing a partially crossed design | As far as I can tell you are describing a partially crossed design. The good news is that this is one of Doug Bates's main development goals for lme4: efficiently fitting large, partially crossed linear mixed models. Disclaimer: I don't know that much about Rasch models nor how close a partially nested model like thi... | Analyzing a partially crossed design | As far as I can tell you are describing a partially crossed design. The good news is that this is one of Doug Bates's main development goals for lme4: efficiently fitting large, partially crossed lin | Analyzing a partially crossed design
As far as I can tell you are describing a partially crossed design. The good news is that this is one of Doug Bates's main development goals for lme4: efficiently fitting large, partially crossed linear mixed models. Disclaimer: I don't know that much about Rasch models nor how cl... | Analyzing a partially crossed design
As far as I can tell you are describing a partially crossed design. The good news is that this is one of Doug Bates's main development goals for lme4: efficiently fitting large, partially crossed lin |
40,212 | Is there a difference in interpretation between $Y|X = m(X) + \epsilon$ vs. $Y = m(X) + \epsilon$? | There is actually no such object as $Y|X$ --- whenever this notation appears, it is an abuse of notation which operates as shorthand for specifying the conditional distribution of a random variable conditional on another random variable.$^\dagger$ Thus, the statement $Y|X = m(X) + \epsilon$ actually doesn't make any s... | Is there a difference in interpretation between $Y|X = m(X) + \epsilon$ vs. $Y = m(X) + \epsilon$? | There is actually no such object as $Y|X$ --- whenever this notation appears, it is an abuse of notation which operates as shorthand for specifying the conditional distribution of a random variable co | Is there a difference in interpretation between $Y|X = m(X) + \epsilon$ vs. $Y = m(X) + \epsilon$?
There is actually no such object as $Y|X$ --- whenever this notation appears, it is an abuse of notation which operates as shorthand for specifying the conditional distribution of a random variable conditional on another ... | Is there a difference in interpretation between $Y|X = m(X) + \epsilon$ vs. $Y = m(X) + \epsilon$?
There is actually no such object as $Y|X$ --- whenever this notation appears, it is an abuse of notation which operates as shorthand for specifying the conditional distribution of a random variable co |
40,213 | Is there a difference in interpretation between $Y|X = m(X) + \epsilon$ vs. $Y = m(X) + \epsilon$? | In my opinion, the use of the equality makes dependence on $X$ explicit. The only place I have seen notation like $y \vert X$ is when the distribution of $y$ is being discussed. You see this frequently in Bayesian models like
$$ y\vert \mu , \sigma \sim \mathcal{N}(\mu, \sigma) $$
This notation tells me that there is... | Is there a difference in interpretation between $Y|X = m(X) + \epsilon$ vs. $Y = m(X) + \epsilon$? | In my opinion, the use of the equality makes dependence on $X$ explicit. The only place I have seen notation like $y \vert X$ is when the distribution of $y$ is being discussed. You see this frequen | Is there a difference in interpretation between $Y|X = m(X) + \epsilon$ vs. $Y = m(X) + \epsilon$?
In my opinion, the use of the equality makes dependence on $X$ explicit. The only place I have seen notation like $y \vert X$ is when the distribution of $y$ is being discussed. You see this frequently in Bayesian model... | Is there a difference in interpretation between $Y|X = m(X) + \epsilon$ vs. $Y = m(X) + \epsilon$?
In my opinion, the use of the equality makes dependence on $X$ explicit. The only place I have seen notation like $y \vert X$ is when the distribution of $y$ is being discussed. You see this frequen |
40,214 | Why `arima()` and `Arima()` give different AIC and sigma2 while giving the same coefficients and same likelihood? | stats::arima() estimates $\sigma^2$ using the MLE of the innovations variance, while forecast::Arima() uses the unbiased estimate $\sum e_i^2/(n-k)$ where $n$ is the number of observations available and $k$ is the number of parameters estimated.
stats::arima() does not count $\sigma^2$ as a parameter in the computation... | Why `arima()` and `Arima()` give different AIC and sigma2 while giving the same coefficients and sam | stats::arima() estimates $\sigma^2$ using the MLE of the innovations variance, while forecast::Arima() uses the unbiased estimate $\sum e_i^2/(n-k)$ where $n$ is the number of observations available a | Why `arima()` and `Arima()` give different AIC and sigma2 while giving the same coefficients and same likelihood?
stats::arima() estimates $\sigma^2$ using the MLE of the innovations variance, while forecast::Arima() uses the unbiased estimate $\sum e_i^2/(n-k)$ where $n$ is the number of observations available and $k$... | Why `arima()` and `Arima()` give different AIC and sigma2 while giving the same coefficients and sam
stats::arima() estimates $\sigma^2$ using the MLE of the innovations variance, while forecast::Arima() uses the unbiased estimate $\sum e_i^2/(n-k)$ where $n$ is the number of observations available a |
40,215 | How to integrate the marginal likelihood numerically? | The marginal log-likelihood in mixed models is typically written as:
$$\ell(\theta) = \sum_{i = 1}^n \log \int p(y_i \mid b_i) \, p(b_i) \, db_i.$$
In specific settings, e.g., in linear mixed model, where both terms in the integrand are normal densities, this integral has a closed-form solution. But in general you need... | How to integrate the marginal likelihood numerically? | The marginal log-likelihood in mixed models is typically written as:
$$\ell(\theta) = \sum_{i = 1}^n \log \int p(y_i \mid b_i) \, p(b_i) \, db_i.$$
In specific settings, e.g., in linear mixed model, w | How to integrate the marginal likelihood numerically?
The marginal log-likelihood in mixed models is typically written as:
$$\ell(\theta) = \sum_{i = 1}^n \log \int p(y_i \mid b_i) \, p(b_i) \, db_i.$$
In specific settings, e.g., in linear mixed model, where both terms in the integrand are normal densities, this integr... | How to integrate the marginal likelihood numerically?
The marginal log-likelihood in mixed models is typically written as:
$$\ell(\theta) = \sum_{i = 1}^n \log \int p(y_i \mid b_i) \, p(b_i) \, db_i.$$
In specific settings, e.g., in linear mixed model, w |
40,216 | How to integrate the marginal likelihood numerically? | The log-sum-exp trick is a way to calculate sums over finite sets, operating in the log domain to avoid overflow. I'll show how to generalize this trick to integrals, giving a way to rewrite the log of your marginal likelihood.
The log marginal likelihood is:
$$\log \ell_m(\theta) =
\log \int \exp \big( \ell(\theta, b)... | How to integrate the marginal likelihood numerically? | The log-sum-exp trick is a way to calculate sums over finite sets, operating in the log domain to avoid overflow. I'll show how to generalize this trick to integrals, giving a way to rewrite the log o | How to integrate the marginal likelihood numerically?
The log-sum-exp trick is a way to calculate sums over finite sets, operating in the log domain to avoid overflow. I'll show how to generalize this trick to integrals, giving a way to rewrite the log of your marginal likelihood.
The log marginal likelihood is:
$$\log... | How to integrate the marginal likelihood numerically?
The log-sum-exp trick is a way to calculate sums over finite sets, operating in the log domain to avoid overflow. I'll show how to generalize this trick to integrals, giving a way to rewrite the log o |
40,217 | How to integrate the marginal likelihood numerically? | Accurate integration of this kind of function will require you to work in log-space, which means that you will use the $\text{logsumexp}$ function for sums of terms. You can then use any standard method of numerical integration (e.g., quadrature, importance sampling, etc.)
To give you a more specific idea of how to im... | How to integrate the marginal likelihood numerically? | Accurate integration of this kind of function will require you to work in log-space, which means that you will use the $\text{logsumexp}$ function for sums of terms. You can then use any standard met | How to integrate the marginal likelihood numerically?
Accurate integration of this kind of function will require you to work in log-space, which means that you will use the $\text{logsumexp}$ function for sums of terms. You can then use any standard method of numerical integration (e.g., quadrature, importance samplin... | How to integrate the marginal likelihood numerically?
Accurate integration of this kind of function will require you to work in log-space, which means that you will use the $\text{logsumexp}$ function for sums of terms. You can then use any standard met |
40,218 | Probability mass function of product of two binomial variables | There are various ways you could write the mass function of this distribution. All of them will be messy, since they involve checking the possible products that give a stipulated value for the product variable. Here is the most obvious way to write the distribution.
Let $X, Y \sim \text{IID Bin}(n, p)$ and let $Z=XY... | Probability mass function of product of two binomial variables | There are various ways you could write the mass function of this distribution. All of them will be messy, since they involve checking the possible products that give a stipulated value for the produc | Probability mass function of product of two binomial variables
There are various ways you could write the mass function of this distribution. All of them will be messy, since they involve checking the possible products that give a stipulated value for the product variable. Here is the most obvious way to write the di... | Probability mass function of product of two binomial variables
There are various ways you could write the mass function of this distribution. All of them will be messy, since they involve checking the possible products that give a stipulated value for the produc |
40,219 | Where can I find standards for statistical acronyms and whether they should be capitalized or lower case? | If you need to include a statistical acronym in a report or manuscript, the best thing you can do in my view is to define its meaning in that write-up the first time you use the acronym and then reference the acronym in the remainder of the write-up. This way, your readers will be clear on how YOU want them to interpre... | Where can I find standards for statistical acronyms and whether they should be capitalized or lower | If you need to include a statistical acronym in a report or manuscript, the best thing you can do in my view is to define its meaning in that write-up the first time you use the acronym and then refer | Where can I find standards for statistical acronyms and whether they should be capitalized or lower case?
If you need to include a statistical acronym in a report or manuscript, the best thing you can do in my view is to define its meaning in that write-up the first time you use the acronym and then reference the acron... | Where can I find standards for statistical acronyms and whether they should be capitalized or lower
If you need to include a statistical acronym in a report or manuscript, the best thing you can do in my view is to define its meaning in that write-up the first time you use the acronym and then refer |
40,220 | Causality: Structural Causal Model and DAG | Your model statement specifies a class of DAGs, not a single DAG. That is, all DAGs in which $x_1, \dots, x_n$ are direct causes of $y$, and $e$ is exogenous are DAGs compatibles with your assumptions.
For instance, for simplicity, say we have only $x_1$ and $x_2$. Then, among several other alternatives, the following... | Causality: Structural Causal Model and DAG | Your model statement specifies a class of DAGs, not a single DAG. That is, all DAGs in which $x_1, \dots, x_n$ are direct causes of $y$, and $e$ is exogenous are DAGs compatibles with your assumptions | Causality: Structural Causal Model and DAG
Your model statement specifies a class of DAGs, not a single DAG. That is, all DAGs in which $x_1, \dots, x_n$ are direct causes of $y$, and $e$ is exogenous are DAGs compatibles with your assumptions.
For instance, for simplicity, say we have only $x_1$ and $x_2$. Then, amon... | Causality: Structural Causal Model and DAG
Your model statement specifies a class of DAGs, not a single DAG. That is, all DAGs in which $x_1, \dots, x_n$ are direct causes of $y$, and $e$ is exogenous are DAGs compatibles with your assumptions |
40,221 | Definition of exponential family with dispersion parameter | The definition you quote which is used with generalized linear models (glm) is not an exponential family, it is an exponential dispersion family. For a fixed value of the dispersion parameter $\phi$ it is an exponential family (indexed by $\theta$), but when $\phi$ varies it is not.
When used in glm's, the exponentia... | Definition of exponential family with dispersion parameter | The definition you quote which is used with generalized linear models (glm) is not an exponential family, it is an exponential dispersion family. For a fixed value of the dispersion parameter $\phi$ | Definition of exponential family with dispersion parameter
The definition you quote which is used with generalized linear models (glm) is not an exponential family, it is an exponential dispersion family. For a fixed value of the dispersion parameter $\phi$ it is an exponential family (indexed by $\theta$), but when $... | Definition of exponential family with dispersion parameter
The definition you quote which is used with generalized linear models (glm) is not an exponential family, it is an exponential dispersion family. For a fixed value of the dispersion parameter $\phi$ |
40,222 | Why do stabilized IPW weights give the same estimates and SEs as unstabilized weights? | This is because the marginal structural models you're fitting (objects fitw and fitsw) are so-called saturated models. For saturated models, using weight stabilization does not change the relative weights of outcomes in subgroups defined by the treatment levels, because in any subgroup the weight is multiplied by a fac... | Why do stabilized IPW weights give the same estimates and SEs as unstabilized weights? | This is because the marginal structural models you're fitting (objects fitw and fitsw) are so-called saturated models. For saturated models, using weight stabilization does not change the relative wei | Why do stabilized IPW weights give the same estimates and SEs as unstabilized weights?
This is because the marginal structural models you're fitting (objects fitw and fitsw) are so-called saturated models. For saturated models, using weight stabilization does not change the relative weights of outcomes in subgroups def... | Why do stabilized IPW weights give the same estimates and SEs as unstabilized weights?
This is because the marginal structural models you're fitting (objects fitw and fitsw) are so-called saturated models. For saturated models, using weight stabilization does not change the relative wei |
40,223 | Relation between F test and T test. Are they mutually exclusive? | The terms t-test and F-Test are ambiguous, because any test where the test statistic has a t-distribution (under the null hypothesis) is called t-test and any test where the test statistic has an F-distribution is called F-test. There is more than one instance of these.
This is relevant to your question because there i... | Relation between F test and T test. Are they mutually exclusive? | The terms t-test and F-Test are ambiguous, because any test where the test statistic has a t-distribution (under the null hypothesis) is called t-test and any test where the test statistic has an F-di | Relation between F test and T test. Are they mutually exclusive?
The terms t-test and F-Test are ambiguous, because any test where the test statistic has a t-distribution (under the null hypothesis) is called t-test and any test where the test statistic has an F-distribution is called F-test. There is more than one ins... | Relation between F test and T test. Are they mutually exclusive?
The terms t-test and F-Test are ambiguous, because any test where the test statistic has a t-distribution (under the null hypothesis) is called t-test and any test where the test statistic has an F-di |
40,224 | Relation between F test and T test. Are they mutually exclusive? | If you are comparing more than two groups and are interested in comparing their means then it is usual to do ANOVA as you say which tests the hypothesis that all group means are equal. Doing multiple $t$-tests is not quite equivalent because each test only tets if the means in those two groups are equal. Your point 1)
... | Relation between F test and T test. Are they mutually exclusive? | If you are comparing more than two groups and are interested in comparing their means then it is usual to do ANOVA as you say which tests the hypothesis that all group means are equal. Doing multiple | Relation between F test and T test. Are they mutually exclusive?
If you are comparing more than two groups and are interested in comparing their means then it is usual to do ANOVA as you say which tests the hypothesis that all group means are equal. Doing multiple $t$-tests is not quite equivalent because each test onl... | Relation between F test and T test. Are they mutually exclusive?
If you are comparing more than two groups and are interested in comparing their means then it is usual to do ANOVA as you say which tests the hypothesis that all group means are equal. Doing multiple |
40,225 | Relation between F test and T test. Are they mutually exclusive? | It is simple and depends upon your problem statement. If you want the comparsion based on an average you can use a t-test and if you want the comparision that how the data variate within the data then you will use the F-test. | Relation between F test and T test. Are they mutually exclusive? | It is simple and depends upon your problem statement. If you want the comparsion based on an average you can use a t-test and if you want the comparision that how the data variate within the data then | Relation between F test and T test. Are they mutually exclusive?
It is simple and depends upon your problem statement. If you want the comparsion based on an average you can use a t-test and if you want the comparision that how the data variate within the data then you will use the F-test. | Relation between F test and T test. Are they mutually exclusive?
It is simple and depends upon your problem statement. If you want the comparsion based on an average you can use a t-test and if you want the comparision that how the data variate within the data then |
40,226 | Relation between F test and T test. Are they mutually exclusive? | Consider this formula
Ho: group1 and group2 has the same average
(e.g. do they have the same average height)
t = (mean-k)/(s/sqrt(n)), basic assumption. variance is known.
Ho: Different level of fertilizer (NPK) has no significant effect on plants.
F = n(mean-k)^2 / s^2, w/c is simply t^2
from Practicality point o... | Relation between F test and T test. Are they mutually exclusive? | Consider this formula
Ho: group1 and group2 has the same average
(e.g. do they have the same average height)
t = (mean-k)/(s/sqrt(n)), basic assumption. variance is known.
Ho: Different level of fert | Relation between F test and T test. Are they mutually exclusive?
Consider this formula
Ho: group1 and group2 has the same average
(e.g. do they have the same average height)
t = (mean-k)/(s/sqrt(n)), basic assumption. variance is known.
Ho: Different level of fertilizer (NPK) has no significant effect on plants.
F = n... | Relation between F test and T test. Are they mutually exclusive?
Consider this formula
Ho: group1 and group2 has the same average
(e.g. do they have the same average height)
t = (mean-k)/(s/sqrt(n)), basic assumption. variance is known.
Ho: Different level of fert |
40,227 | Is it appropriate to estimate a random slope without estimating the overall mean slope? | Fitting random slopes with the population-level slope fixed to zero is not out of the question - it's not mathematically or statistically ill-posed - but it's a rather weird model that would require some extra justification. Why would you expect that the average slope across cities would be exactly zero (which is what ... | Is it appropriate to estimate a random slope without estimating the overall mean slope? | Fitting random slopes with the population-level slope fixed to zero is not out of the question - it's not mathematically or statistically ill-posed - but it's a rather weird model that would require s | Is it appropriate to estimate a random slope without estimating the overall mean slope?
Fitting random slopes with the population-level slope fixed to zero is not out of the question - it's not mathematically or statistically ill-posed - but it's a rather weird model that would require some extra justification. Why wou... | Is it appropriate to estimate a random slope without estimating the overall mean slope?
Fitting random slopes with the population-level slope fixed to zero is not out of the question - it's not mathematically or statistically ill-posed - but it's a rather weird model that would require s |
40,228 | Kolmogorov Smirnov test vs. Anderson Darling test | The Kolmogorov-Smirnov looks for the largest difference between the cdf and the empirical cdf of the data.
There's another test -- the Cramér-von Mises test -- which looks at the sum of squares of the differences in cdf (at the data). It's often somewhat more sensitive than the Kolmogorov-Smirnov to the kind of differe... | Kolmogorov Smirnov test vs. Anderson Darling test | The Kolmogorov-Smirnov looks for the largest difference between the cdf and the empirical cdf of the data.
There's another test -- the Cramér-von Mises test -- which looks at the sum of squares of the | Kolmogorov Smirnov test vs. Anderson Darling test
The Kolmogorov-Smirnov looks for the largest difference between the cdf and the empirical cdf of the data.
There's another test -- the Cramér-von Mises test -- which looks at the sum of squares of the differences in cdf (at the data). It's often somewhat more sensitive ... | Kolmogorov Smirnov test vs. Anderson Darling test
The Kolmogorov-Smirnov looks for the largest difference between the cdf and the empirical cdf of the data.
There's another test -- the Cramér-von Mises test -- which looks at the sum of squares of the |
40,229 | Logistic regression BIC: what's the right N? | The BIC (and the AIC) are relative measures for comparing models. However, it makes no sense to compare what is otherwise the same model between using an aggregated vs. a disaggregated response. Nor would it make sense to compare models that would otherwise be different (e.g., different regressors), but where one mod... | Logistic regression BIC: what's the right N? | The BIC (and the AIC) are relative measures for comparing models. However, it makes no sense to compare what is otherwise the same model between using an aggregated vs. a disaggregated response. Nor | Logistic regression BIC: what's the right N?
The BIC (and the AIC) are relative measures for comparing models. However, it makes no sense to compare what is otherwise the same model between using an aggregated vs. a disaggregated response. Nor would it make sense to compare models that would otherwise be different (e... | Logistic regression BIC: what's the right N?
The BIC (and the AIC) are relative measures for comparing models. However, it makes no sense to compare what is otherwise the same model between using an aggregated vs. a disaggregated response. Nor |
40,230 | Logistic regression BIC: what's the right N? | Interesting question! Coming at this from an applied setting, I think you need to remember that both BIC and AIC are measures of relative model fit.
In other words, these measures don't tell you much when you examine them for a single model, but can help you to select an appropriate model among a set of competing mode... | Logistic regression BIC: what's the right N? | Interesting question! Coming at this from an applied setting, I think you need to remember that both BIC and AIC are measures of relative model fit.
In other words, these measures don't tell you much | Logistic regression BIC: what's the right N?
Interesting question! Coming at this from an applied setting, I think you need to remember that both BIC and AIC are measures of relative model fit.
In other words, these measures don't tell you much when you examine them for a single model, but can help you to select an ap... | Logistic regression BIC: what's the right N?
Interesting question! Coming at this from an applied setting, I think you need to remember that both BIC and AIC are measures of relative model fit.
In other words, these measures don't tell you much |
40,231 | How is it possible for both the likelihood and log-likelihood to be asymptotically normal? | I think you just have to be precise about what you mean by "asymptotically normal." For example, when people say that "a sum of random variables is asymptotically normal by the central limit theorem," they usually really mean a precise statement about convergence in distribution, e.g.,
Central Limit Theorem (Lindeberg... | How is it possible for both the likelihood and log-likelihood to be asymptotically normal? | I think you just have to be precise about what you mean by "asymptotically normal." For example, when people say that "a sum of random variables is asymptotically normal by the central limit theorem," | How is it possible for both the likelihood and log-likelihood to be asymptotically normal?
I think you just have to be precise about what you mean by "asymptotically normal." For example, when people say that "a sum of random variables is asymptotically normal by the central limit theorem," they usually really mean a p... | How is it possible for both the likelihood and log-likelihood to be asymptotically normal?
I think you just have to be precise about what you mean by "asymptotically normal." For example, when people say that "a sum of random variables is asymptotically normal by the central limit theorem," |
40,232 | On masked multi-head attention and layer normalization in transformer model | This is answered in the Attention is All You Need paper by Vaswani et al (see also recording of the talk by one of the co-authors, and those three blogs: here, here, and here).
How is it possible to mask out illegal connections in decoder multi-head attention?
This is pretty simple. Attention can be defined as
$$... | On masked multi-head attention and layer normalization in transformer model | This is answered in the Attention is All You Need paper by Vaswani et al (see also recording of the talk by one of the co-authors, and those three blogs: here, here, and here).
How is it possible t | On masked multi-head attention and layer normalization in transformer model
This is answered in the Attention is All You Need paper by Vaswani et al (see also recording of the talk by one of the co-authors, and those three blogs: here, here, and here).
How is it possible to mask out illegal connections in decoder mu... | On masked multi-head attention and layer normalization in transformer model
This is answered in the Attention is All You Need paper by Vaswani et al (see also recording of the talk by one of the co-authors, and those three blogs: here, here, and here).
How is it possible t |
40,233 | Fit data to parametric distribution | The histogram, as presented by the OP, gives the impression that the data is symmetrical. Given that the data is noticeably more peaked than Normal, and if the data is roughly symmetrical, then a natural suggestion to try is the Student's t with location parameter $\mu$, scale parameter $\sigma$, and $v$ degrees of fr... | Fit data to parametric distribution | The histogram, as presented by the OP, gives the impression that the data is symmetrical. Given that the data is noticeably more peaked than Normal, and if the data is roughly symmetrical, then a natu | Fit data to parametric distribution
The histogram, as presented by the OP, gives the impression that the data is symmetrical. Given that the data is noticeably more peaked than Normal, and if the data is roughly symmetrical, then a natural suggestion to try is the Student's t with location parameter $\mu$, scale param... | Fit data to parametric distribution
The histogram, as presented by the OP, gives the impression that the data is symmetrical. Given that the data is noticeably more peaked than Normal, and if the data is roughly symmetrical, then a natu |
40,234 | Fit data to parametric distribution | In short: your two plots show a big discrepancy, the smallest values shown in the histogram is about $-30$, while the qqplot shows values down to around $-900$. All those lom-tailed outliers is about 0.7% of the sample, but dominates the qqplot. So you need to ask yourself what produces those outliers! and that should... | Fit data to parametric distribution | In short: your two plots show a big discrepancy, the smallest values shown in the histogram is about $-30$, while the qqplot shows values down to around $-900$. All those lom-tailed outliers is about | Fit data to parametric distribution
In short: your two plots show a big discrepancy, the smallest values shown in the histogram is about $-30$, while the qqplot shows values down to around $-900$. All those lom-tailed outliers is about 0.7% of the sample, but dominates the qqplot. So you need to ask yourself what prod... | Fit data to parametric distribution
In short: your two plots show a big discrepancy, the smallest values shown in the histogram is about $-30$, while the qqplot shows values down to around $-900$. All those lom-tailed outliers is about |
40,235 | Fit data to parametric distribution | You might try a Gaussian mixture, which is easy using Mclust in the mclust library of R.
library(mclust)
mc.fit = Mclust(data$V1)
summary(mc.fit,parameters=TRUE)
This gives a three-component Gaussian mixture (8 parameters total), with components
1: N(-69.269908, 6995.71627), p1 = 0.003970506
2: N( -4.314187, 171.7687... | Fit data to parametric distribution | You might try a Gaussian mixture, which is easy using Mclust in the mclust library of R.
library(mclust)
mc.fit = Mclust(data$V1)
summary(mc.fit,parameters=TRUE)
This gives a three-component Gaussian | Fit data to parametric distribution
You might try a Gaussian mixture, which is easy using Mclust in the mclust library of R.
library(mclust)
mc.fit = Mclust(data$V1)
summary(mc.fit,parameters=TRUE)
This gives a three-component Gaussian mixture (8 parameters total), with components
1: N(-69.269908, 6995.71627), p1 = 0.0... | Fit data to parametric distribution
You might try a Gaussian mixture, which is easy using Mclust in the mclust library of R.
library(mclust)
mc.fit = Mclust(data$V1)
summary(mc.fit,parameters=TRUE)
This gives a three-component Gaussian |
40,236 | Proof of Approximate / Exact Bayesian Computation | This case is the original version of the algorithm, as in Rubin (1984) and Tavaré et al. (1997). Assuming that $$\mathbb{P}_\theta(X=D)>0$$ the values of $\theta$ that come out of the algorithm are distributed from a distribution with density proportional to
$$\pi(\theta) \times \mathbb{P}_\theta(X=D)$$
since the algor... | Proof of Approximate / Exact Bayesian Computation | This case is the original version of the algorithm, as in Rubin (1984) and Tavaré et al. (1997). Assuming that $$\mathbb{P}_\theta(X=D)>0$$ the values of $\theta$ that come out of the algorithm are di | Proof of Approximate / Exact Bayesian Computation
This case is the original version of the algorithm, as in Rubin (1984) and Tavaré et al. (1997). Assuming that $$\mathbb{P}_\theta(X=D)>0$$ the values of $\theta$ that come out of the algorithm are distributed from a distribution with density proportional to
$$\pi(\thet... | Proof of Approximate / Exact Bayesian Computation
This case is the original version of the algorithm, as in Rubin (1984) and Tavaré et al. (1997). Assuming that $$\mathbb{P}_\theta(X=D)>0$$ the values of $\theta$ that come out of the algorithm are di |
40,237 | How to handle a changing action space in Reinforcement Learning | You don't need to do anything special to handle this. The only thing you need to change is to not take any illegal actions.
The typical Q-learning greedy policy is $\pi(s) = \text{argmax}_{a \in \mathcal{A}} \hat q(s,a)$ and the epsilon-greedy rollout policy is very similar. Simply replace the action space $\mathcal{A}... | How to handle a changing action space in Reinforcement Learning | You don't need to do anything special to handle this. The only thing you need to change is to not take any illegal actions.
The typical Q-learning greedy policy is $\pi(s) = \text{argmax}_{a \in \math | How to handle a changing action space in Reinforcement Learning
You don't need to do anything special to handle this. The only thing you need to change is to not take any illegal actions.
The typical Q-learning greedy policy is $\pi(s) = \text{argmax}_{a \in \mathcal{A}} \hat q(s,a)$ and the epsilon-greedy rollout poli... | How to handle a changing action space in Reinforcement Learning
You don't need to do anything special to handle this. The only thing you need to change is to not take any illegal actions.
The typical Q-learning greedy policy is $\pi(s) = \text{argmax}_{a \in \math |
40,238 | Acceptance-Rejection Method Acceptance Probability Proof | If you target $f$ with $g$, and you know $f(x) \le g(x)c$, then
\begin{align*}
P(\text{accept proposal}) &= P\left( U \le \frac{f(X)}{g(X)c} \right) \\
&= E\left( \mathbf{1}\left[U \le \frac{f(X)}{g(X)c}\right] \right) \tag{*}\\
&= E\left( E\left[ \mathbf{1}\left\{U \le \frac{f(X)}{g(X)c}\right\} \bigg\rvert X \right]\... | Acceptance-Rejection Method Acceptance Probability Proof | If you target $f$ with $g$, and you know $f(x) \le g(x)c$, then
\begin{align*}
P(\text{accept proposal}) &= P\left( U \le \frac{f(X)}{g(X)c} \right) \\
&= E\left( \mathbf{1}\left[U \le \frac{f(X)}{g(X | Acceptance-Rejection Method Acceptance Probability Proof
If you target $f$ with $g$, and you know $f(x) \le g(x)c$, then
\begin{align*}
P(\text{accept proposal}) &= P\left( U \le \frac{f(X)}{g(X)c} \right) \\
&= E\left( \mathbf{1}\left[U \le \frac{f(X)}{g(X)c}\right] \right) \tag{*}\\
&= E\left( E\left[ \mathbf{1}\left... | Acceptance-Rejection Method Acceptance Probability Proof
If you target $f$ with $g$, and you know $f(x) \le g(x)c$, then
\begin{align*}
P(\text{accept proposal}) &= P\left( U \le \frac{f(X)}{g(X)c} \right) \\
&= E\left( \mathbf{1}\left[U \le \frac{f(X)}{g(X |
40,239 | Converting the beta coefficient from matrix to scalar notation in OLS regression | Solution
The matrix algebra can be dismaying and, if not carried out elegantly, can require an awful lot of (superfluous) algebraic manipulation. However, the situation is much simpler than it looks, because (creating the matrix $X$ by putting a column of ones in first, and then the column of independent values $(x_i)... | Converting the beta coefficient from matrix to scalar notation in OLS regression | Solution
The matrix algebra can be dismaying and, if not carried out elegantly, can require an awful lot of (superfluous) algebraic manipulation. However, the situation is much simpler than it looks, | Converting the beta coefficient from matrix to scalar notation in OLS regression
Solution
The matrix algebra can be dismaying and, if not carried out elegantly, can require an awful lot of (superfluous) algebraic manipulation. However, the situation is much simpler than it looks, because (creating the matrix $X$ by pu... | Converting the beta coefficient from matrix to scalar notation in OLS regression
Solution
The matrix algebra can be dismaying and, if not carried out elegantly, can require an awful lot of (superfluous) algebraic manipulation. However, the situation is much simpler than it looks, |
40,240 | Converting the beta coefficient from matrix to scalar notation in OLS regression | If you regress on a constant and $x_i$, your matrix $X$ is
\begin{pmatrix}1 &x_1\\
\vdots&\vdots\\1 &x_n
\end{pmatrix}
Hence,
$$
X'X=\begin{pmatrix}n &\sum_ix_i\\
\sum_ix_i&\sum_ix_i^2\\
\end{pmatrix}
$$
and
$$(X'X)^{-1}=\frac{1}{n\sum_ix_i^2-(\sum_ix_i)^2}
\begin{pmatrix}\sum_ix_i^2 &-\sum_ix_i\\
-\sum_ix_i&n\\
\end{p... | Converting the beta coefficient from matrix to scalar notation in OLS regression | If you regress on a constant and $x_i$, your matrix $X$ is
\begin{pmatrix}1 &x_1\\
\vdots&\vdots\\1 &x_n
\end{pmatrix}
Hence,
$$
X'X=\begin{pmatrix}n &\sum_ix_i\\
\sum_ix_i&\sum_ix_i^2\\
\end{pmatrix} | Converting the beta coefficient from matrix to scalar notation in OLS regression
If you regress on a constant and $x_i$, your matrix $X$ is
\begin{pmatrix}1 &x_1\\
\vdots&\vdots\\1 &x_n
\end{pmatrix}
Hence,
$$
X'X=\begin{pmatrix}n &\sum_ix_i\\
\sum_ix_i&\sum_ix_i^2\\
\end{pmatrix}
$$
and
$$(X'X)^{-1}=\frac{1}{n\sum_ix_... | Converting the beta coefficient from matrix to scalar notation in OLS regression
If you regress on a constant and $x_i$, your matrix $X$ is
\begin{pmatrix}1 &x_1\\
\vdots&\vdots\\1 &x_n
\end{pmatrix}
Hence,
$$
X'X=\begin{pmatrix}n &\sum_ix_i\\
\sum_ix_i&\sum_ix_i^2\\
\end{pmatrix} |
40,241 | Converting the beta coefficient from matrix to scalar notation in OLS regression | For anyone else out there that might be struggling with this, I've written it all out below step by step.
Suppose for the ease of explanation we have a minimum sample of 1 $x$ variable ($k=1$) and only 2 observations ($n=2$); Our estimation in scalar is $\hat{y_i} = \hat{\beta_0}+\hat{\beta_1}x_i$
\begin{equation*}
\bo... | Converting the beta coefficient from matrix to scalar notation in OLS regression | For anyone else out there that might be struggling with this, I've written it all out below step by step.
Suppose for the ease of explanation we have a minimum sample of 1 $x$ variable ($k=1$) and onl | Converting the beta coefficient from matrix to scalar notation in OLS regression
For anyone else out there that might be struggling with this, I've written it all out below step by step.
Suppose for the ease of explanation we have a minimum sample of 1 $x$ variable ($k=1$) and only 2 observations ($n=2$); Our estimatio... | Converting the beta coefficient from matrix to scalar notation in OLS regression
For anyone else out there that might be struggling with this, I've written it all out below step by step.
Suppose for the ease of explanation we have a minimum sample of 1 $x$ variable ($k=1$) and onl |
40,242 | Why does Deep Q-Learning have "do nothing" actions? | At the start of every game, a random number of no-op actions are played (with the maximum number of such actions controlled by that parameter) to introduce variety in the initial game states.
If an agent starts from exactly the same initial state every time it plays the same game, they're afraid that the Reinforcement... | Why does Deep Q-Learning have "do nothing" actions? | At the start of every game, a random number of no-op actions are played (with the maximum number of such actions controlled by that parameter) to introduce variety in the initial game states.
If an a | Why does Deep Q-Learning have "do nothing" actions?
At the start of every game, a random number of no-op actions are played (with the maximum number of such actions controlled by that parameter) to introduce variety in the initial game states.
If an agent starts from exactly the same initial state every time it plays ... | Why does Deep Q-Learning have "do nothing" actions?
At the start of every game, a random number of no-op actions are played (with the maximum number of such actions controlled by that parameter) to introduce variety in the initial game states.
If an a |
40,243 | Is Cross Validation useless unless the Hypotheses are nested? | My logic tells me the answer is yes.
And, as @amoeba pointed out: your logic is right.
how is Cross Validation different than this procedure?
CV in itself has nothing to do with your overfitting. CV is just a scheme how to retain independent cases to test some model.
Note that if you select a model based on the... | Is Cross Validation useless unless the Hypotheses are nested? | My logic tells me the answer is yes.
And, as @amoeba pointed out: your logic is right.
how is Cross Validation different than this procedure?
CV in itself has nothing to do with your overfitting | Is Cross Validation useless unless the Hypotheses are nested?
My logic tells me the answer is yes.
And, as @amoeba pointed out: your logic is right.
how is Cross Validation different than this procedure?
CV in itself has nothing to do with your overfitting. CV is just a scheme how to retain independent cases to t... | Is Cross Validation useless unless the Hypotheses are nested?
My logic tells me the answer is yes.
And, as @amoeba pointed out: your logic is right.
how is Cross Validation different than this procedure?
CV in itself has nothing to do with your overfitting |
40,244 | Is Cross Validation useless unless the Hypotheses are nested? | EDIT:
Tuning or selecting a model based on cross-validation is essentially trying to minimize the prediction error (e.g., mean-squared prediction error). You select a model conditional on some subset of input data and predict the output at the left out locations. Intuitively, it is a prediction because you are evaluati... | Is Cross Validation useless unless the Hypotheses are nested? | EDIT:
Tuning or selecting a model based on cross-validation is essentially trying to minimize the prediction error (e.g., mean-squared prediction error). You select a model conditional on some subset | Is Cross Validation useless unless the Hypotheses are nested?
EDIT:
Tuning or selecting a model based on cross-validation is essentially trying to minimize the prediction error (e.g., mean-squared prediction error). You select a model conditional on some subset of input data and predict the output at the left out locat... | Is Cross Validation useless unless the Hypotheses are nested?
EDIT:
Tuning or selecting a model based on cross-validation is essentially trying to minimize the prediction error (e.g., mean-squared prediction error). You select a model conditional on some subset |
40,245 | Distribution of $-\log f_X(X)$ | The book mentioned by Xi'an is from 2004. It refers to an article from the year 1991 in which the following theorem appears.
From: Troutt M.D. 1991 A theorem on the density of the density ordinate
and an alternative interpretation of the Box-Muller
method
If a random variable X has a density $f(x)$, $x \in \mathbb... | Distribution of $-\log f_X(X)$ | The book mentioned by Xi'an is from 2004. It refers to an article from the year 1991 in which the following theorem appears.
From: Troutt M.D. 1991 A theorem on the density of the density ordinate
| Distribution of $-\log f_X(X)$
The book mentioned by Xi'an is from 2004. It refers to an article from the year 1991 in which the following theorem appears.
From: Troutt M.D. 1991 A theorem on the density of the density ordinate
and an alternative interpretation of the Box-Muller
method
If a random variable X has a... | Distribution of $-\log f_X(X)$
The book mentioned by Xi'an is from 2004. It refers to an article from the year 1991 in which the following theorem appears.
From: Troutt M.D. 1991 A theorem on the density of the density ordinate
|
40,246 | Why does sklearn Ridge not accept warm start? | Ridge regression can be solved in one shot as a system of linear equations:
$$ \hat \beta = (X^t X + \lambda I)^{-1} X^t y $$
So ridge regression is usually solved with a linear equation solver, just like linear regression.
For example, sklearn uses the singular value decomposition of the matrix $X$:
$$ X = UDV^{-1} $$... | Why does sklearn Ridge not accept warm start? | Ridge regression can be solved in one shot as a system of linear equations:
$$ \hat \beta = (X^t X + \lambda I)^{-1} X^t y $$
So ridge regression is usually solved with a linear equation solver, just | Why does sklearn Ridge not accept warm start?
Ridge regression can be solved in one shot as a system of linear equations:
$$ \hat \beta = (X^t X + \lambda I)^{-1} X^t y $$
So ridge regression is usually solved with a linear equation solver, just like linear regression.
For example, sklearn uses the singular value decom... | Why does sklearn Ridge not accept warm start?
Ridge regression can be solved in one shot as a system of linear equations:
$$ \hat \beta = (X^t X + \lambda I)^{-1} X^t y $$
So ridge regression is usually solved with a linear equation solver, just |
40,247 | Is the LASSO really applicable for binary classification problems? | It is valid. Note the family="binomial" argument which is appropriate for a classification problem. A normal lasso regression problem would use the gaussian link function.
In this setting, it allows you to estimate the parameters of the binomial GLM by optimising the binomial likelihood whilst imposing the lasso penalt... | Is the LASSO really applicable for binary classification problems? | It is valid. Note the family="binomial" argument which is appropriate for a classification problem. A normal lasso regression problem would use the gaussian link function.
In this setting, it allows y | Is the LASSO really applicable for binary classification problems?
It is valid. Note the family="binomial" argument which is appropriate for a classification problem. A normal lasso regression problem would use the gaussian link function.
In this setting, it allows you to estimate the parameters of the binomial GLM by ... | Is the LASSO really applicable for binary classification problems?
It is valid. Note the family="binomial" argument which is appropriate for a classification problem. A normal lasso regression problem would use the gaussian link function.
In this setting, it allows y |
40,248 | Standard Error of the MLE for Laplace Distribution | Appeal to the Fisher information gives you an asymptotic approximation to the standard error. As whuber correctly points out in the comments, so long as this function is almost surely differentiable, that should be sufficient to obtain your result.
However, in the present case it is also possible to obtain the exact d... | Standard Error of the MLE for Laplace Distribution | Appeal to the Fisher information gives you an asymptotic approximation to the standard error. As whuber correctly points out in the comments, so long as this function is almost surely differentiable, | Standard Error of the MLE for Laplace Distribution
Appeal to the Fisher information gives you an asymptotic approximation to the standard error. As whuber correctly points out in the comments, so long as this function is almost surely differentiable, that should be sufficient to obtain your result.
However, in the pre... | Standard Error of the MLE for Laplace Distribution
Appeal to the Fisher information gives you an asymptotic approximation to the standard error. As whuber correctly points out in the comments, so long as this function is almost surely differentiable, |
40,249 | Stochastic gradient descent Vs Mini-batch size 1 | Standard gradient descent and batch gradient descent were originally used to describe taking the gradient over all data points, and by some definitions, mini-batch corresponds to taking a small number of data points (the mini-batch size) to approximate the gradient in each iteration. Then officially, stochastic gradien... | Stochastic gradient descent Vs Mini-batch size 1 | Standard gradient descent and batch gradient descent were originally used to describe taking the gradient over all data points, and by some definitions, mini-batch corresponds to taking a small number | Stochastic gradient descent Vs Mini-batch size 1
Standard gradient descent and batch gradient descent were originally used to describe taking the gradient over all data points, and by some definitions, mini-batch corresponds to taking a small number of data points (the mini-batch size) to approximate the gradient in ea... | Stochastic gradient descent Vs Mini-batch size 1
Standard gradient descent and batch gradient descent were originally used to describe taking the gradient over all data points, and by some definitions, mini-batch corresponds to taking a small number |
40,250 | Stochastic gradient descent Vs Mini-batch size 1 | Is stochastic gradient descent basically the name given to mini-batch
training where batch size = 1 and selecting random training rows?
Yes. Though shuffling the rows isn't necessarily implied. | Stochastic gradient descent Vs Mini-batch size 1 | Is stochastic gradient descent basically the name given to mini-batch
training where batch size = 1 and selecting random training rows?
Yes. Though shuffling the rows isn't necessarily implied. | Stochastic gradient descent Vs Mini-batch size 1
Is stochastic gradient descent basically the name given to mini-batch
training where batch size = 1 and selecting random training rows?
Yes. Though shuffling the rows isn't necessarily implied. | Stochastic gradient descent Vs Mini-batch size 1
Is stochastic gradient descent basically the name given to mini-batch
training where batch size = 1 and selecting random training rows?
Yes. Though shuffling the rows isn't necessarily implied. |
40,251 | Generalized Normal Distribution | One option are Lambert W random variables (skewed, heavy-tailed), which can be parameterized either as $f(y \mid \mu_x, \sigma_x, \gamma)$ or $f(y \mid \mu_x, \sigma_x, \delta_{\ell}, \delta_r, \alpha)$, respectively (Disclaimer: I am the author of these, so I am biased on whether they are interpretable or not -- I fin... | Generalized Normal Distribution | One option are Lambert W random variables (skewed, heavy-tailed), which can be parameterized either as $f(y \mid \mu_x, \sigma_x, \gamma)$ or $f(y \mid \mu_x, \sigma_x, \delta_{\ell}, \delta_r, \alpha | Generalized Normal Distribution
One option are Lambert W random variables (skewed, heavy-tailed), which can be parameterized either as $f(y \mid \mu_x, \sigma_x, \gamma)$ or $f(y \mid \mu_x, \sigma_x, \delta_{\ell}, \delta_r, \alpha)$, respectively (Disclaimer: I am the author of these, so I am biased on whether they a... | Generalized Normal Distribution
One option are Lambert W random variables (skewed, heavy-tailed), which can be parameterized either as $f(y \mid \mu_x, \sigma_x, \gamma)$ or $f(y \mid \mu_x, \sigma_x, \delta_{\ell}, \delta_r, \alpha |
40,252 | Generating t-distributed random numbers: lesser numbers near zero. | Short version: the problem stands with NumPy x.std() which does not
divide by the right degrees of freedom.
Repeating the experiment in R shows no discrepancy: either by comparing the histogram with the theoretical Student's $t$ density with three degrees of freedom
or the uniformity of the transform of the sample ... | Generating t-distributed random numbers: lesser numbers near zero. | Short version: the problem stands with NumPy x.std() which does not
divide by the right degrees of freedom.
Repeating the experiment in R shows no discrepancy: either by comparing the histogram wit | Generating t-distributed random numbers: lesser numbers near zero.
Short version: the problem stands with NumPy x.std() which does not
divide by the right degrees of freedom.
Repeating the experiment in R shows no discrepancy: either by comparing the histogram with the theoretical Student's $t$ density with three de... | Generating t-distributed random numbers: lesser numbers near zero.
Short version: the problem stands with NumPy x.std() which does not
divide by the right degrees of freedom.
Repeating the experiment in R shows no discrepancy: either by comparing the histogram wit |
40,253 | Why does t-SNE not separate linearly separable classes? | Yes.
You can use the following code to convince yourself.
N <- 1000
P <- 3
# Generates some random data
data <- matrix(data = rnorm(N*P), nrow = N, ncol = P)
# Assignate linearly separable classes
labels <- (data[,1]+data[,2]>0)+1.
# Make sure that the data can be separated
plot(data[,1],data[,2], col = labels, xla... | Why does t-SNE not separate linearly separable classes? | Yes.
You can use the following code to convince yourself.
N <- 1000
P <- 3
# Generates some random data
data <- matrix(data = rnorm(N*P), nrow = N, ncol = P)
# Assignate linearly separable classes
| Why does t-SNE not separate linearly separable classes?
Yes.
You can use the following code to convince yourself.
N <- 1000
P <- 3
# Generates some random data
data <- matrix(data = rnorm(N*P), nrow = N, ncol = P)
# Assignate linearly separable classes
labels <- (data[,1]+data[,2]>0)+1.
# Make sure that the data ca... | Why does t-SNE not separate linearly separable classes?
Yes.
You can use the following code to convince yourself.
N <- 1000
P <- 3
# Generates some random data
data <- matrix(data = rnorm(N*P), nrow = N, ncol = P)
# Assignate linearly separable classes
|
40,254 | What's the point of reporting bootstrap bias? | The bootstrap bias estimate is an estimate of $E(\hat \theta_n) - \theta$, where $\theta$ is some function of the population and $\hat \theta_n$ is that function evaluated in your sample of size $n$. It estimates the bias in approximating $\theta$ with $\hat \theta_n$, for which you only have $n$ observations. A well-k... | What's the point of reporting bootstrap bias? | The bootstrap bias estimate is an estimate of $E(\hat \theta_n) - \theta$, where $\theta$ is some function of the population and $\hat \theta_n$ is that function evaluated in your sample of size $n$. | What's the point of reporting bootstrap bias?
The bootstrap bias estimate is an estimate of $E(\hat \theta_n) - \theta$, where $\theta$ is some function of the population and $\hat \theta_n$ is that function evaluated in your sample of size $n$. It estimates the bias in approximating $\theta$ with $\hat \theta_n$, for ... | What's the point of reporting bootstrap bias?
The bootstrap bias estimate is an estimate of $E(\hat \theta_n) - \theta$, where $\theta$ is some function of the population and $\hat \theta_n$ is that function evaluated in your sample of size $n$. |
40,255 | Is spline basis orthogonal? | Computationally, sometimes; conceptually, rarely. (This started as comment...)
As already presented here (upvote it if you don't have already) when we use a spline in the context a generalised additive model as soon as the spline basis is created, fitting reverts to standard GLM modelling basis coefficients for each se... | Is spline basis orthogonal? | Computationally, sometimes; conceptually, rarely. (This started as comment...)
As already presented here (upvote it if you don't have already) when we use a spline in the context a generalised additiv | Is spline basis orthogonal?
Computationally, sometimes; conceptually, rarely. (This started as comment...)
As already presented here (upvote it if you don't have already) when we use a spline in the context a generalised additive model as soon as the spline basis is created, fitting reverts to standard GLM modelling ba... | Is spline basis orthogonal?
Computationally, sometimes; conceptually, rarely. (This started as comment...)
As already presented here (upvote it if you don't have already) when we use a spline in the context a generalised additiv |
40,256 | What is steepest descent? Is it gradient descent with exact line search? | Steepest descent is a special case of gradient descent where the step length is chosen to minimize the objective function value. Gradient descent refers to any of a class of algorithms that calculate the gradient of the objective function, then move "downhill" in the indicated direction; the step length can be fixed, ... | What is steepest descent? Is it gradient descent with exact line search? | Steepest descent is a special case of gradient descent where the step length is chosen to minimize the objective function value. Gradient descent refers to any of a class of algorithms that calculate | What is steepest descent? Is it gradient descent with exact line search?
Steepest descent is a special case of gradient descent where the step length is chosen to minimize the objective function value. Gradient descent refers to any of a class of algorithms that calculate the gradient of the objective function, then m... | What is steepest descent? Is it gradient descent with exact line search?
Steepest descent is a special case of gradient descent where the step length is chosen to minimize the objective function value. Gradient descent refers to any of a class of algorithms that calculate |
40,257 | What is steepest descent? Is it gradient descent with exact line search? | Gradient is a multi-variable generalization of the derivative (at a point). While a derivative can be defined on functions of a single variable, for functions of several variables.
Since descent is negative sloped, and to perform gradient descent, we are minimizing error, then maximum steepness is the most negative slo... | What is steepest descent? Is it gradient descent with exact line search? | Gradient is a multi-variable generalization of the derivative (at a point). While a derivative can be defined on functions of a single variable, for functions of several variables.
Since descent is ne | What is steepest descent? Is it gradient descent with exact line search?
Gradient is a multi-variable generalization of the derivative (at a point). While a derivative can be defined on functions of a single variable, for functions of several variables.
Since descent is negative sloped, and to perform gradient descent,... | What is steepest descent? Is it gradient descent with exact line search?
Gradient is a multi-variable generalization of the derivative (at a point). While a derivative can be defined on functions of a single variable, for functions of several variables.
Since descent is ne |
40,258 | General principles for extending the Elo system to games in which the margin of victory matters | A simple version of ELO can be cast as a logistic regression: for players $i,j$ with ratings $R_i,R_j$,
$$P(i\mbox{ beats }j)=\frac{1}{1+\exp(\beta(R_i-R_j))}.$$
So you could just as easily predict score instead by using a different link function, for example a lorentzian or gaussian:
$$P(\mbox{Game score}=x)=a\exp(-... | General principles for extending the Elo system to games in which the margin of victory matters | A simple version of ELO can be cast as a logistic regression: for players $i,j$ with ratings $R_i,R_j$,
$$P(i\mbox{ beats }j)=\frac{1}{1+\exp(\beta(R_i-R_j))}.$$
So you could just as easily predict s | General principles for extending the Elo system to games in which the margin of victory matters
A simple version of ELO can be cast as a logistic regression: for players $i,j$ with ratings $R_i,R_j$,
$$P(i\mbox{ beats }j)=\frac{1}{1+\exp(\beta(R_i-R_j))}.$$
So you could just as easily predict score instead by using a ... | General principles for extending the Elo system to games in which the margin of victory matters
A simple version of ELO can be cast as a logistic regression: for players $i,j$ with ratings $R_i,R_j$,
$$P(i\mbox{ beats }j)=\frac{1}{1+\exp(\beta(R_i-R_j))}.$$
So you could just as easily predict s |
40,259 | General principles for extending the Elo system to games in which the margin of victory matters | There are some works intended to include the margin of victory in rating system (e.g. FiveThirtyEight for NFL), but usually ranking systems (e.g. Elo, Glicko, or our rankade - here's a comparison) don't incorporate the margin of victory.
In most sports/games the margin of victory is not significant.
In chess the goal i... | General principles for extending the Elo system to games in which the margin of victory matters | There are some works intended to include the margin of victory in rating system (e.g. FiveThirtyEight for NFL), but usually ranking systems (e.g. Elo, Glicko, or our rankade - here's a comparison) don | General principles for extending the Elo system to games in which the margin of victory matters
There are some works intended to include the margin of victory in rating system (e.g. FiveThirtyEight for NFL), but usually ranking systems (e.g. Elo, Glicko, or our rankade - here's a comparison) don't incorporate the margi... | General principles for extending the Elo system to games in which the margin of victory matters
There are some works intended to include the margin of victory in rating system (e.g. FiveThirtyEight for NFL), but usually ranking systems (e.g. Elo, Glicko, or our rankade - here's a comparison) don |
40,260 | Gradient Descent (GD) vs Stochastic Gradient Descent (SGD) | Gradient Descent is an iterative method to solve the optimization problem. There is no concept of "epoch" or "batch" in classical gradient decent. The key of gradient decent are
Update the weights by the gradient direction.
The gradient is calculated precisely from all the data points.
Stochastic Gradient Descent ca... | Gradient Descent (GD) vs Stochastic Gradient Descent (SGD) | Gradient Descent is an iterative method to solve the optimization problem. There is no concept of "epoch" or "batch" in classical gradient decent. The key of gradient decent are
Update the weights b | Gradient Descent (GD) vs Stochastic Gradient Descent (SGD)
Gradient Descent is an iterative method to solve the optimization problem. There is no concept of "epoch" or "batch" in classical gradient decent. The key of gradient decent are
Update the weights by the gradient direction.
The gradient is calculated precisel... | Gradient Descent (GD) vs Stochastic Gradient Descent (SGD)
Gradient Descent is an iterative method to solve the optimization problem. There is no concept of "epoch" or "batch" in classical gradient decent. The key of gradient decent are
Update the weights b |
40,261 | On Stationarity and Invertibility of a process | The confusion comes from the fact that these conditions (that you state under the label "can be easily proven") pertain to the $Y_t=\varepsilon_t-\theta_1\varepsilon_{t-1}-\theta_2\varepsilon_{t-2}$ formulation. In your case this means $\theta_1=1.3$, but $\theta_2=-0.4$ (not $0.4$!). Substituting these to the conditio... | On Stationarity and Invertibility of a process | The confusion comes from the fact that these conditions (that you state under the label "can be easily proven") pertain to the $Y_t=\varepsilon_t-\theta_1\varepsilon_{t-1}-\theta_2\varepsilon_{t-2}$ f | On Stationarity and Invertibility of a process
The confusion comes from the fact that these conditions (that you state under the label "can be easily proven") pertain to the $Y_t=\varepsilon_t-\theta_1\varepsilon_{t-1}-\theta_2\varepsilon_{t-2}$ formulation. In your case this means $\theta_1=1.3$, but $\theta_2=-0.4$ (... | On Stationarity and Invertibility of a process
The confusion comes from the fact that these conditions (that you state under the label "can be easily proven") pertain to the $Y_t=\varepsilon_t-\theta_1\varepsilon_{t-1}-\theta_2\varepsilon_{t-2}$ f |
40,262 | On Stationarity and Invertibility of a process | It's causal and stationary because the AR roots are outside the unit circle.
polyroot(c(1,-.5)) # 2+0i
It's invertible because the MA roots are outside the unit circle.
> polyroot(c(1,-1.3,.4)) #1.25-0i 2.00+0i
You got these already, so nice.
The other restrictions you're writing down must be equivalent to the above... | On Stationarity and Invertibility of a process | It's causal and stationary because the AR roots are outside the unit circle.
polyroot(c(1,-.5)) # 2+0i
It's invertible because the MA roots are outside the unit circle.
> polyroot(c(1,-1.3,.4)) #1.2 | On Stationarity and Invertibility of a process
It's causal and stationary because the AR roots are outside the unit circle.
polyroot(c(1,-.5)) # 2+0i
It's invertible because the MA roots are outside the unit circle.
> polyroot(c(1,-1.3,.4)) #1.25-0i 2.00+0i
You got these already, so nice.
The other restrictions you'... | On Stationarity and Invertibility of a process
It's causal and stationary because the AR roots are outside the unit circle.
polyroot(c(1,-.5)) # 2+0i
It's invertible because the MA roots are outside the unit circle.
> polyroot(c(1,-1.3,.4)) #1.2 |
40,263 | Empirical PDF from Empirical CDF | One of two things:
1) make fixed histogram bucket sizes and then count the number of points you get that occur in each bucket. In other words, break up the range of $x$ into n equal intervals, and then the count for each interval is the number of times your CDF has a 'step' up in that interval, for each interval. Cave... | Empirical PDF from Empirical CDF | One of two things:
1) make fixed histogram bucket sizes and then count the number of points you get that occur in each bucket. In other words, break up the range of $x$ into n equal intervals, and th | Empirical PDF from Empirical CDF
One of two things:
1) make fixed histogram bucket sizes and then count the number of points you get that occur in each bucket. In other words, break up the range of $x$ into n equal intervals, and then the count for each interval is the number of times your CDF has a 'step' up in that ... | Empirical PDF from Empirical CDF
One of two things:
1) make fixed histogram bucket sizes and then count the number of points you get that occur in each bucket. In other words, break up the range of $x$ into n equal intervals, and th |
40,264 | Empirical PDF from Empirical CDF | The empirical PDF of a random sample is a discrete probability distribution which assigns probability mass $1/N$ to each observation if there are no ties, 2 if there are 2 tied observations, 3 and so on. | Empirical PDF from Empirical CDF | The empirical PDF of a random sample is a discrete probability distribution which assigns probability mass $1/N$ to each observation if there are no ties, 2 if there are 2 tied observations, 3 and so | Empirical PDF from Empirical CDF
The empirical PDF of a random sample is a discrete probability distribution which assigns probability mass $1/N$ to each observation if there are no ties, 2 if there are 2 tied observations, 3 and so on. | Empirical PDF from Empirical CDF
The empirical PDF of a random sample is a discrete probability distribution which assigns probability mass $1/N$ to each observation if there are no ties, 2 if there are 2 tied observations, 3 and so |
40,265 | Variance of residuals vs. MLE of the variance of the error term | If $Y \sim \mathcal N(X\beta, \sigma^2 I)$ then the log likelihood is
$$
l(\beta, \sigma^2|y) = -\frac n2 \log (2\pi) - \frac n2 \log(\sigma^2) - \frac 1{2\sigma^2}||y-X\beta||^2
$$
and assuming non-stochastic and full rank predictors. From this we find that
$$
\frac{\partial l}{\partial \sigma^2} = 0 \implies \hat \si... | Variance of residuals vs. MLE of the variance of the error term | If $Y \sim \mathcal N(X\beta, \sigma^2 I)$ then the log likelihood is
$$
l(\beta, \sigma^2|y) = -\frac n2 \log (2\pi) - \frac n2 \log(\sigma^2) - \frac 1{2\sigma^2}||y-X\beta||^2
$$
and assuming non-s | Variance of residuals vs. MLE of the variance of the error term
If $Y \sim \mathcal N(X\beta, \sigma^2 I)$ then the log likelihood is
$$
l(\beta, \sigma^2|y) = -\frac n2 \log (2\pi) - \frac n2 \log(\sigma^2) - \frac 1{2\sigma^2}||y-X\beta||^2
$$
and assuming non-stochastic and full rank predictors. From this we find th... | Variance of residuals vs. MLE of the variance of the error term
If $Y \sim \mathcal N(X\beta, \sigma^2 I)$ then the log likelihood is
$$
l(\beta, \sigma^2|y) = -\frac n2 \log (2\pi) - \frac n2 \log(\sigma^2) - \frac 1{2\sigma^2}||y-X\beta||^2
$$
and assuming non-s |
40,266 | Faster R-CNN: How to avoid multiple detection in same area? | This is a common property of object detectors such as Faster R-CNN: They predict every object several times. It is the job of a Non-maximum suppression function to filter out the duplicates. Loosely explained, the NMS takes couples of overlapping boxes having equal class, and if their overlap is greater than some thres... | Faster R-CNN: How to avoid multiple detection in same area? | This is a common property of object detectors such as Faster R-CNN: They predict every object several times. It is the job of a Non-maximum suppression function to filter out the duplicates. Loosely e | Faster R-CNN: How to avoid multiple detection in same area?
This is a common property of object detectors such as Faster R-CNN: They predict every object several times. It is the job of a Non-maximum suppression function to filter out the duplicates. Loosely explained, the NMS takes couples of overlapping boxes having ... | Faster R-CNN: How to avoid multiple detection in same area?
This is a common property of object detectors such as Faster R-CNN: They predict every object several times. It is the job of a Non-maximum suppression function to filter out the duplicates. Loosely e |
40,267 | Faster R-CNN: How to avoid multiple detection in same area? | As mentioned before NMS is used to remove false positives.
Since you are using faster R-CNN, NMS is automatically set up at 0.7 in terms of the threshold.
Therefore, You can use OpenCV function cv2.dnn.NMSBoxes(boxes, confidences, confid, thresh)
You can dive into it deeper for any further information. | Faster R-CNN: How to avoid multiple detection in same area? | As mentioned before NMS is used to remove false positives.
Since you are using faster R-CNN, NMS is automatically set up at 0.7 in terms of the threshold.
Therefore, You can use OpenCV function cv2.dn | Faster R-CNN: How to avoid multiple detection in same area?
As mentioned before NMS is used to remove false positives.
Since you are using faster R-CNN, NMS is automatically set up at 0.7 in terms of the threshold.
Therefore, You can use OpenCV function cv2.dnn.NMSBoxes(boxes, confidences, confid, thresh)
You can dive ... | Faster R-CNN: How to avoid multiple detection in same area?
As mentioned before NMS is used to remove false positives.
Since you are using faster R-CNN, NMS is automatically set up at 0.7 in terms of the threshold.
Therefore, You can use OpenCV function cv2.dn |
40,268 | Clustering with Latent dirichlet allocation (LDA): Distance Measure | LDA does not have a distance metric
The intuition behind the LDA topic model is that words belonging to a topic appear together in documents. Unlike typical clustering algorithms like K-Means, it does not assume any distance measure between topics. Instead it infers topics purely based on word counts, based on the bag-... | Clustering with Latent dirichlet allocation (LDA): Distance Measure | LDA does not have a distance metric
The intuition behind the LDA topic model is that words belonging to a topic appear together in documents. Unlike typical clustering algorithms like K-Means, it does | Clustering with Latent dirichlet allocation (LDA): Distance Measure
LDA does not have a distance metric
The intuition behind the LDA topic model is that words belonging to a topic appear together in documents. Unlike typical clustering algorithms like K-Means, it does not assume any distance measure between topics. Ins... | Clustering with Latent dirichlet allocation (LDA): Distance Measure
LDA does not have a distance metric
The intuition behind the LDA topic model is that words belonging to a topic appear together in documents. Unlike typical clustering algorithms like K-Means, it does |
40,269 | Can we think of a Random Variable as an instantiation of its distribution? | Yes it is a value, but no it doesn't necessarily have to be realized. A random variable can be realized or unrealized. Just as a house can be built or unfinished. The analogy is meant to emphasize that a random variable can be thought of as the value, while a distribution is a function that describe the probability of ... | Can we think of a Random Variable as an instantiation of its distribution? | Yes it is a value, but no it doesn't necessarily have to be realized. A random variable can be realized or unrealized. Just as a house can be built or unfinished. The analogy is meant to emphasize tha | Can we think of a Random Variable as an instantiation of its distribution?
Yes it is a value, but no it doesn't necessarily have to be realized. A random variable can be realized or unrealized. Just as a house can be built or unfinished. The analogy is meant to emphasize that a random variable can be thought of as the ... | Can we think of a Random Variable as an instantiation of its distribution?
Yes it is a value, but no it doesn't necessarily have to be realized. A random variable can be realized or unrealized. Just as a house can be built or unfinished. The analogy is meant to emphasize tha |
40,270 | Can we think of a Random Variable as an instantiation of its distribution? | I'm going through the course, too. The Aha moment came with the distinction that a random variable is a function. Blitzstein isn't the only one who says this, but it was the first time I finally got it.
An r.v. is not an algebraic variable. In fact, it even makes sense if you make up privately, for didactic purposes on... | Can we think of a Random Variable as an instantiation of its distribution? | I'm going through the course, too. The Aha moment came with the distinction that a random variable is a function. Blitzstein isn't the only one who says this, but it was the first time I finally got i | Can we think of a Random Variable as an instantiation of its distribution?
I'm going through the course, too. The Aha moment came with the distinction that a random variable is a function. Blitzstein isn't the only one who says this, but it was the first time I finally got it.
An r.v. is not an algebraic variable. In f... | Can we think of a Random Variable as an instantiation of its distribution?
I'm going through the course, too. The Aha moment came with the distinction that a random variable is a function. Blitzstein isn't the only one who says this, but it was the first time I finally got i |
40,271 | Can we think of a Random Variable as an instantiation of its distribution? | Yes you can --- this is both technically feasible and it can also aid intuition
Intuition: Probabilistic intuition is best when it is built on an epistemic foundation that views probability as a belief based on available information. For this reason, it is generally a bad idea to try to build up intuition by thinking... | Can we think of a Random Variable as an instantiation of its distribution? | Yes you can --- this is both technically feasible and it can also aid intuition
Intuition: Probabilistic intuition is best when it is built on an epistemic foundation that views probability as a beli | Can we think of a Random Variable as an instantiation of its distribution?
Yes you can --- this is both technically feasible and it can also aid intuition
Intuition: Probabilistic intuition is best when it is built on an epistemic foundation that views probability as a belief based on available information. For this ... | Can we think of a Random Variable as an instantiation of its distribution?
Yes you can --- this is both technically feasible and it can also aid intuition
Intuition: Probabilistic intuition is best when it is built on an epistemic foundation that views probability as a beli |
40,272 | Can we think of a Random Variable as an instantiation of its distribution? | One intuitive distribution is the Bernoulli distribution. It describes the outcome of throwing a coin, which lands head with probability $p$ and tails with prob. $q=1-p$.
If you throw the coin once, you will observe either head or tail. However, this outcome is the random variable, it is not the distribution. The dis... | Can we think of a Random Variable as an instantiation of its distribution? | One intuitive distribution is the Bernoulli distribution. It describes the outcome of throwing a coin, which lands head with probability $p$ and tails with prob. $q=1-p$.
If you throw the coin once, | Can we think of a Random Variable as an instantiation of its distribution?
One intuitive distribution is the Bernoulli distribution. It describes the outcome of throwing a coin, which lands head with probability $p$ and tails with prob. $q=1-p$.
If you throw the coin once, you will observe either head or tail. Howeve... | Can we think of a Random Variable as an instantiation of its distribution?
One intuitive distribution is the Bernoulli distribution. It describes the outcome of throwing a coin, which lands head with probability $p$ and tails with prob. $q=1-p$.
If you throw the coin once, |
40,273 | Can we think of a Random Variable as an instantiation of its distribution? | No. In lose sense a random sample can be seen as some sort of instantiation of the random variable. However, the RV itself is not an instance of its distribution in any meaningful context. The distribution function doesn't have an instance. | Can we think of a Random Variable as an instantiation of its distribution? | No. In lose sense a random sample can be seen as some sort of instantiation of the random variable. However, the RV itself is not an instance of its distribution in any meaningful context. The distrib | Can we think of a Random Variable as an instantiation of its distribution?
No. In lose sense a random sample can be seen as some sort of instantiation of the random variable. However, the RV itself is not an instance of its distribution in any meaningful context. The distribution function doesn't have an instance. | Can we think of a Random Variable as an instantiation of its distribution?
No. In lose sense a random sample can be seen as some sort of instantiation of the random variable. However, the RV itself is not an instance of its distribution in any meaningful context. The distrib |
40,274 | L1 (MAE) vs L2 (MSE) when data is normalized between 0 and 1 | Scaling does not change relations between the values, because when scaling you divide all the values by the same constant. Outliers will stay outliers. If there is a big difference between two values $x_1,x_2$ squared and smaller difference between $x_1,x_3$ squared, then after normalizing the values, the differences b... | L1 (MAE) vs L2 (MSE) when data is normalized between 0 and 1 | Scaling does not change relations between the values, because when scaling you divide all the values by the same constant. Outliers will stay outliers. If there is a big difference between two values | L1 (MAE) vs L2 (MSE) when data is normalized between 0 and 1
Scaling does not change relations between the values, because when scaling you divide all the values by the same constant. Outliers will stay outliers. If there is a big difference between two values $x_1,x_2$ squared and smaller difference between $x_1,x_3$ ... | L1 (MAE) vs L2 (MSE) when data is normalized between 0 and 1
Scaling does not change relations between the values, because when scaling you divide all the values by the same constant. Outliers will stay outliers. If there is a big difference between two values |
40,275 | What is the backpropagation formula for Selu activation function? | Ok, let's try it myself. For the backward pass we get:
$$
\frac{\partial E}{\partial Y}\frac{\partial Y}{\partial X} = λ, x>0
$$
$$
\frac{\partial E}{\partial Y}\frac{\partial Y}{\partial X} = λ * a * e ^x , x=<0
$$
with $ λ=1.0507, a=1.6733$ | What is the backpropagation formula for Selu activation function? | Ok, let's try it myself. For the backward pass we get:
$$
\frac{\partial E}{\partial Y}\frac{\partial Y}{\partial X} = λ, x>0
$$
$$
\frac{\partial E}{\partial Y}\frac{\partial Y}{\partial X} = λ * a * | What is the backpropagation formula for Selu activation function?
Ok, let's try it myself. For the backward pass we get:
$$
\frac{\partial E}{\partial Y}\frac{\partial Y}{\partial X} = λ, x>0
$$
$$
\frac{\partial E}{\partial Y}\frac{\partial Y}{\partial X} = λ * a * e ^x , x=<0
$$
with $ λ=1.0507, a=1.6733$ | What is the backpropagation formula for Selu activation function?
Ok, let's try it myself. For the backward pass we get:
$$
\frac{\partial E}{\partial Y}\frac{\partial Y}{\partial X} = λ, x>0
$$
$$
\frac{\partial E}{\partial Y}\frac{\partial Y}{\partial X} = λ * a * |
40,276 | What is the backpropagation formula for Selu activation function? | The derivative (d) of the Selu function can be found from both the input (x) into and the output (y) from the Selu function.
To find derivative from the input:
$$
d = seluDerivative(x) =
\begin{cases}
\lambda & \text{if } x > 0\\
\lambda\alpha e^x & \text{if } x \leqslant 0\\
\end{cases}
$$
The problem with using this ... | What is the backpropagation formula for Selu activation function? | The derivative (d) of the Selu function can be found from both the input (x) into and the output (y) from the Selu function.
To find derivative from the input:
$$
d = seluDerivative(x) =
\begin{cases} | What is the backpropagation formula for Selu activation function?
The derivative (d) of the Selu function can be found from both the input (x) into and the output (y) from the Selu function.
To find derivative from the input:
$$
d = seluDerivative(x) =
\begin{cases}
\lambda & \text{if } x > 0\\
\lambda\alpha e^x & \tex... | What is the backpropagation formula for Selu activation function?
The derivative (d) of the Selu function can be found from both the input (x) into and the output (y) from the Selu function.
To find derivative from the input:
$$
d = seluDerivative(x) =
\begin{cases} |
40,277 | Forward-backward model selection: What is the starting model? | I believe "forward-backward" selection is another name for "forward-stepwise" selection. This is the default approach used by stepAIC. In this procedure, you start with an empty model and build up sequentially just like in forward selection. The only caveat is that every time you add a new variable, $X_{new}$, you have... | Forward-backward model selection: What is the starting model? | I believe "forward-backward" selection is another name for "forward-stepwise" selection. This is the default approach used by stepAIC. In this procedure, you start with an empty model and build up seq | Forward-backward model selection: What is the starting model?
I believe "forward-backward" selection is another name for "forward-stepwise" selection. This is the default approach used by stepAIC. In this procedure, you start with an empty model and build up sequentially just like in forward selection. The only caveat ... | Forward-backward model selection: What is the starting model?
I believe "forward-backward" selection is another name for "forward-stepwise" selection. This is the default approach used by stepAIC. In this procedure, you start with an empty model and build up seq |
40,278 | Forward-backward model selection: What is the starting model? | Forward-backward model selection are two greedy approaches to solve the combinatorial optimization problem of finding the optimal combination of features (which is known to be NP-complete). Hence, you need to look for suboptimal, computationally efficient strategies. See for example Floating search methods in feature s... | Forward-backward model selection: What is the starting model? | Forward-backward model selection are two greedy approaches to solve the combinatorial optimization problem of finding the optimal combination of features (which is known to be NP-complete). Hence, you | Forward-backward model selection: What is the starting model?
Forward-backward model selection are two greedy approaches to solve the combinatorial optimization problem of finding the optimal combination of features (which is known to be NP-complete). Hence, you need to look for suboptimal, computationally efficient st... | Forward-backward model selection: What is the starting model?
Forward-backward model selection are two greedy approaches to solve the combinatorial optimization problem of finding the optimal combination of features (which is known to be NP-complete). Hence, you |
40,279 | How to select hyperparameters for SVM regression after grid search? | Though I haven't fully understood the problem, I am answering as per my understanding of the question.
Have you tried including Epsilon in param_grid Dictionary of Grid_searchCV.
I see you have only used the C and gamma as the parameters in param_grid dict.
Then i think the system would itself pick the best Epsilon fo... | How to select hyperparameters for SVM regression after grid search? | Though I haven't fully understood the problem, I am answering as per my understanding of the question.
Have you tried including Epsilon in param_grid Dictionary of Grid_searchCV.
I see you have only | How to select hyperparameters for SVM regression after grid search?
Though I haven't fully understood the problem, I am answering as per my understanding of the question.
Have you tried including Epsilon in param_grid Dictionary of Grid_searchCV.
I see you have only used the C and gamma as the parameters in param_grid... | How to select hyperparameters for SVM regression after grid search?
Though I haven't fully understood the problem, I am answering as per my understanding of the question.
Have you tried including Epsilon in param_grid Dictionary of Grid_searchCV.
I see you have only |
40,280 | Is there a counterexample to the claim that throwing away "insignificant" predictors doesn't generally harm a model? | I think your question(s) have four answers in total:
1) Will dropping non-significant predictors increase the root-mean-square error? Yes, virtually always, in the same way and for the same reason that it will always increase the R-squared: a model will only ever use a predictor to improve its predictions (or, rather, ... | Is there a counterexample to the claim that throwing away "insignificant" predictors doesn't general | I think your question(s) have four answers in total:
1) Will dropping non-significant predictors increase the root-mean-square error? Yes, virtually always, in the same way and for the same reason tha | Is there a counterexample to the claim that throwing away "insignificant" predictors doesn't generally harm a model?
I think your question(s) have four answers in total:
1) Will dropping non-significant predictors increase the root-mean-square error? Yes, virtually always, in the same way and for the same reason that i... | Is there a counterexample to the claim that throwing away "insignificant" predictors doesn't general
I think your question(s) have four answers in total:
1) Will dropping non-significant predictors increase the root-mean-square error? Yes, virtually always, in the same way and for the same reason tha |
40,281 | What's the receptive field of a stack of dilated convolutions? | I think it should be 1024*3.
After the first block, the indices of the receptive fields of the outputs should be 1-1024, 2-1025, 3-1026, etc. (assuming no padding, but receptive field size should be same with padding anyways).
When you make the second block with a receptive field size of 1024, the first output of that ... | What's the receptive field of a stack of dilated convolutions? | I think it should be 1024*3.
After the first block, the indices of the receptive fields of the outputs should be 1-1024, 2-1025, 3-1026, etc. (assuming no padding, but receptive field size should be s | What's the receptive field of a stack of dilated convolutions?
I think it should be 1024*3.
After the first block, the indices of the receptive fields of the outputs should be 1-1024, 2-1025, 3-1026, etc. (assuming no padding, but receptive field size should be same with padding anyways).
When you make the second block... | What's the receptive field of a stack of dilated convolutions?
I think it should be 1024*3.
After the first block, the indices of the receptive fields of the outputs should be 1-1024, 2-1025, 3-1026, etc. (assuming no padding, but receptive field size should be s |
40,282 | What's the receptive field of a stack of dilated convolutions? | I created a script (github gist) that uses the equation above and plots the receptive field for a pixel on a 2D image.
The same can be understood for 1D signals.
Some examples | What's the receptive field of a stack of dilated convolutions? | I created a script (github gist) that uses the equation above and plots the receptive field for a pixel on a 2D image.
The same can be understood for 1D signals.
Some examples | What's the receptive field of a stack of dilated convolutions?
I created a script (github gist) that uses the equation above and plots the receptive field for a pixel on a 2D image.
The same can be understood for 1D signals.
Some examples | What's the receptive field of a stack of dilated convolutions?
I created a script (github gist) that uses the equation above and plots the receptive field for a pixel on a 2D image.
The same can be understood for 1D signals.
Some examples |
40,283 | Use loess regression with many zero values | A Loess confidence interval doesn't mean much unless the Loess parameters have been cross-validated (which usually is not the case). When you use Loess for exploration, as it was originally intended, understanding how to control it will help you guide your exploration and interpret its results better.
Consider this s... | Use loess regression with many zero values | A Loess confidence interval doesn't mean much unless the Loess parameters have been cross-validated (which usually is not the case). When you use Loess for exploration, as it was originally intended, | Use loess regression with many zero values
A Loess confidence interval doesn't mean much unless the Loess parameters have been cross-validated (which usually is not the case). When you use Loess for exploration, as it was originally intended, understanding how to control it will help you guide your exploration and int... | Use loess regression with many zero values
A Loess confidence interval doesn't mean much unless the Loess parameters have been cross-validated (which usually is not the case). When you use Loess for exploration, as it was originally intended, |
40,284 | Do I have to add the seasonal effect and trend back to ARIMA forecast? | No, you do not need to remove trend and/or seasonality before fitting an ARIMA model.
These models can handle certain types of trends and certain types of seasonality by themselves, or by including external regressors (the xreg argument, where you could include more complicated related effects like moving holidays, or... | Do I have to add the seasonal effect and trend back to ARIMA forecast? | No, you do not need to remove trend and/or seasonality before fitting an ARIMA model.
These models can handle certain types of trends and certain types of seasonality by themselves, or by including e | Do I have to add the seasonal effect and trend back to ARIMA forecast?
No, you do not need to remove trend and/or seasonality before fitting an ARIMA model.
These models can handle certain types of trends and certain types of seasonality by themselves, or by including external regressors (the xreg argument, where you ... | Do I have to add the seasonal effect and trend back to ARIMA forecast?
No, you do not need to remove trend and/or seasonality before fitting an ARIMA model.
These models can handle certain types of trends and certain types of seasonality by themselves, or by including e |
40,285 | What does one mean by ARCH effect? | If the squared residuals/errors of your time series model exhibit autocorrelation, then ARCH effects are present.
A quick google search offers a clear definition:
A time series exhibiting conditional heteroscedasticity—or autocorrelation in the squared series—is said to have autoregressive conditional heteroscedastic... | What does one mean by ARCH effect? | If the squared residuals/errors of your time series model exhibit autocorrelation, then ARCH effects are present.
A quick google search offers a clear definition:
A time series exhibiting conditiona | What does one mean by ARCH effect?
If the squared residuals/errors of your time series model exhibit autocorrelation, then ARCH effects are present.
A quick google search offers a clear definition:
A time series exhibiting conditional heteroscedasticity—or autocorrelation in the squared series—is said to have autoreg... | What does one mean by ARCH effect?
If the squared residuals/errors of your time series model exhibit autocorrelation, then ARCH effects are present.
A quick google search offers a clear definition:
A time series exhibiting conditiona |
40,286 | What does one mean by ARCH effect? | I think that by ARCH effect they mean the correlation between volatility of a time series, measured by conditional variance, and its values or innovations in the past. The letter AR stands for auto regressive, C for conditional (i.e conditional variance), and H for heteroskedasticity. So if non-constant conditional var... | What does one mean by ARCH effect? | I think that by ARCH effect they mean the correlation between volatility of a time series, measured by conditional variance, and its values or innovations in the past. The letter AR stands for auto re | What does one mean by ARCH effect?
I think that by ARCH effect they mean the correlation between volatility of a time series, measured by conditional variance, and its values or innovations in the past. The letter AR stands for auto regressive, C for conditional (i.e conditional variance), and H for heteroskedasticity.... | What does one mean by ARCH effect?
I think that by ARCH effect they mean the correlation between volatility of a time series, measured by conditional variance, and its values or innovations in the past. The letter AR stands for auto re |
40,287 | What is Sequential MNIST, Permuted MNIST? | As in comment by @Batman, sequential MNIST is explained in section 4.3 of your link: https://arxiv.org/abs/1610.09038.
We evaluated Professor Forcing on the task of sequentially generating the pixels in MNIST digits.
As far as I am aware, sequential MNIST always implies the model does not get to see/generate the whol... | What is Sequential MNIST, Permuted MNIST? | As in comment by @Batman, sequential MNIST is explained in section 4.3 of your link: https://arxiv.org/abs/1610.09038.
We evaluated Professor Forcing on the task of sequentially generating the pixels | What is Sequential MNIST, Permuted MNIST?
As in comment by @Batman, sequential MNIST is explained in section 4.3 of your link: https://arxiv.org/abs/1610.09038.
We evaluated Professor Forcing on the task of sequentially generating the pixels in MNIST digits.
As far as I am aware, sequential MNIST always implies the m... | What is Sequential MNIST, Permuted MNIST?
As in comment by @Batman, sequential MNIST is explained in section 4.3 of your link: https://arxiv.org/abs/1610.09038.
We evaluated Professor Forcing on the task of sequentially generating the pixels |
40,288 | What is Sequential MNIST, Permuted MNIST? | Permutated Sequential MNIST is introduced in the "A Simple Way to Initialize Recurrent Networks of Rectified Linear Units" paper from 2015 which has Hinton as a co-author.
Sequential MNIST: "classify the MNIST digits [21] when the 784 pixels
are presented sequentially to the recurrent net"
Permutated Sequential MNIST: ... | What is Sequential MNIST, Permuted MNIST? | Permutated Sequential MNIST is introduced in the "A Simple Way to Initialize Recurrent Networks of Rectified Linear Units" paper from 2015 which has Hinton as a co-author.
Sequential MNIST: "classify | What is Sequential MNIST, Permuted MNIST?
Permutated Sequential MNIST is introduced in the "A Simple Way to Initialize Recurrent Networks of Rectified Linear Units" paper from 2015 which has Hinton as a co-author.
Sequential MNIST: "classify the MNIST digits [21] when the 784 pixels
are presented sequentially to the re... | What is Sequential MNIST, Permuted MNIST?
Permutated Sequential MNIST is introduced in the "A Simple Way to Initialize Recurrent Networks of Rectified Linear Units" paper from 2015 which has Hinton as a co-author.
Sequential MNIST: "classify |
40,289 | How can I calculate the AICc if the number of samples equals the number of parameters plus one | The case $n = k + 1$ corresponds to a saturated model,
$$
\# \textrm{parameters} = \# \textrm{observations}
$$
which is why you are seeing effectively an "infinite" penalisation.
One of the contexts in which Akaike's Information Criterion along with a host of others were developed, and is used frequently today, is lin... | How can I calculate the AICc if the number of samples equals the number of parameters plus one | The case $n = k + 1$ corresponds to a saturated model,
$$
\# \textrm{parameters} = \# \textrm{observations}
$$
which is why you are seeing effectively an "infinite" penalisation.
One of the contexts | How can I calculate the AICc if the number of samples equals the number of parameters plus one
The case $n = k + 1$ corresponds to a saturated model,
$$
\# \textrm{parameters} = \# \textrm{observations}
$$
which is why you are seeing effectively an "infinite" penalisation.
One of the contexts in which Akaike's Informa... | How can I calculate the AICc if the number of samples equals the number of parameters plus one
The case $n = k + 1$ corresponds to a saturated model,
$$
\# \textrm{parameters} = \# \textrm{observations}
$$
which is why you are seeing effectively an "infinite" penalisation.
One of the contexts |
40,290 | Comparing t-SNE solutions using their Kullback-Leibler divergences | Unfortunately, no; comparing the optimality of a perplexity parameter through the correspond $KL(P||Q)$ divergence is not a valid approach. As I explained in this question: "The perplexity parameter increases monotonically with the variance of the Gaussian used to calculate the distances/probabilities $P$. Therefore as... | Comparing t-SNE solutions using their Kullback-Leibler divergences | Unfortunately, no; comparing the optimality of a perplexity parameter through the correspond $KL(P||Q)$ divergence is not a valid approach. As I explained in this question: "The perplexity parameter i | Comparing t-SNE solutions using their Kullback-Leibler divergences
Unfortunately, no; comparing the optimality of a perplexity parameter through the correspond $KL(P||Q)$ divergence is not a valid approach. As I explained in this question: "The perplexity parameter increases monotonically with the variance of the Gauss... | Comparing t-SNE solutions using their Kullback-Leibler divergences
Unfortunately, no; comparing the optimality of a perplexity parameter through the correspond $KL(P||Q)$ divergence is not a valid approach. As I explained in this question: "The perplexity parameter i |
40,291 | Finding variance of AR process | $$\text{Var}(y_t)=\text{Var}(\phi y_{t-1}) + \text{Var}(\varepsilon_{t}).$$
As we know, $E(\varepsilon_{t}^2)=\sigma^2$. Then we have:
$$\text{Var}(y_t)=\text{Var}(\phi y_{t-1}) + \sigma^2.$$
Now using variance properties we take out $\phi$ from the variance:
$$\text{Var}(y_t)=\phi^2\text{Var}(y_{t-1}) + \sigma^2.$... | Finding variance of AR process | $$\text{Var}(y_t)=\text{Var}(\phi y_{t-1}) + \text{Var}(\varepsilon_{t}).$$
As we know, $E(\varepsilon_{t}^2)=\sigma^2$. Then we have:
$$\text{Var}(y_t)=\text{Var}(\phi y_{t-1}) + \sigma^2.$$
Now u | Finding variance of AR process
$$\text{Var}(y_t)=\text{Var}(\phi y_{t-1}) + \text{Var}(\varepsilon_{t}).$$
As we know, $E(\varepsilon_{t}^2)=\sigma^2$. Then we have:
$$\text{Var}(y_t)=\text{Var}(\phi y_{t-1}) + \sigma^2.$$
Now using variance properties we take out $\phi$ from the variance:
$$\text{Var}(y_t)=\phi^2\... | Finding variance of AR process
$$\text{Var}(y_t)=\text{Var}(\phi y_{t-1}) + \text{Var}(\varepsilon_{t}).$$
As we know, $E(\varepsilon_{t}^2)=\sigma^2$. Then we have:
$$\text{Var}(y_t)=\text{Var}(\phi y_{t-1}) + \sigma^2.$$
Now u |
40,292 | Finding variance of AR process | $$y_t = \varepsilon_{t} +\phi y_{t-1}= \varepsilon_{t} +\phi (\varepsilon_{t-1} +\phi y_{t-2}) = \sum_{j=0}^{\infty}\phi^j \varepsilon_{t-j},$$ and If $|\phi|<1$, then $$\text{Var}(y_t) = \sum_{j=0}^{\infty}(\phi^j)^2 \text{Var}(\varepsilon_{t-j})=\sigma^2 (1+\phi^2+\phi^4+\dots) = \sigma^2\frac{1-\lim_{n \rightarrow ... | Finding variance of AR process | $$y_t = \varepsilon_{t} +\phi y_{t-1}= \varepsilon_{t} +\phi (\varepsilon_{t-1} +\phi y_{t-2}) = \sum_{j=0}^{\infty}\phi^j \varepsilon_{t-j},$$ and If $|\phi|<1$, then $$\text{Var}(y_t) = \sum_{j=0}^ | Finding variance of AR process
$$y_t = \varepsilon_{t} +\phi y_{t-1}= \varepsilon_{t} +\phi (\varepsilon_{t-1} +\phi y_{t-2}) = \sum_{j=0}^{\infty}\phi^j \varepsilon_{t-j},$$ and If $|\phi|<1$, then $$\text{Var}(y_t) = \sum_{j=0}^{\infty}(\phi^j)^2 \text{Var}(\varepsilon_{t-j})=\sigma^2 (1+\phi^2+\phi^4+\dots) = \sigm... | Finding variance of AR process
$$y_t = \varepsilon_{t} +\phi y_{t-1}= \varepsilon_{t} +\phi (\varepsilon_{t-1} +\phi y_{t-2}) = \sum_{j=0}^{\infty}\phi^j \varepsilon_{t-j},$$ and If $|\phi|<1$, then $$\text{Var}(y_t) = \sum_{j=0}^ |
40,293 | Constructing features from k-means | There is a great paper relating k-means with sparse coding of features, and how to address some of its weaknesses to produce good features. Even through it is focused on the particular case of image processing, it has valuable advice for the general case (how to do prewhitening to decorrelate data and so on).
Finally, ... | Constructing features from k-means | There is a great paper relating k-means with sparse coding of features, and how to address some of its weaknesses to produce good features. Even through it is focused on the particular case of image p | Constructing features from k-means
There is a great paper relating k-means with sparse coding of features, and how to address some of its weaknesses to produce good features. Even through it is focused on the particular case of image processing, it has valuable advice for the general case (how to do prewhitening to dec... | Constructing features from k-means
There is a great paper relating k-means with sparse coding of features, and how to address some of its weaknesses to produce good features. Even through it is focused on the particular case of image p |
40,294 | Constructing features from k-means | Basically there is no you must add this or this.....you actually should add features that verifiable improve your classification.
You can be creative here and try several things.
E.g. you can create statistics for variables (mean, sd,...) for each cluster and add these. You can also then add the difference to this new... | Constructing features from k-means | Basically there is no you must add this or this.....you actually should add features that verifiable improve your classification.
You can be creative here and try several things.
E.g. you can create | Constructing features from k-means
Basically there is no you must add this or this.....you actually should add features that verifiable improve your classification.
You can be creative here and try several things.
E.g. you can create statistics for variables (mean, sd,...) for each cluster and add these. You can also ... | Constructing features from k-means
Basically there is no you must add this or this.....you actually should add features that verifiable improve your classification.
You can be creative here and try several things.
E.g. you can create |
40,295 | K-Means Cluster has over 50% of the points in one cluster. How to optimize it? | This is very typical behavior of k-means when applies to non-continuous data. It's not what k-means is designed for, you are essentially operating it out of its specifications. Also, k-means is very sensitive to noise. You probably have a lot of one-element clusters, too?
Also Spark is one of the worst tools for cluste... | K-Means Cluster has over 50% of the points in one cluster. How to optimize it? | This is very typical behavior of k-means when applies to non-continuous data. It's not what k-means is designed for, you are essentially operating it out of its specifications. Also, k-means is very s | K-Means Cluster has over 50% of the points in one cluster. How to optimize it?
This is very typical behavior of k-means when applies to non-continuous data. It's not what k-means is designed for, you are essentially operating it out of its specifications. Also, k-means is very sensitive to noise. You probably have a lo... | K-Means Cluster has over 50% of the points in one cluster. How to optimize it?
This is very typical behavior of k-means when applies to non-continuous data. It's not what k-means is designed for, you are essentially operating it out of its specifications. Also, k-means is very s |
40,296 | K-Means Cluster has over 50% of the points in one cluster. How to optimize it? | I am using K means clustering on the "words" matrix from an SVD of a Tf Idf matrix and got similar results. I found the sum of the squares of the features for this large cluster and found they were all low magnitude words.
Also similar to your situation, I got a lot of 1 word clusters. To combat this, I only chose d... | K-Means Cluster has over 50% of the points in one cluster. How to optimize it? | I am using K means clustering on the "words" matrix from an SVD of a Tf Idf matrix and got similar results. I found the sum of the squares of the features for this large cluster and found they were a | K-Means Cluster has over 50% of the points in one cluster. How to optimize it?
I am using K means clustering on the "words" matrix from an SVD of a Tf Idf matrix and got similar results. I found the sum of the squares of the features for this large cluster and found they were all low magnitude words.
Also similar to ... | K-Means Cluster has over 50% of the points in one cluster. How to optimize it?
I am using K means clustering on the "words" matrix from an SVD of a Tf Idf matrix and got similar results. I found the sum of the squares of the features for this large cluster and found they were a |
40,297 | K-Means Cluster has over 50% of the points in one cluster. How to optimize it? | It's very interesting that you are getting a giant cluster with 400k entries using bisecting k-means.
Bisecting k-means iteratively breaks down the cluster with the highest dissimilarity into smaller clusters. Since you are already producing 100+ clusters, it seems to me that maybe the 400k entry cluster has a very hig... | K-Means Cluster has over 50% of the points in one cluster. How to optimize it? | It's very interesting that you are getting a giant cluster with 400k entries using bisecting k-means.
Bisecting k-means iteratively breaks down the cluster with the highest dissimilarity into smaller | K-Means Cluster has over 50% of the points in one cluster. How to optimize it?
It's very interesting that you are getting a giant cluster with 400k entries using bisecting k-means.
Bisecting k-means iteratively breaks down the cluster with the highest dissimilarity into smaller clusters. Since you are already producing... | K-Means Cluster has over 50% of the points in one cluster. How to optimize it?
It's very interesting that you are getting a giant cluster with 400k entries using bisecting k-means.
Bisecting k-means iteratively breaks down the cluster with the highest dissimilarity into smaller |
40,298 | K-Means Cluster has over 50% of the points in one cluster. How to optimize it? | When you say "optimise the clustering", I take this to mean that you wish to divide your clusters in an efficient manner.
Before running k-means or bisecting k-means, it is advisable to run a principal component analysis (PCA) on your data. The PCA generates a scree plot of the Number of Clusters and the Within Groups ... | K-Means Cluster has over 50% of the points in one cluster. How to optimize it? | When you say "optimise the clustering", I take this to mean that you wish to divide your clusters in an efficient manner.
Before running k-means or bisecting k-means, it is advisable to run a principa | K-Means Cluster has over 50% of the points in one cluster. How to optimize it?
When you say "optimise the clustering", I take this to mean that you wish to divide your clusters in an efficient manner.
Before running k-means or bisecting k-means, it is advisable to run a principal component analysis (PCA) on your data. ... | K-Means Cluster has over 50% of the points in one cluster. How to optimize it?
When you say "optimise the clustering", I take this to mean that you wish to divide your clusters in an efficient manner.
Before running k-means or bisecting k-means, it is advisable to run a principa |
40,299 | K-Means Cluster has over 50% of the points in one cluster. How to optimize it? | In several situations like this, I found it helpful to cluster the big cluster into subclusters. It doesn't make sense every time, but if your data has a lot of separate little islands, your K probably will never be enough to cover the biggest "island".
Another approach would be dropping the smallest centroids with the... | K-Means Cluster has over 50% of the points in one cluster. How to optimize it? | In several situations like this, I found it helpful to cluster the big cluster into subclusters. It doesn't make sense every time, but if your data has a lot of separate little islands, your K probabl | K-Means Cluster has over 50% of the points in one cluster. How to optimize it?
In several situations like this, I found it helpful to cluster the big cluster into subclusters. It doesn't make sense every time, but if your data has a lot of separate little islands, your K probably will never be enough to cover the bigge... | K-Means Cluster has over 50% of the points in one cluster. How to optimize it?
In several situations like this, I found it helpful to cluster the big cluster into subclusters. It doesn't make sense every time, but if your data has a lot of separate little islands, your K probabl |
40,300 | How to get the confidence interval of a Bernoulli trial if $\hat{p} = 0$? | The reason the usual "CLT" confidence interval becomes 0 is because when $p$ is very close to 0 or 1 (and the relative number of samples is low), the CLT becomes a bad approximation. This is because when $p=0,1$, your random variable is constant. On the other hand, when $p$ is very close to 1 or 0, you need a very larg... | How to get the confidence interval of a Bernoulli trial if $\hat{p} = 0$? | The reason the usual "CLT" confidence interval becomes 0 is because when $p$ is very close to 0 or 1 (and the relative number of samples is low), the CLT becomes a bad approximation. This is because w | How to get the confidence interval of a Bernoulli trial if $\hat{p} = 0$?
The reason the usual "CLT" confidence interval becomes 0 is because when $p$ is very close to 0 or 1 (and the relative number of samples is low), the CLT becomes a bad approximation. This is because when $p=0,1$, your random variable is constant.... | How to get the confidence interval of a Bernoulli trial if $\hat{p} = 0$?
The reason the usual "CLT" confidence interval becomes 0 is because when $p$ is very close to 0 or 1 (and the relative number of samples is low), the CLT becomes a bad approximation. This is because w |
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