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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42,001 | What is the motivation for the entropy term in the proof of EM algorithm? | A bit late to add my contribution. I think there is another (longer) scheme to demonstrate the EM algorithm that uses the KL divergence. What is sure is that the Jensen inequality is also used in that scheme.
The EM algorithm seeks to maximize a lower bound of a likelihood.
Let $Y=(Y_1, ..., Y_n)$ be the set of possibl... | What is the motivation for the entropy term in the proof of EM algorithm? | A bit late to add my contribution. I think there is another (longer) scheme to demonstrate the EM algorithm that uses the KL divergence. What is sure is that the Jensen inequality is also used in that | What is the motivation for the entropy term in the proof of EM algorithm?
A bit late to add my contribution. I think there is another (longer) scheme to demonstrate the EM algorithm that uses the KL divergence. What is sure is that the Jensen inequality is also used in that scheme.
The EM algorithm seeks to maximize a ... | What is the motivation for the entropy term in the proof of EM algorithm?
A bit late to add my contribution. I think there is another (longer) scheme to demonstrate the EM algorithm that uses the KL divergence. What is sure is that the Jensen inequality is also used in that |
42,002 | Understanding of the specification of the Johansen Cointegration test in R | The lag selection for cointegration test is the same as selecting lags for VAR model, since cointegration is a actually a special feature of VAR model. Use VARselect to choose number of lags.
The two statistics test the same thing and are constructed from the same eigenvalues of a certain matrix. For practical purposes... | Understanding of the specification of the Johansen Cointegration test in R | The lag selection for cointegration test is the same as selecting lags for VAR model, since cointegration is a actually a special feature of VAR model. Use VARselect to choose number of lags.
The two | Understanding of the specification of the Johansen Cointegration test in R
The lag selection for cointegration test is the same as selecting lags for VAR model, since cointegration is a actually a special feature of VAR model. Use VARselect to choose number of lags.
The two statistics test the same thing and are constr... | Understanding of the specification of the Johansen Cointegration test in R
The lag selection for cointegration test is the same as selecting lags for VAR model, since cointegration is a actually a special feature of VAR model. Use VARselect to choose number of lags.
The two |
42,003 | Can I fit logistic regression over a dataset with only categorical data? | Yes of course you can. Just be aware of the nature of your categorical data - is it ordered or unordered?
If ordered (e.g. small, medium, large) you might want a single feature X1 with values like (1, 1, 3, 2, 3, 1, ...) where 1 represents small, 2 represents medium, etc.
If unordered (e.g. red, blue, green) you'll wan... | Can I fit logistic regression over a dataset with only categorical data? | Yes of course you can. Just be aware of the nature of your categorical data - is it ordered or unordered?
If ordered (e.g. small, medium, large) you might want a single feature X1 with values like (1, | Can I fit logistic regression over a dataset with only categorical data?
Yes of course you can. Just be aware of the nature of your categorical data - is it ordered or unordered?
If ordered (e.g. small, medium, large) you might want a single feature X1 with values like (1, 1, 3, 2, 3, 1, ...) where 1 represents small, ... | Can I fit logistic regression over a dataset with only categorical data?
Yes of course you can. Just be aware of the nature of your categorical data - is it ordered or unordered?
If ordered (e.g. small, medium, large) you might want a single feature X1 with values like (1, |
42,004 | Can I fit logistic regression over a dataset with only categorical data? | Yes, this is doable.
The (potentially) unseen pitfall is that your model may require a great deal more data than you expect. A general rule of thumb for logistic regression is that you need at least $15$ observations in the less commonly occurring category (i.e., either $0$s or $1$s) for each variable in the model (... | Can I fit logistic regression over a dataset with only categorical data? | Yes, this is doable.
The (potentially) unseen pitfall is that your model may require a great deal more data than you expect. A general rule of thumb for logistic regression is that you need at leas | Can I fit logistic regression over a dataset with only categorical data?
Yes, this is doable.
The (potentially) unseen pitfall is that your model may require a great deal more data than you expect. A general rule of thumb for logistic regression is that you need at least $15$ observations in the less commonly occurr... | Can I fit logistic regression over a dataset with only categorical data?
Yes, this is doable.
The (potentially) unseen pitfall is that your model may require a great deal more data than you expect. A general rule of thumb for logistic regression is that you need at leas |
42,005 | Can I fit logistic regression over a dataset with only categorical data? | Of course it is possible.
You just need to transform your categorical variables into binary variables and to remove each time one item. For instance, if the variable X takes two values A and B, you need to create the variable which is equal to 1 if X == A and to 0 otherwise. Since X == A implies X != B, you'll have a ... | Can I fit logistic regression over a dataset with only categorical data? | Of course it is possible.
You just need to transform your categorical variables into binary variables and to remove each time one item. For instance, if the variable X takes two values A and B, you n | Can I fit logistic regression over a dataset with only categorical data?
Of course it is possible.
You just need to transform your categorical variables into binary variables and to remove each time one item. For instance, if the variable X takes two values A and B, you need to create the variable which is equal to 1 ... | Can I fit logistic regression over a dataset with only categorical data?
Of course it is possible.
You just need to transform your categorical variables into binary variables and to remove each time one item. For instance, if the variable X takes two values A and B, you n |
42,006 | Exponential family form of multinomial distribution | Exponential families are characterised by their densities, which are such that the interaction between the outcome $x$ of the random variable and the parameter $\theta$ occurs in an exponential scalar product,
$$\exp\{T(\theta)^\text{T} S(x)\}$$
The other terms in the density are the normalising constant $C(\theta)=\e... | Exponential family form of multinomial distribution | Exponential families are characterised by their densities, which are such that the interaction between the outcome $x$ of the random variable and the parameter $\theta$ occurs in an exponential scalar | Exponential family form of multinomial distribution
Exponential families are characterised by their densities, which are such that the interaction between the outcome $x$ of the random variable and the parameter $\theta$ occurs in an exponential scalar product,
$$\exp\{T(\theta)^\text{T} S(x)\}$$
The other terms in th... | Exponential family form of multinomial distribution
Exponential families are characterised by their densities, which are such that the interaction between the outcome $x$ of the random variable and the parameter $\theta$ occurs in an exponential scalar |
42,007 | Exponential family form of multinomial distribution | I was trying to build the softmax regression from scratch, and got stuck here also: why all the posts just silently omit the coefficient $\frac{n!}{x_1! x_2! \dots x_k!}$ totally, after some research and thinking i share my understanding here:
In reality, we always use a special form of the multinomial distribution wit... | Exponential family form of multinomial distribution | I was trying to build the softmax regression from scratch, and got stuck here also: why all the posts just silently omit the coefficient $\frac{n!}{x_1! x_2! \dots x_k!}$ totally, after some research | Exponential family form of multinomial distribution
I was trying to build the softmax regression from scratch, and got stuck here also: why all the posts just silently omit the coefficient $\frac{n!}{x_1! x_2! \dots x_k!}$ totally, after some research and thinking i share my understanding here:
In reality, we always us... | Exponential family form of multinomial distribution
I was trying to build the softmax regression from scratch, and got stuck here also: why all the posts just silently omit the coefficient $\frac{n!}{x_1! x_2! \dots x_k!}$ totally, after some research |
42,008 | Exponential family form of multinomial distribution | Let
$Y_{i}$ be a random variable, $i=1\dots k$.
$n\in \mathbb{N}$ be the number of trials.
$y_{i}\in \mathbb{N}$ be the number of $i$-th events in a sequence of $n$ trials.
$p_{i}\in [0,1]$ be the probability of the $i$-th event of each trial.
The probability mass function of multinomial distribution is
$\begin{equat... | Exponential family form of multinomial distribution | Let
$Y_{i}$ be a random variable, $i=1\dots k$.
$n\in \mathbb{N}$ be the number of trials.
$y_{i}\in \mathbb{N}$ be the number of $i$-th events in a sequence of $n$ trials.
$p_{i}\in [0,1]$ be the pr | Exponential family form of multinomial distribution
Let
$Y_{i}$ be a random variable, $i=1\dots k$.
$n\in \mathbb{N}$ be the number of trials.
$y_{i}\in \mathbb{N}$ be the number of $i$-th events in a sequence of $n$ trials.
$p_{i}\in [0,1]$ be the probability of the $i$-th event of each trial.
The probability mass f... | Exponential family form of multinomial distribution
Let
$Y_{i}$ be a random variable, $i=1\dots k$.
$n\in \mathbb{N}$ be the number of trials.
$y_{i}\in \mathbb{N}$ be the number of $i$-th events in a sequence of $n$ trials.
$p_{i}\in [0,1]$ be the pr |
42,009 | Feature importance for random forest classification of a sample | Variable importance accounts for the increase in out-of-bag cross-validated prediction error. It would be possible but not meaningful to account for the change of prediction error by one sample only. As one sample only can be correctly or wrongly predicted, such a term would be very unstable and crude.
You could check ... | Feature importance for random forest classification of a sample | Variable importance accounts for the increase in out-of-bag cross-validated prediction error. It would be possible but not meaningful to account for the change of prediction error by one sample only. | Feature importance for random forest classification of a sample
Variable importance accounts for the increase in out-of-bag cross-validated prediction error. It would be possible but not meaningful to account for the change of prediction error by one sample only. As one sample only can be correctly or wrongly predicted... | Feature importance for random forest classification of a sample
Variable importance accounts for the increase in out-of-bag cross-validated prediction error. It would be possible but not meaningful to account for the change of prediction error by one sample only. |
42,010 | Comparing & clustering time series with unequal lengths | It just happened that few days ago I read Marco Cuturi's paper on "Fast Global Alignment Kernels" [1]. The idea is to cast the well-known DTW distances as similarities eligible for use in kernel machines, e.g. SVM. You cannot directly transform DTW distance into similarity and hope it will work (e.g. negative exponenti... | Comparing & clustering time series with unequal lengths | It just happened that few days ago I read Marco Cuturi's paper on "Fast Global Alignment Kernels" [1]. The idea is to cast the well-known DTW distances as similarities eligible for use in kernel machi | Comparing & clustering time series with unequal lengths
It just happened that few days ago I read Marco Cuturi's paper on "Fast Global Alignment Kernels" [1]. The idea is to cast the well-known DTW distances as similarities eligible for use in kernel machines, e.g. SVM. You cannot directly transform DTW distance into s... | Comparing & clustering time series with unequal lengths
It just happened that few days ago I read Marco Cuturi's paper on "Fast Global Alignment Kernels" [1]. The idea is to cast the well-known DTW distances as similarities eligible for use in kernel machi |
42,011 | Comparing & clustering time series with unequal lengths | You can simply extend what I responded in How to statistically compare two time series? to more than two series . Essentially identify a common model and estimate the parameters both globally and locally. Perform an F test and either accept or reject the hypothesis of common parameters. Another post gives a similar vie... | Comparing & clustering time series with unequal lengths | You can simply extend what I responded in How to statistically compare two time series? to more than two series . Essentially identify a common model and estimate the parameters both globally and loca | Comparing & clustering time series with unequal lengths
You can simply extend what I responded in How to statistically compare two time series? to more than two series . Essentially identify a common model and estimate the parameters both globally and locally. Perform an F test and either accept or reject the hypothesi... | Comparing & clustering time series with unequal lengths
You can simply extend what I responded in How to statistically compare two time series? to more than two series . Essentially identify a common model and estimate the parameters both globally and loca |
42,012 | Reporting the Actual Formula/Equation of an LME model (with factors) used in R? | Your second formulation,
$$ y_{imj} = \beta_0 + \sum\beta_{1m}[year]_{im} + b_{0j}[building.id]_j + \epsilon_{imj},
$$
is correct. Depending on your audience, it might be slightly clearer to use the slightly more general mixed model notation and write this as
$$
\begin{split}
y_i & \sim N(\eta_i,\sigma^2) \\
\eta_{imj... | Reporting the Actual Formula/Equation of an LME model (with factors) used in R? | Your second formulation,
$$ y_{imj} = \beta_0 + \sum\beta_{1m}[year]_{im} + b_{0j}[building.id]_j + \epsilon_{imj},
$$
is correct. Depending on your audience, it might be slightly clearer to use the | Reporting the Actual Formula/Equation of an LME model (with factors) used in R?
Your second formulation,
$$ y_{imj} = \beta_0 + \sum\beta_{1m}[year]_{im} + b_{0j}[building.id]_j + \epsilon_{imj},
$$
is correct. Depending on your audience, it might be slightly clearer to use the slightly more general mixed model notati... | Reporting the Actual Formula/Equation of an LME model (with factors) used in R?
Your second formulation,
$$ y_{imj} = \beta_0 + \sum\beta_{1m}[year]_{im} + b_{0j}[building.id]_j + \epsilon_{imj},
$$
is correct. Depending on your audience, it might be slightly clearer to use the |
42,013 | regression analysis with confounding variables, how to interpret your main coefficient when controlling for confounders | One purpose of regression is to control for the effects of covariates. This question is predicated on the (correct) understanding that this purpose should not be confused with testing the significance of those covariates.
In a linear multiple regression model
$$\mathbb{E}(y) = \alpha + \beta_1 x_1 + \cdots + \beta_k ... | regression analysis with confounding variables, how to interpret your main coefficient when controll | One purpose of regression is to control for the effects of covariates. This question is predicated on the (correct) understanding that this purpose should not be confused with testing the significanc | regression analysis with confounding variables, how to interpret your main coefficient when controlling for confounders
One purpose of regression is to control for the effects of covariates. This question is predicated on the (correct) understanding that this purpose should not be confused with testing the significanc... | regression analysis with confounding variables, how to interpret your main coefficient when controll
One purpose of regression is to control for the effects of covariates. This question is predicated on the (correct) understanding that this purpose should not be confused with testing the significanc |
42,014 | regression analysis with confounding variables, how to interpret your main coefficient when controlling for confounders | Null hypothesis under the Overall F-test is the following:
H0: β1 = β2 = ... = βm= 0
Ha: At least one of the slope parameters is not equal to 0.
Looking at the alternative hypothesis (Ha), I doubt you can say anything about individual coefficients once you fail to reject the Null.
Having said that, failing to rejec... | regression analysis with confounding variables, how to interpret your main coefficient when controll | Null hypothesis under the Overall F-test is the following:
H0: β1 = β2 = ... = βm= 0
Ha: At least one of the slope parameters is not equal to 0.
Looking at the alternative hypothesis (Ha), I doubt | regression analysis with confounding variables, how to interpret your main coefficient when controlling for confounders
Null hypothesis under the Overall F-test is the following:
H0: β1 = β2 = ... = βm= 0
Ha: At least one of the slope parameters is not equal to 0.
Looking at the alternative hypothesis (Ha), I doubt... | regression analysis with confounding variables, how to interpret your main coefficient when controll
Null hypothesis under the Overall F-test is the following:
H0: β1 = β2 = ... = βm= 0
Ha: At least one of the slope parameters is not equal to 0.
Looking at the alternative hypothesis (Ha), I doubt |
42,015 | How sum of squares is calculated by R ANOVA function fo non-factor variables in linear model | One method (the easiest to grasp in one sentence) is to look at the increment in sums of squares due to regression when a covariate is added. This is R's ANOVA (or AOV) strategy, which implies that the order of addition of variables is important:
> anova( lm(mpg ~ cyl, mtcars))
Analysis of Variance Table
Response: mpg... | How sum of squares is calculated by R ANOVA function fo non-factor variables in linear model | One method (the easiest to grasp in one sentence) is to look at the increment in sums of squares due to regression when a covariate is added. This is R's ANOVA (or AOV) strategy, which implies that th | How sum of squares is calculated by R ANOVA function fo non-factor variables in linear model
One method (the easiest to grasp in one sentence) is to look at the increment in sums of squares due to regression when a covariate is added. This is R's ANOVA (or AOV) strategy, which implies that the order of addition of vari... | How sum of squares is calculated by R ANOVA function fo non-factor variables in linear model
One method (the easiest to grasp in one sentence) is to look at the increment in sums of squares due to regression when a covariate is added. This is R's ANOVA (or AOV) strategy, which implies that th |
42,016 | Hypothesis test based on entropy | A fantastic reference that I have been using for self study on this topic is Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach by Kenneth Burnham. In brief, a hypothesis test compares a test statistic, $T$, calculated from the data on hand (assumed to be from some distribution, usuall... | Hypothesis test based on entropy | A fantastic reference that I have been using for self study on this topic is Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach by Kenneth Burnham. In brief, a hypoth | Hypothesis test based on entropy
A fantastic reference that I have been using for self study on this topic is Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach by Kenneth Burnham. In brief, a hypothesis test compares a test statistic, $T$, calculated from the data on hand (assumed to ... | Hypothesis test based on entropy
A fantastic reference that I have been using for self study on this topic is Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach by Kenneth Burnham. In brief, a hypoth |
42,017 | Hypothesis test based on entropy | To test for the significance of the difference between two entropy values, compute the maximum possible entropy, Log2N, then take the ratio with the actual entropy. The Z-test for proportions is an appropriate test. | Hypothesis test based on entropy | To test for the significance of the difference between two entropy values, compute the maximum possible entropy, Log2N, then take the ratio with the actual entropy. The Z-test for proportions is an ap | Hypothesis test based on entropy
To test for the significance of the difference between two entropy values, compute the maximum possible entropy, Log2N, then take the ratio with the actual entropy. The Z-test for proportions is an appropriate test. | Hypothesis test based on entropy
To test for the significance of the difference between two entropy values, compute the maximum possible entropy, Log2N, then take the ratio with the actual entropy. The Z-test for proportions is an ap |
42,018 | GARCH vs SV for Forecasting | This is more like an extended comment than an answer as the answer really depends on the data series at hand.
1)
For the purpose of probabilistic forecasting of financial and
macro-economic time series: Is it known whether one class of model has
a tendency to perform better than the other in general?
There are ... | GARCH vs SV for Forecasting | This is more like an extended comment than an answer as the answer really depends on the data series at hand.
1)
For the purpose of probabilistic forecasting of financial and
macro-economic time | GARCH vs SV for Forecasting
This is more like an extended comment than an answer as the answer really depends on the data series at hand.
1)
For the purpose of probabilistic forecasting of financial and
macro-economic time series: Is it known whether one class of model has
a tendency to perform better than the o... | GARCH vs SV for Forecasting
This is more like an extended comment than an answer as the answer really depends on the data series at hand.
1)
For the purpose of probabilistic forecasting of financial and
macro-economic time |
42,019 | VGAM fitting a betabinomial model | The binomial distribution is the distribution of the number of 'successes' out of a known, finite number of 'trials' (e.g., heads on a certain number of coin flips). With a fixed probability of success, $\pi$, and a fixed number of trials, $n$, the variance of the number of successes is fixed as well. A typical logis... | VGAM fitting a betabinomial model | The binomial distribution is the distribution of the number of 'successes' out of a known, finite number of 'trials' (e.g., heads on a certain number of coin flips). With a fixed probability of succe | VGAM fitting a betabinomial model
The binomial distribution is the distribution of the number of 'successes' out of a known, finite number of 'trials' (e.g., heads on a certain number of coin flips). With a fixed probability of success, $\pi$, and a fixed number of trials, $n$, the variance of the number of successes ... | VGAM fitting a betabinomial model
The binomial distribution is the distribution of the number of 'successes' out of a known, finite number of 'trials' (e.g., heads on a certain number of coin flips). With a fixed probability of succe |
42,020 | Variable importance in party vs randomForest | The two importances agree for a and c actually. There is a good tutorial about variable importance here. These are some of the guys who worked in cforest.
Also, I think the values are different in absolute value because if you check the documentation of the randomForest package it says:
importance(x, type=NULL, class=N... | Variable importance in party vs randomForest | The two importances agree for a and c actually. There is a good tutorial about variable importance here. These are some of the guys who worked in cforest.
Also, I think the values are different in abs | Variable importance in party vs randomForest
The two importances agree for a and c actually. There is a good tutorial about variable importance here. These are some of the guys who worked in cforest.
Also, I think the values are different in absolute value because if you check the documentation of the randomForest pack... | Variable importance in party vs randomForest
The two importances agree for a and c actually. There is a good tutorial about variable importance here. These are some of the guys who worked in cforest.
Also, I think the values are different in abs |
42,021 | Variable importance in party vs randomForest | Traditional Random Forest uses "Gini Gain" splitting criterion in assessing Variable Importance, which is biased towards factor variables with many levels/categories. In contract, cforest function creates random forests not from CART trees, but from unbiased classification trees based on conditional inference, which gi... | Variable importance in party vs randomForest | Traditional Random Forest uses "Gini Gain" splitting criterion in assessing Variable Importance, which is biased towards factor variables with many levels/categories. In contract, cforest function cre | Variable importance in party vs randomForest
Traditional Random Forest uses "Gini Gain" splitting criterion in assessing Variable Importance, which is biased towards factor variables with many levels/categories. In contract, cforest function creates random forests not from CART trees, but from unbiased classification t... | Variable importance in party vs randomForest
Traditional Random Forest uses "Gini Gain" splitting criterion in assessing Variable Importance, which is biased towards factor variables with many levels/categories. In contract, cforest function cre |
42,022 | How to build a confidence interval with only binary test results? | Interesting question. Your data is Bernoulli which is a binary distribution with probability of sucess equal to $p$. The simplest thing you can do is compute the probability of success from your sample and use the Central Limit Theorem to arrive at an asymptotic 95% confidence interval. If we denote the sample proporti... | How to build a confidence interval with only binary test results? | Interesting question. Your data is Bernoulli which is a binary distribution with probability of sucess equal to $p$. The simplest thing you can do is compute the probability of success from your sampl | How to build a confidence interval with only binary test results?
Interesting question. Your data is Bernoulli which is a binary distribution with probability of sucess equal to $p$. The simplest thing you can do is compute the probability of success from your sample and use the Central Limit Theorem to arrive at an as... | How to build a confidence interval with only binary test results?
Interesting question. Your data is Bernoulli which is a binary distribution with probability of sucess equal to $p$. The simplest thing you can do is compute the probability of success from your sampl |
42,023 | On the sample complexity of mean estimation in $\ell_p$-norm | A closely related topic is that of concentration inequalities, which give you a bound (of the sort that you are looking for) which also depends on the number of samples (among other things).
Concretely, the concept of Rademacher complexity is a standard tool to address this sort of problems. The Rademacher complexity c... | On the sample complexity of mean estimation in $\ell_p$-norm | A closely related topic is that of concentration inequalities, which give you a bound (of the sort that you are looking for) which also depends on the number of samples (among other things).
Concretel | On the sample complexity of mean estimation in $\ell_p$-norm
A closely related topic is that of concentration inequalities, which give you a bound (of the sort that you are looking for) which also depends on the number of samples (among other things).
Concretely, the concept of Rademacher complexity is a standard tool ... | On the sample complexity of mean estimation in $\ell_p$-norm
A closely related topic is that of concentration inequalities, which give you a bound (of the sort that you are looking for) which also depends on the number of samples (among other things).
Concretel |
42,024 | On the sample complexity of mean estimation in $\ell_p$-norm | Let me follow up on this question and answer.
Indeed, the connection to Rademacher complexity of the linear functions from the dual body can be used to provide upper bounds for the problem. But this is not quite what Cristobal and myself are asking about.
(Not to mention that the question we ask is even more fundament... | On the sample complexity of mean estimation in $\ell_p$-norm | Let me follow up on this question and answer.
Indeed, the connection to Rademacher complexity of the linear functions from the dual body can be used to provide upper bounds for the problem. But this i | On the sample complexity of mean estimation in $\ell_p$-norm
Let me follow up on this question and answer.
Indeed, the connection to Rademacher complexity of the linear functions from the dual body can be used to provide upper bounds for the problem. But this is not quite what Cristobal and myself are asking about.
(N... | On the sample complexity of mean estimation in $\ell_p$-norm
Let me follow up on this question and answer.
Indeed, the connection to Rademacher complexity of the linear functions from the dual body can be used to provide upper bounds for the problem. But this i |
42,025 | On the sample complexity of mean estimation in $\ell_p$-norm | Thanks everybody for the answers. Rademacher complexity is in fact a useful tool to derive upper bounds. However, the sample complexity can also depend on the geometry of the convex body we are interested in. In this regard, one can use ideas of uniform smoothness and uniform convexity from Banach space theory to get t... | On the sample complexity of mean estimation in $\ell_p$-norm | Thanks everybody for the answers. Rademacher complexity is in fact a useful tool to derive upper bounds. However, the sample complexity can also depend on the geometry of the convex body we are intere | On the sample complexity of mean estimation in $\ell_p$-norm
Thanks everybody for the answers. Rademacher complexity is in fact a useful tool to derive upper bounds. However, the sample complexity can also depend on the geometry of the convex body we are interested in. In this regard, one can use ideas of uniform smoot... | On the sample complexity of mean estimation in $\ell_p$-norm
Thanks everybody for the answers. Rademacher complexity is in fact a useful tool to derive upper bounds. However, the sample complexity can also depend on the geometry of the convex body we are intere |
42,026 | Interpretation of Saturated Model vs. Model with Interaction and One Main Effect | Throughout my answer, the usual conditional mean independence
$\mathbb{E}(\varepsilon_{i}\vert X_{i},Z_{i})=0$ is maintained.
It is instructive to consider a concrete
example. Let $X_{i}$ be a dummy of college education, such that $X_{i}=1$
if worker $i$ is a college graduate, and $X_{i}=0$ otherwise; and let $Z_{i}$
b... | Interpretation of Saturated Model vs. Model with Interaction and One Main Effect | Throughout my answer, the usual conditional mean independence
$\mathbb{E}(\varepsilon_{i}\vert X_{i},Z_{i})=0$ is maintained.
It is instructive to consider a concrete
example. Let $X_{i}$ be a dummy o | Interpretation of Saturated Model vs. Model with Interaction and One Main Effect
Throughout my answer, the usual conditional mean independence
$\mathbb{E}(\varepsilon_{i}\vert X_{i},Z_{i})=0$ is maintained.
It is instructive to consider a concrete
example. Let $X_{i}$ be a dummy of college education, such that $X_{i}=1... | Interpretation of Saturated Model vs. Model with Interaction and One Main Effect
Throughout my answer, the usual conditional mean independence
$\mathbb{E}(\varepsilon_{i}\vert X_{i},Z_{i})=0$ is maintained.
It is instructive to consider a concrete
example. Let $X_{i}$ be a dummy o |
42,027 | Why is the Hessian of the log likelihood function in the logit model not negative *semi*definite? | When they say the Hessian is always negative definite, they are assuming that $X$ is a full rank matrix, which is a very typical assumption for regression models.
So it is true that in your example, the Hessian would not be negative definite. However, they assume that you have informative data: you can't expect to est... | Why is the Hessian of the log likelihood function in the logit model not negative *semi*definite? | When they say the Hessian is always negative definite, they are assuming that $X$ is a full rank matrix, which is a very typical assumption for regression models.
So it is true that in your example, | Why is the Hessian of the log likelihood function in the logit model not negative *semi*definite?
When they say the Hessian is always negative definite, they are assuming that $X$ is a full rank matrix, which is a very typical assumption for regression models.
So it is true that in your example, the Hessian would not ... | Why is the Hessian of the log likelihood function in the logit model not negative *semi*definite?
When they say the Hessian is always negative definite, they are assuming that $X$ is a full rank matrix, which is a very typical assumption for regression models.
So it is true that in your example, |
42,028 | R: how to interpret mosaic and association plots | In the mosaic plot you see that the first split is wrt gender with about 2/3 female and about 1/3 male. The second split is wrt to alcohol (conditional on gender) showing that only about 1/6 of females drink alcohol while it is about 3/4 of the males. The final split is wrt to cigarettes (conditional on gender and alco... | R: how to interpret mosaic and association plots | In the mosaic plot you see that the first split is wrt gender with about 2/3 female and about 1/3 male. The second split is wrt to alcohol (conditional on gender) showing that only about 1/6 of female | R: how to interpret mosaic and association plots
In the mosaic plot you see that the first split is wrt gender with about 2/3 female and about 1/3 male. The second split is wrt to alcohol (conditional on gender) showing that only about 1/6 of females drink alcohol while it is about 3/4 of the males. The final split is ... | R: how to interpret mosaic and association plots
In the mosaic plot you see that the first split is wrt gender with about 2/3 female and about 1/3 male. The second split is wrt to alcohol (conditional on gender) showing that only about 1/6 of female |
42,029 | R: how to interpret mosaic and association plots | For reporting, I think following statement may be right:
Association of smoking and alcohol intake in males was found to be
statistically most significant finding. | R: how to interpret mosaic and association plots | For reporting, I think following statement may be right:
Association of smoking and alcohol intake in males was found to be
statistically most significant finding. | R: how to interpret mosaic and association plots
For reporting, I think following statement may be right:
Association of smoking and alcohol intake in males was found to be
statistically most significant finding. | R: how to interpret mosaic and association plots
For reporting, I think following statement may be right:
Association of smoking and alcohol intake in males was found to be
statistically most significant finding. |
42,030 | How to Balance my Dataset? | You can oversample your minority class examples by simply duplicating them, or you can use the SMOTE algorithm (DMwR package in R, function SMOTE), that generates synthetic minority class examples while downsampling the majority category at the same time. Since you have a pretty high number of cases, downsampling shoul... | How to Balance my Dataset? | You can oversample your minority class examples by simply duplicating them, or you can use the SMOTE algorithm (DMwR package in R, function SMOTE), that generates synthetic minority class examples whi | How to Balance my Dataset?
You can oversample your minority class examples by simply duplicating them, or you can use the SMOTE algorithm (DMwR package in R, function SMOTE), that generates synthetic minority class examples while downsampling the majority category at the same time. Since you have a pretty high number o... | How to Balance my Dataset?
You can oversample your minority class examples by simply duplicating them, or you can use the SMOTE algorithm (DMwR package in R, function SMOTE), that generates synthetic minority class examples whi |
42,031 | How to Balance my Dataset? | You failed to tell us about your classification approach and your dataset characteristics. If you are using any other method that takes ages, to train and tune, I would recommend using cost sensitive learning. Oversampling burdens the training without adding much in return, tough it is very simple. Undersampling on the... | How to Balance my Dataset? | You failed to tell us about your classification approach and your dataset characteristics. If you are using any other method that takes ages, to train and tune, I would recommend using cost sensitive | How to Balance my Dataset?
You failed to tell us about your classification approach and your dataset characteristics. If you are using any other method that takes ages, to train and tune, I would recommend using cost sensitive learning. Oversampling burdens the training without adding much in return, tough it is very s... | How to Balance my Dataset?
You failed to tell us about your classification approach and your dataset characteristics. If you are using any other method that takes ages, to train and tune, I would recommend using cost sensitive |
42,032 | R-squared value when using offset -- how is it calculated? | $R^2$ is computed in terms of the sum of squares of fitted values $\text{MSS}=\sum (\hat{y}_i - \bar y_i)^2$ (assuming an intercept term is present) and sum of squares of residuals $\text{RSS} = \sum \left(y_i - \hat{y}_i\right)^2$ as
$$R^2 = \frac{\text{MSS}}{\text{MSS} + \text{RSS}}:$$
it is the fraction of the total... | R-squared value when using offset -- how is it calculated? | $R^2$ is computed in terms of the sum of squares of fitted values $\text{MSS}=\sum (\hat{y}_i - \bar y_i)^2$ (assuming an intercept term is present) and sum of squares of residuals $\text{RSS} = \sum | R-squared value when using offset -- how is it calculated?
$R^2$ is computed in terms of the sum of squares of fitted values $\text{MSS}=\sum (\hat{y}_i - \bar y_i)^2$ (assuming an intercept term is present) and sum of squares of residuals $\text{RSS} = \sum \left(y_i - \hat{y}_i\right)^2$ as
$$R^2 = \frac{\text{MSS}}{... | R-squared value when using offset -- how is it calculated?
$R^2$ is computed in terms of the sum of squares of fitted values $\text{MSS}=\sum (\hat{y}_i - \bar y_i)^2$ (assuming an intercept term is present) and sum of squares of residuals $\text{RSS} = \sum |
42,033 | Comparing and visualising highly skewed distributions | Note that your gamma data are not at zero, they are near zero, so you can work with logarithms. If your actual data do contain zeros and you only used skewed gammas to create an example here, you could shift your data by a small $\epsilon$ to make them positive and then take logs.
set.seed(1)
gamma1 <- rgamma(10000, sh... | Comparing and visualising highly skewed distributions | Note that your gamma data are not at zero, they are near zero, so you can work with logarithms. If your actual data do contain zeros and you only used skewed gammas to create an example here, you coul | Comparing and visualising highly skewed distributions
Note that your gamma data are not at zero, they are near zero, so you can work with logarithms. If your actual data do contain zeros and you only used skewed gammas to create an example here, you could shift your data by a small $\epsilon$ to make them positive and ... | Comparing and visualising highly skewed distributions
Note that your gamma data are not at zero, they are near zero, so you can work with logarithms. If your actual data do contain zeros and you only used skewed gammas to create an example here, you coul |
42,034 | What are the mean and variance of the ratio of two normal variables, with non-zero means? | Since, as pointed by Alexander Chervov, the mean of $1/X$ does not exist when $X\sim\mathcal{N}(\mu,\sigma^2)$, the mean of $Y/X$, which, were it to exist, would be equal to the mean of $Y$ times the mean of $1/X$ does not exist either. Since the mean does not exist, the variance does not exist either.
To make the abov... | What are the mean and variance of the ratio of two normal variables, with non-zero means? | Since, as pointed by Alexander Chervov, the mean of $1/X$ does not exist when $X\sim\mathcal{N}(\mu,\sigma^2)$, the mean of $Y/X$, which, were it to exist, would be equal to the mean of $Y$ times the | What are the mean and variance of the ratio of two normal variables, with non-zero means?
Since, as pointed by Alexander Chervov, the mean of $1/X$ does not exist when $X\sim\mathcal{N}(\mu,\sigma^2)$, the mean of $Y/X$, which, were it to exist, would be equal to the mean of $Y$ times the mean of $1/X$ does not exist e... | What are the mean and variance of the ratio of two normal variables, with non-zero means?
Since, as pointed by Alexander Chervov, the mean of $1/X$ does not exist when $X\sim\mathcal{N}(\mu,\sigma^2)$, the mean of $Y/X$, which, were it to exist, would be equal to the mean of $Y$ times the |
42,035 | OLS with ordinal dependent variable - do the coefficients mean anything? | Interpretive issues for the OLS estimator notwithstanding, the real issue here is in the treatment of an ordinal variable as if it were a variable on the ratio scale. By using standard linear regression analysis, the researchers are essentially treating the ordinal response as if it were a continuous quantity. By ave... | OLS with ordinal dependent variable - do the coefficients mean anything? | Interpretive issues for the OLS estimator notwithstanding, the real issue here is in the treatment of an ordinal variable as if it were a variable on the ratio scale. By using standard linear regress | OLS with ordinal dependent variable - do the coefficients mean anything?
Interpretive issues for the OLS estimator notwithstanding, the real issue here is in the treatment of an ordinal variable as if it were a variable on the ratio scale. By using standard linear regression analysis, the researchers are essentially t... | OLS with ordinal dependent variable - do the coefficients mean anything?
Interpretive issues for the OLS estimator notwithstanding, the real issue here is in the treatment of an ordinal variable as if it were a variable on the ratio scale. By using standard linear regress |
42,036 | OLS with ordinal dependent variable - do the coefficients mean anything? | Q1: The OLS is consistent and unbiased by standard theory. There are assumptions for this, but these don't seem more problematic for the outcome variables you have here than for "standard" applications of linear regression. These assumptions in particular do not say anything about how the quantitative outcome variable ... | OLS with ordinal dependent variable - do the coefficients mean anything? | Q1: The OLS is consistent and unbiased by standard theory. There are assumptions for this, but these don't seem more problematic for the outcome variables you have here than for "standard" application | OLS with ordinal dependent variable - do the coefficients mean anything?
Q1: The OLS is consistent and unbiased by standard theory. There are assumptions for this, but these don't seem more problematic for the outcome variables you have here than for "standard" applications of linear regression. These assumptions in pa... | OLS with ordinal dependent variable - do the coefficients mean anything?
Q1: The OLS is consistent and unbiased by standard theory. There are assumptions for this, but these don't seem more problematic for the outcome variables you have here than for "standard" application |
42,037 | Has there been a project to apply machine learning to generation of indices for books? | To add on to the answer by @denis-tarasov, I would refer you to this amazing article by the Guardian.
Take a look at this passage:
One of the things that’s commonly imagined is that indexing is, in the age of Google, something that can be outsourced to a computer algorithm. Dead wrong. A concordance – essentially, an ... | Has there been a project to apply machine learning to generation of indices for books? | To add on to the answer by @denis-tarasov, I would refer you to this amazing article by the Guardian.
Take a look at this passage:
One of the things that’s commonly imagined is that indexing is, in t | Has there been a project to apply machine learning to generation of indices for books?
To add on to the answer by @denis-tarasov, I would refer you to this amazing article by the Guardian.
Take a look at this passage:
One of the things that’s commonly imagined is that indexing is, in the age of Google, something that ... | Has there been a project to apply machine learning to generation of indices for books?
To add on to the answer by @denis-tarasov, I would refer you to this amazing article by the Guardian.
Take a look at this passage:
One of the things that’s commonly imagined is that indexing is, in t |
42,038 | Has there been a project to apply machine learning to generation of indices for books? | I think this problem is very similar to keywords/keyphrases extraction problem. Keywords extraction is well studied task (see for example this paper for review). Possible approaches include heuristics, supervised machine learning (with a number of special feautures like TD/IDF, position in the sentence and other) and ... | Has there been a project to apply machine learning to generation of indices for books? | I think this problem is very similar to keywords/keyphrases extraction problem. Keywords extraction is well studied task (see for example this paper for review). Possible approaches include heuristic | Has there been a project to apply machine learning to generation of indices for books?
I think this problem is very similar to keywords/keyphrases extraction problem. Keywords extraction is well studied task (see for example this paper for review). Possible approaches include heuristics, supervised machine learning (w... | Has there been a project to apply machine learning to generation of indices for books?
I think this problem is very similar to keywords/keyphrases extraction problem. Keywords extraction is well studied task (see for example this paper for review). Possible approaches include heuristic |
42,039 | Translate glmer (lme4) model specification into MCMCglmm | According to MCMCglmm documentation: "Multiple random terms can be passed using the + operator" (as you already do). Having said that you appear to be defining multiple random intercepts and no random slopes.
In general you need to use a syntax similar to ~us(1+x1):x2, where x2 is your discrete variables (for the inte... | Translate glmer (lme4) model specification into MCMCglmm | According to MCMCglmm documentation: "Multiple random terms can be passed using the + operator" (as you already do). Having said that you appear to be defining multiple random intercepts and no random | Translate glmer (lme4) model specification into MCMCglmm
According to MCMCglmm documentation: "Multiple random terms can be passed using the + operator" (as you already do). Having said that you appear to be defining multiple random intercepts and no random slopes.
In general you need to use a syntax similar to ~us(1+... | Translate glmer (lme4) model specification into MCMCglmm
According to MCMCglmm documentation: "Multiple random terms can be passed using the + operator" (as you already do). Having said that you appear to be defining multiple random intercepts and no random |
42,040 | Translate glmer (lme4) model specification into MCMCglmm | To my understanding, MCMCglmm poisson models include an observation-level random effect by default, as the author seems to believe that over-dispersion is the regular case, not the exception. In the manual it is called additive over-dispersion. In MCMCglmm summaries it is called the unit effect | Translate glmer (lme4) model specification into MCMCglmm | To my understanding, MCMCglmm poisson models include an observation-level random effect by default, as the author seems to believe that over-dispersion is the regular case, not the exception. In the m | Translate glmer (lme4) model specification into MCMCglmm
To my understanding, MCMCglmm poisson models include an observation-level random effect by default, as the author seems to believe that over-dispersion is the regular case, not the exception. In the manual it is called additive over-dispersion. In MCMCglmm summar... | Translate glmer (lme4) model specification into MCMCglmm
To my understanding, MCMCglmm poisson models include an observation-level random effect by default, as the author seems to believe that over-dispersion is the regular case, not the exception. In the m |
42,041 | Parameters in a non-parametric model | Nonparametric methods don't specify something (maybe the distribution, maybe a relationship between two variables*) with a fixed finite number of parameters; they're (potentially) infinite parametric.
Consider a loess curve (a form of nonparametric regression), for example; the parameters not only aren't explicit, if y... | Parameters in a non-parametric model | Nonparametric methods don't specify something (maybe the distribution, maybe a relationship between two variables*) with a fixed finite number of parameters; they're (potentially) infinite parametric. | Parameters in a non-parametric model
Nonparametric methods don't specify something (maybe the distribution, maybe a relationship between two variables*) with a fixed finite number of parameters; they're (potentially) infinite parametric.
Consider a loess curve (a form of nonparametric regression), for example; the para... | Parameters in a non-parametric model
Nonparametric methods don't specify something (maybe the distribution, maybe a relationship between two variables*) with a fixed finite number of parameters; they're (potentially) infinite parametric. |
42,042 | Why is the complement to Power not $\alpha$? | if I had to verbalize the complement of Power given its definition in statement iii), I would arrive at "wrongly rejecting H0" (simply by kind of flipping "correctly" to "wrongly").
The problem is that it's not that simple. Everyday English (at least when expressed that way) doesn't quite so simply take complements of... | Why is the complement to Power not $\alpha$? | if I had to verbalize the complement of Power given its definition in statement iii), I would arrive at "wrongly rejecting H0" (simply by kind of flipping "correctly" to "wrongly").
The problem is th | Why is the complement to Power not $\alpha$?
if I had to verbalize the complement of Power given its definition in statement iii), I would arrive at "wrongly rejecting H0" (simply by kind of flipping "correctly" to "wrongly").
The problem is that it's not that simple. Everyday English (at least when expressed that way... | Why is the complement to Power not $\alpha$?
if I had to verbalize the complement of Power given its definition in statement iii), I would arrive at "wrongly rejecting H0" (simply by kind of flipping "correctly" to "wrongly").
The problem is th |
42,043 | Why is the complement to Power not $\alpha$? | I think if you form these statements into statements of probability it will make more sense. It is much harder for me to "take the compliment" of a sentence than it is to take the compliment of a conditional probability and then form it as a sentence.
Below I'm using the fact that the complement of $P(A|B)$ is $P(A^c|... | Why is the complement to Power not $\alpha$? | I think if you form these statements into statements of probability it will make more sense. It is much harder for me to "take the compliment" of a sentence than it is to take the compliment of a cond | Why is the complement to Power not $\alpha$?
I think if you form these statements into statements of probability it will make more sense. It is much harder for me to "take the compliment" of a sentence than it is to take the compliment of a conditional probability and then form it as a sentence.
Below I'm using the fa... | Why is the complement to Power not $\alpha$?
I think if you form these statements into statements of probability it will make more sense. It is much harder for me to "take the compliment" of a sentence than it is to take the compliment of a cond |
42,044 | Combining Poisson estimates | You can use maximum likelihood. Let $X$ be the number of buses, $Y$ be the number of cars. Then, with $\lambda$ the observation period in hours, we have $X\sim \text{Po}(10\lambda), Y\sim \text{Po}(60\lambda)$, so the likelihood function based on assuming that $X, Y$ are independent, is proportional to
$$
L(\lambda)... | Combining Poisson estimates | You can use maximum likelihood. Let $X$ be the number of buses, $Y$ be the number of cars. Then, with $\lambda$ the observation period in hours, we have $X\sim \text{Po}(10\lambda), Y\sim \text{Po}(6 | Combining Poisson estimates
You can use maximum likelihood. Let $X$ be the number of buses, $Y$ be the number of cars. Then, with $\lambda$ the observation period in hours, we have $X\sim \text{Po}(10\lambda), Y\sim \text{Po}(60\lambda)$, so the likelihood function based on assuming that $X, Y$ are independent, is pro... | Combining Poisson estimates
You can use maximum likelihood. Let $X$ be the number of buses, $Y$ be the number of cars. Then, with $\lambda$ the observation period in hours, we have $X\sim \text{Po}(10\lambda), Y\sim \text{Po}(6 |
42,045 | How bad can heteroscedasticity be before causing problems? | It is true that heteroscedasticity reduce your power (see: Efficiency of beta estimates with heteroscedasticity), but it can also inflate type I errors. Consider the following simulation (coded in R):
set.seed(1044) # this makes the example exactly reproducible
b0 = 10 ... | How bad can heteroscedasticity be before causing problems? | It is true that heteroscedasticity reduce your power (see: Efficiency of beta estimates with heteroscedasticity), but it can also inflate type I errors. Consider the following simulation (coded in R) | How bad can heteroscedasticity be before causing problems?
It is true that heteroscedasticity reduce your power (see: Efficiency of beta estimates with heteroscedasticity), but it can also inflate type I errors. Consider the following simulation (coded in R):
set.seed(1044) # this makes the ... | How bad can heteroscedasticity be before causing problems?
It is true that heteroscedasticity reduce your power (see: Efficiency of beta estimates with heteroscedasticity), but it can also inflate type I errors. Consider the following simulation (coded in R) |
42,046 | Comparing inter-rater agreement between classes of raters | Here is an approach you could take. I'm going to first assume you need agreement, not consistency, but I'll show you how you can use consistency afterwards. For a great review of the difference, see this paper.
Agreement. This focuses on absolute agreement between raters - if I give it a 2, you will give it a 2. Here a... | Comparing inter-rater agreement between classes of raters | Here is an approach you could take. I'm going to first assume you need agreement, not consistency, but I'll show you how you can use consistency afterwards. For a great review of the difference, see t | Comparing inter-rater agreement between classes of raters
Here is an approach you could take. I'm going to first assume you need agreement, not consistency, but I'll show you how you can use consistency afterwards. For a great review of the difference, see this paper.
Agreement. This focuses on absolute agreement betwe... | Comparing inter-rater agreement between classes of raters
Here is an approach you could take. I'm going to first assume you need agreement, not consistency, but I'll show you how you can use consistency afterwards. For a great review of the difference, see t |
42,047 | Find Neural Network Inputs Given Outputs | I'm no expert in this field, so I might be wrong. Therefore, correct me
if I'm wrong.
consider this neural network (which I suppose is equivalent to yours):
A---H1
\ / \
X C
/ \ /
B---H2
consider that the activation function of H1, H2 and C is the bipolar
sigmoid, to which we'll refer to as "bsig(x)"
also, we... | Find Neural Network Inputs Given Outputs | I'm no expert in this field, so I might be wrong. Therefore, correct me
if I'm wrong.
consider this neural network (which I suppose is equivalent to yours):
A---H1
\ / \
X C
/ \ /
B---H2
con | Find Neural Network Inputs Given Outputs
I'm no expert in this field, so I might be wrong. Therefore, correct me
if I'm wrong.
consider this neural network (which I suppose is equivalent to yours):
A---H1
\ / \
X C
/ \ /
B---H2
consider that the activation function of H1, H2 and C is the bipolar
sigmoid, to w... | Find Neural Network Inputs Given Outputs
I'm no expert in this field, so I might be wrong. Therefore, correct me
if I'm wrong.
consider this neural network (which I suppose is equivalent to yours):
A---H1
\ / \
X C
/ \ /
B---H2
con |
42,048 | Find Neural Network Inputs Given Outputs | The answer is simple: backpropagation.
Say you have a trained net $f$ which maps some $x$ to some $y$, which you'd ideally want to be $z$. You then use a different loss, which is the deviation from $y$ to $z$, e.g.:
$$
\mathcal{C} = ||z - y||_2^2.
$$
In back propagation, you typically follow the gradient of the loss $\... | Find Neural Network Inputs Given Outputs | The answer is simple: backpropagation.
Say you have a trained net $f$ which maps some $x$ to some $y$, which you'd ideally want to be $z$. You then use a different loss, which is the deviation from $y | Find Neural Network Inputs Given Outputs
The answer is simple: backpropagation.
Say you have a trained net $f$ which maps some $x$ to some $y$, which you'd ideally want to be $z$. You then use a different loss, which is the deviation from $y$ to $z$, e.g.:
$$
\mathcal{C} = ||z - y||_2^2.
$$
In back propagation, you typ... | Find Neural Network Inputs Given Outputs
The answer is simple: backpropagation.
Say you have a trained net $f$ which maps some $x$ to some $y$, which you'd ideally want to be $z$. You then use a different loss, which is the deviation from $y |
42,049 | Find Neural Network Inputs Given Outputs | You could use reconstruction error and consider your second input as a parameter.
Suppose your fixed input is $x_1$ and your latent input is $x_2$. The output $y$ can be:
$$y = s(W_1 \cdot x_1 + W_2 \cdot x_2 + b)$$
$s$ being your bipolar sigmoid.
You then use a decoder to map back into a reconstruction $z$:
$$z = s(W'... | Find Neural Network Inputs Given Outputs | You could use reconstruction error and consider your second input as a parameter.
Suppose your fixed input is $x_1$ and your latent input is $x_2$. The output $y$ can be:
$$y = s(W_1 \cdot x_1 + W_2 \ | Find Neural Network Inputs Given Outputs
You could use reconstruction error and consider your second input as a parameter.
Suppose your fixed input is $x_1$ and your latent input is $x_2$. The output $y$ can be:
$$y = s(W_1 \cdot x_1 + W_2 \cdot x_2 + b)$$
$s$ being your bipolar sigmoid.
You then use a decoder to map b... | Find Neural Network Inputs Given Outputs
You could use reconstruction error and consider your second input as a parameter.
Suppose your fixed input is $x_1$ and your latent input is $x_2$. The output $y$ can be:
$$y = s(W_1 \cdot x_1 + W_2 \ |
42,050 | Find Neural Network Inputs Given Outputs | I agree with the backpropagation.
However, if the question is more general, especially for bigger nets, you can train another network with many generated input outputs from your original network and approximate the backpropagation with the 2nd network.
Hope it helps | Find Neural Network Inputs Given Outputs | I agree with the backpropagation.
However, if the question is more general, especially for bigger nets, you can train another network with many generated input outputs from your original network and a | Find Neural Network Inputs Given Outputs
I agree with the backpropagation.
However, if the question is more general, especially for bigger nets, you can train another network with many generated input outputs from your original network and approximate the backpropagation with the 2nd network.
Hope it helps | Find Neural Network Inputs Given Outputs
I agree with the backpropagation.
However, if the question is more general, especially for bigger nets, you can train another network with many generated input outputs from your original network and a |
42,051 | Find Neural Network Inputs Given Outputs | I believe bernardo may have made an error. At the hidden layer h there my not be a function sigmoid since sigmoid is the function applied to h1 and h2 to give result c. Therefore to correct his assumption h1 = awa1 + bwb1. Hence, h2 follows suit. Rendering the function sigmoid to process h1 and h2. C= sig(h1 + h2)
The... | Find Neural Network Inputs Given Outputs | I believe bernardo may have made an error. At the hidden layer h there my not be a function sigmoid since sigmoid is the function applied to h1 and h2 to give result c. Therefore to correct his assump | Find Neural Network Inputs Given Outputs
I believe bernardo may have made an error. At the hidden layer h there my not be a function sigmoid since sigmoid is the function applied to h1 and h2 to give result c. Therefore to correct his assumption h1 = awa1 + bwb1. Hence, h2 follows suit. Rendering the function sigmoid t... | Find Neural Network Inputs Given Outputs
I believe bernardo may have made an error. At the hidden layer h there my not be a function sigmoid since sigmoid is the function applied to h1 and h2 to give result c. Therefore to correct his assump |
42,052 | How can heteroskedasticity that is only contingent on omitted variables not effect the validity of standard errors? | I don't have access to the book, but I think there should be an additional caveat. The omitted variable[s] should be uncorrelated with the explanatory variables that appear in the model. If the omitted variable, on which the conditional variance depends, is correlated with the included variables, then the residual va... | How can heteroskedasticity that is only contingent on omitted variables not effect the validity of s | I don't have access to the book, but I think there should be an additional caveat. The omitted variable[s] should be uncorrelated with the explanatory variables that appear in the model. If the omit | How can heteroskedasticity that is only contingent on omitted variables not effect the validity of standard errors?
I don't have access to the book, but I think there should be an additional caveat. The omitted variable[s] should be uncorrelated with the explanatory variables that appear in the model. If the omitted ... | How can heteroskedasticity that is only contingent on omitted variables not effect the validity of s
I don't have access to the book, but I think there should be an additional caveat. The omitted variable[s] should be uncorrelated with the explanatory variables that appear in the model. If the omit |
42,053 | Can somebody identify this distribution? | I think it relates to a Gumbel distribution:
if I define $S=R^2$, when $R\sim p(r|\lambda)$, the density of $S$ is given by the Jacobian formula:
\begin{align*}
q(s|\lambda) &= p(\sqrt{s}|\lambda)\times \left|\frac{\text{d}r}{\text{d}s}\right|\\
&= p(\sqrt{s}|\lambda)\times \frac{1}{2\sqrt{s}}\\
&= \frac{2\lambda \sqrt... | Can somebody identify this distribution? | I think it relates to a Gumbel distribution:
if I define $S=R^2$, when $R\sim p(r|\lambda)$, the density of $S$ is given by the Jacobian formula:
\begin{align*}
q(s|\lambda) &= p(\sqrt{s}|\lambda)\tim | Can somebody identify this distribution?
I think it relates to a Gumbel distribution:
if I define $S=R^2$, when $R\sim p(r|\lambda)$, the density of $S$ is given by the Jacobian formula:
\begin{align*}
q(s|\lambda) &= p(\sqrt{s}|\lambda)\times \left|\frac{\text{d}r}{\text{d}s}\right|\\
&= p(\sqrt{s}|\lambda)\times \fra... | Can somebody identify this distribution?
I think it relates to a Gumbel distribution:
if I define $S=R^2$, when $R\sim p(r|\lambda)$, the density of $S$ is given by the Jacobian formula:
\begin{align*}
q(s|\lambda) &= p(\sqrt{s}|\lambda)\tim |
42,054 | How to transform continuous data with extreme bimodal distribution | 1) There's no way to transform a discrete random variable to be continuous. If it takes $k$ distinct values, no transformation will leave you with more than $k$ distinct values.
So you can't transform this to be normal. It's always going to have two big spikes (or worse, with non-monotonic transformations you might en... | How to transform continuous data with extreme bimodal distribution | 1) There's no way to transform a discrete random variable to be continuous. If it takes $k$ distinct values, no transformation will leave you with more than $k$ distinct values.
So you can't transfor | How to transform continuous data with extreme bimodal distribution
1) There's no way to transform a discrete random variable to be continuous. If it takes $k$ distinct values, no transformation will leave you with more than $k$ distinct values.
So you can't transform this to be normal. It's always going to have two bi... | How to transform continuous data with extreme bimodal distribution
1) There's no way to transform a discrete random variable to be continuous. If it takes $k$ distinct values, no transformation will leave you with more than $k$ distinct values.
So you can't transfor |
42,055 | Expected value of least squares estimator $\hat{\beta}$ | Note that in regression we condition on $X$.
Hence expressions like $(X^TX)^{-1}X^T$ will be a matrix of constants.
Recall that $Y=X\beta+e$, and just apply linearity of expectation, and that E[e]=0.
Edit:
$E[\hat{\beta}]=E[(X^TX)^{-1}X^TY]=E[(X^TX)^{-1}X^T(X\beta+e)]$
$\hspace{1cm}=(X^TX)^{-1}X^TX E[\beta]+(X^TX)^{-1}... | Expected value of least squares estimator $\hat{\beta}$ | Note that in regression we condition on $X$.
Hence expressions like $(X^TX)^{-1}X^T$ will be a matrix of constants.
Recall that $Y=X\beta+e$, and just apply linearity of expectation, and that E[e]=0.
| Expected value of least squares estimator $\hat{\beta}$
Note that in regression we condition on $X$.
Hence expressions like $(X^TX)^{-1}X^T$ will be a matrix of constants.
Recall that $Y=X\beta+e$, and just apply linearity of expectation, and that E[e]=0.
Edit:
$E[\hat{\beta}]=E[(X^TX)^{-1}X^TY]=E[(X^TX)^{-1}X^T(X\beta... | Expected value of least squares estimator $\hat{\beta}$
Note that in regression we condition on $X$.
Hence expressions like $(X^TX)^{-1}X^T$ will be a matrix of constants.
Recall that $Y=X\beta+e$, and just apply linearity of expectation, and that E[e]=0.
|
42,056 | Effective degrees of freedom for regularized regression | Assume $\mathbb A$ is invertible. Let $\mathbb A = \Sigma^\prime \mathbb U^\prime \mathbb U \Sigma$ where $\mathbb U$ is an orthogonal matrix, $\mathbb {U^\prime U} = \mathbb I$, and write
$$\mathbf \beta = \mathbb U \Sigma \mathbf b$$
so that
$$\mathbf \beta ^\prime \mathbf \beta = \mathbf b^\prime \mathbb A \mathbf ... | Effective degrees of freedom for regularized regression | Assume $\mathbb A$ is invertible. Let $\mathbb A = \Sigma^\prime \mathbb U^\prime \mathbb U \Sigma$ where $\mathbb U$ is an orthogonal matrix, $\mathbb {U^\prime U} = \mathbb I$, and write
$$\mathbf | Effective degrees of freedom for regularized regression
Assume $\mathbb A$ is invertible. Let $\mathbb A = \Sigma^\prime \mathbb U^\prime \mathbb U \Sigma$ where $\mathbb U$ is an orthogonal matrix, $\mathbb {U^\prime U} = \mathbb I$, and write
$$\mathbf \beta = \mathbb U \Sigma \mathbf b$$
so that
$$\mathbf \beta ^\p... | Effective degrees of freedom for regularized regression
Assume $\mathbb A$ is invertible. Let $\mathbb A = \Sigma^\prime \mathbb U^\prime \mathbb U \Sigma$ where $\mathbb U$ is an orthogonal matrix, $\mathbb {U^\prime U} = \mathbb I$, and write
$$\mathbf |
42,057 | Are normally distributed residuals not necessarily homoskedastic? | You're absolutely right, normally distributed does not imply homoskedastic, and your example is great. | Are normally distributed residuals not necessarily homoskedastic? | You're absolutely right, normally distributed does not imply homoskedastic, and your example is great. | Are normally distributed residuals not necessarily homoskedastic?
You're absolutely right, normally distributed does not imply homoskedastic, and your example is great. | Are normally distributed residuals not necessarily homoskedastic?
You're absolutely right, normally distributed does not imply homoskedastic, and your example is great. |
42,058 | In LDA, how to interpret the meaning of topics? | What LDA does, and what it can answer
Consider this snippet from the paper introducing supervised LDA:
Most topic models, such as latent Dirichlet allocation (LDA), are unsupervised: only the words in the documents are modeled. The goal is to infer topics that maximize the likelihood (or the posterior probability) of ... | In LDA, how to interpret the meaning of topics? | What LDA does, and what it can answer
Consider this snippet from the paper introducing supervised LDA:
Most topic models, such as latent Dirichlet allocation (LDA), are unsupervised: only the words i | In LDA, how to interpret the meaning of topics?
What LDA does, and what it can answer
Consider this snippet from the paper introducing supervised LDA:
Most topic models, such as latent Dirichlet allocation (LDA), are unsupervised: only the words in the documents are modeled. The goal is to infer topics that maximize t... | In LDA, how to interpret the meaning of topics?
What LDA does, and what it can answer
Consider this snippet from the paper introducing supervised LDA:
Most topic models, such as latent Dirichlet allocation (LDA), are unsupervised: only the words i |
42,059 | In LDA, how to interpret the meaning of topics? | LDA is an unsupervised learning method that maximizes the probability of word assignments to one of K fixed topics. The topic meaning is extracted by interpreting the top N probability words for a given topic, i.e. LDA will not output the meaning of topics, rather it will organize words by topic to be interpreted by th... | In LDA, how to interpret the meaning of topics? | LDA is an unsupervised learning method that maximizes the probability of word assignments to one of K fixed topics. The topic meaning is extracted by interpreting the top N probability words for a giv | In LDA, how to interpret the meaning of topics?
LDA is an unsupervised learning method that maximizes the probability of word assignments to one of K fixed topics. The topic meaning is extracted by interpreting the top N probability words for a given topic, i.e. LDA will not output the meaning of topics, rather it will... | In LDA, how to interpret the meaning of topics?
LDA is an unsupervised learning method that maximizes the probability of word assignments to one of K fixed topics. The topic meaning is extracted by interpreting the top N probability words for a giv |
42,060 | Survival analysis where P(event) < 1 | One set of models that does what you describe is sometimes called a "cure model". The logic behind the name is based on a question like how long does it take before a cancer patient dies? Some of them are cured and won't die at all (from this occurance of the disease).
For example see here. | Survival analysis where P(event) < 1 | One set of models that does what you describe is sometimes called a "cure model". The logic behind the name is based on a question like how long does it take before a cancer patient dies? Some of them | Survival analysis where P(event) < 1
One set of models that does what you describe is sometimes called a "cure model". The logic behind the name is based on a question like how long does it take before a cancer patient dies? Some of them are cured and won't die at all (from this occurance of the disease).
For example s... | Survival analysis where P(event) < 1
One set of models that does what you describe is sometimes called a "cure model". The logic behind the name is based on a question like how long does it take before a cancer patient dies? Some of them |
42,061 | Propensity Score Analysis with continuous treatment | This has been asked on the Statalist too. The post here mentions the user-written command doseresponse (a multivalued treatment effect evaluation method to assess the effect of a drug that participants could take in different levels of intensity) or the subroutine gpscore. The relevant reference is
Bia, M. and Mattei... | Propensity Score Analysis with continuous treatment | This has been asked on the Statalist too. The post here mentions the user-written command doseresponse (a multivalued treatment effect evaluation method to assess the effect of a drug that participan | Propensity Score Analysis with continuous treatment
This has been asked on the Statalist too. The post here mentions the user-written command doseresponse (a multivalued treatment effect evaluation method to assess the effect of a drug that participants could take in different levels of intensity) or the subroutine gp... | Propensity Score Analysis with continuous treatment
This has been asked on the Statalist too. The post here mentions the user-written command doseresponse (a multivalued treatment effect evaluation method to assess the effect of a drug that participan |
42,062 | Impute missing values using aregImpute | You can't really use $R^2$ in the manner you suggest. If $R^2$ is 0 you can still use multiple imputation; it's just not better than a random guess in that case.
Force linearity of all the variables if you have a very small sample size relative to the number of variables.
aregImpute stores all the multiple imputations... | Impute missing values using aregImpute | You can't really use $R^2$ in the manner you suggest. If $R^2$ is 0 you can still use multiple imputation; it's just not better than a random guess in that case.
Force linearity of all the variables | Impute missing values using aregImpute
You can't really use $R^2$ in the manner you suggest. If $R^2$ is 0 you can still use multiple imputation; it's just not better than a random guess in that case.
Force linearity of all the variables if you have a very small sample size relative to the number of variables.
aregImp... | Impute missing values using aregImpute
You can't really use $R^2$ in the manner you suggest. If $R^2$ is 0 you can still use multiple imputation; it's just not better than a random guess in that case.
Force linearity of all the variables |
42,063 | How does one interpret the distribution over parameters in bayesian estimation? | how do I know what is the relative probability of the process of generation being a gaussian MM with this particular parameter combination instead of say a neural network with that parameter configuration.
Your $\theta$ is the set of parameters in your model. So for a Gaussian mixture model they are the means, covari... | How does one interpret the distribution over parameters in bayesian estimation? | how do I know what is the relative probability of the process of generation being a gaussian MM with this particular parameter combination instead of say a neural network with that parameter configura | How does one interpret the distribution over parameters in bayesian estimation?
how do I know what is the relative probability of the process of generation being a gaussian MM with this particular parameter combination instead of say a neural network with that parameter configuration.
Your $\theta$ is the set of param... | How does one interpret the distribution over parameters in bayesian estimation?
how do I know what is the relative probability of the process of generation being a gaussian MM with this particular parameter combination instead of say a neural network with that parameter configura |
42,064 | How does one interpret the distribution over parameters in bayesian estimation? | This was too long for the comments, so posting it here.
From what the others have pointed out about thinking about the prior as a belief, I think a road-block in understanding had been combining the prior and the conditional.
The prior $P(\theta)$ is understood as a belief in what the true $\theta$ might be. The condit... | How does one interpret the distribution over parameters in bayesian estimation? | This was too long for the comments, so posting it here.
From what the others have pointed out about thinking about the prior as a belief, I think a road-block in understanding had been combining the p | How does one interpret the distribution over parameters in bayesian estimation?
This was too long for the comments, so posting it here.
From what the others have pointed out about thinking about the prior as a belief, I think a road-block in understanding had been combining the prior and the conditional.
The prior $P(\... | How does one interpret the distribution over parameters in bayesian estimation?
This was too long for the comments, so posting it here.
From what the others have pointed out about thinking about the prior as a belief, I think a road-block in understanding had been combining the p |
42,065 | Multi-class logarithmic loss function per class | As you rightly pointed out, a pure classifier (with probability 1) will have log loss of 0, which is the preferred case.
Consider a classifier that assigns labels in a completely random manner. Probability of assigning to the correct class will be 1/M. Therefore, the log loss for each observation will be -log(1/M) = lo... | Multi-class logarithmic loss function per class | As you rightly pointed out, a pure classifier (with probability 1) will have log loss of 0, which is the preferred case.
Consider a classifier that assigns labels in a completely random manner. Probab | Multi-class logarithmic loss function per class
As you rightly pointed out, a pure classifier (with probability 1) will have log loss of 0, which is the preferred case.
Consider a classifier that assigns labels in a completely random manner. Probability of assigning to the correct class will be 1/M. Therefore, the log ... | Multi-class logarithmic loss function per class
As you rightly pointed out, a pure classifier (with probability 1) will have log loss of 0, which is the preferred case.
Consider a classifier that assigns labels in a completely random manner. Probab |
42,066 | Multi-class logarithmic loss function per class | In my understanding of Log loss if you are evaluating an observation where $y_{ij} = 0$ then $y_{ij} \cdot Ln(p_{ij}) = 0$ and so these will decrease the value of the log loss for each instance that doesn't contain this label.
If $p_{ij}$ is high even when $y_{ij} = 0$ it will not affect log loss for the current clas... | Multi-class logarithmic loss function per class | In my understanding of Log loss if you are evaluating an observation where $y_{ij} = 0$ then $y_{ij} \cdot Ln(p_{ij}) = 0$ and so these will decrease the value of the log loss for each instance that d | Multi-class logarithmic loss function per class
In my understanding of Log loss if you are evaluating an observation where $y_{ij} = 0$ then $y_{ij} \cdot Ln(p_{ij}) = 0$ and so these will decrease the value of the log loss for each instance that doesn't contain this label.
If $p_{ij}$ is high even when $y_{ij} = 0$ ... | Multi-class logarithmic loss function per class
In my understanding of Log loss if you are evaluating an observation where $y_{ij} = 0$ then $y_{ij} \cdot Ln(p_{ij}) = 0$ and so these will decrease the value of the log loss for each instance that d |
42,067 | Why (mathematically) is the parametric bootstrap usually better than the empirical one? | Basically, all nonparametric bootstrap procedures underestimate the variance of the sampling distribution. This issue doesn't have a consistent name in the literature, but I like "narrowness bias" from "What Teachers Should Know About the Bootstrap: Resampling in the Undergraduate Statistics Curriculum" by Tim Hesterbe... | Why (mathematically) is the parametric bootstrap usually better than the empirical one? | Basically, all nonparametric bootstrap procedures underestimate the variance of the sampling distribution. This issue doesn't have a consistent name in the literature, but I like "narrowness bias" fro | Why (mathematically) is the parametric bootstrap usually better than the empirical one?
Basically, all nonparametric bootstrap procedures underestimate the variance of the sampling distribution. This issue doesn't have a consistent name in the literature, but I like "narrowness bias" from "What Teachers Should Know Abo... | Why (mathematically) is the parametric bootstrap usually better than the empirical one?
Basically, all nonparametric bootstrap procedures underestimate the variance of the sampling distribution. This issue doesn't have a consistent name in the literature, but I like "narrowness bias" fro |
42,068 | Model with non-linear transformation | You haven't used the full form of the cubic representation and are missing two terms (i.e. have unintentionally constrained their parameters to equal zero):
$$Leads = \beta_{0} + \beta_{ImpA}ImpA + \beta_{ImpA^{2}}ImpA^{2} + \beta_{ImpA^{3}}ImpA^{3} + \varepsilon$$
Per the currently highest voted answer in Fitting pol... | Model with non-linear transformation | You haven't used the full form of the cubic representation and are missing two terms (i.e. have unintentionally constrained their parameters to equal zero):
$$Leads = \beta_{0} + \beta_{ImpA}ImpA + \ | Model with non-linear transformation
You haven't used the full form of the cubic representation and are missing two terms (i.e. have unintentionally constrained their parameters to equal zero):
$$Leads = \beta_{0} + \beta_{ImpA}ImpA + \beta_{ImpA^{2}}ImpA^{2} + \beta_{ImpA^{3}}ImpA^{3} + \varepsilon$$
Per the currentl... | Model with non-linear transformation
You haven't used the full form of the cubic representation and are missing two terms (i.e. have unintentionally constrained their parameters to equal zero):
$$Leads = \beta_{0} + \beta_{ImpA}ImpA + \ |
42,069 | Two or more time series. What is the best way to test whether one of them is leading and by what time period? | You could try cross-correlation analysis with R for example. Cross-correlation at lag h measures temporal dependency of two time series (x{t+h},y{t}) at lag h. If h<0 and cross-correlation is statistically significant then you could say that x series leads y series by h time units. For example approval of building per... | Two or more time series. What is the best way to test whether one of them is leading and by what tim | You could try cross-correlation analysis with R for example. Cross-correlation at lag h measures temporal dependency of two time series (x{t+h},y{t}) at lag h. If h<0 and cross-correlation is statist | Two or more time series. What is the best way to test whether one of them is leading and by what time period?
You could try cross-correlation analysis with R for example. Cross-correlation at lag h measures temporal dependency of two time series (x{t+h},y{t}) at lag h. If h<0 and cross-correlation is statistically sig... | Two or more time series. What is the best way to test whether one of them is leading and by what tim
You could try cross-correlation analysis with R for example. Cross-correlation at lag h measures temporal dependency of two time series (x{t+h},y{t}) at lag h. If h<0 and cross-correlation is statist |
42,070 | Combinef in R HTS package- constrain to keep forecasts positive? | The positive=TRUE argument for forecast.gts and forecast.hts ensures the starting forecasts to be positive, but not the final reconciled forecasts. Even when the starting forecasts are positive, it is possible for the reconciled forecasts to be negative. When you use combinef, you provide your own starting forecasts, s... | Combinef in R HTS package- constrain to keep forecasts positive? | The positive=TRUE argument for forecast.gts and forecast.hts ensures the starting forecasts to be positive, but not the final reconciled forecasts. Even when the starting forecasts are positive, it is | Combinef in R HTS package- constrain to keep forecasts positive?
The positive=TRUE argument for forecast.gts and forecast.hts ensures the starting forecasts to be positive, but not the final reconciled forecasts. Even when the starting forecasts are positive, it is possible for the reconciled forecasts to be negative. ... | Combinef in R HTS package- constrain to keep forecasts positive?
The positive=TRUE argument for forecast.gts and forecast.hts ensures the starting forecasts to be positive, but not the final reconciled forecasts. Even when the starting forecasts are positive, it is |
42,071 | Combinef in R HTS package- constrain to keep forecasts positive? | You can't ensure positivity and sum consistency of hierarchical forecasts if you use forecast::combinef().
What I personally found useful was to set up the summation matrix (see the original publication by Hyndman et al., 2011) and then solve the relevant (weighted) least squares problem with additional nonnegativity c... | Combinef in R HTS package- constrain to keep forecasts positive? | You can't ensure positivity and sum consistency of hierarchical forecasts if you use forecast::combinef().
What I personally found useful was to set up the summation matrix (see the original publicati | Combinef in R HTS package- constrain to keep forecasts positive?
You can't ensure positivity and sum consistency of hierarchical forecasts if you use forecast::combinef().
What I personally found useful was to set up the summation matrix (see the original publication by Hyndman et al., 2011) and then solve the relevant... | Combinef in R HTS package- constrain to keep forecasts positive?
You can't ensure positivity and sum consistency of hierarchical forecasts if you use forecast::combinef().
What I personally found useful was to set up the summation matrix (see the original publicati |
42,072 | Combinef in R HTS package- constrain to keep forecasts positive? | Some code based on Rob's workaround of setting the negatives to zero and reconcile
# Re-reconciliate when zero values present
# Extract groups
groups <- hts.obj %>%
aggts() %>%
get_groups()
x=0 #Counter
# Loop until all positive
while(sum(hts.obj[[1]] <0) > 0){
# Generate all time series
hts.obj <- aggts(ht... | Combinef in R HTS package- constrain to keep forecasts positive? | Some code based on Rob's workaround of setting the negatives to zero and reconcile
# Re-reconciliate when zero values present
# Extract groups
groups <- hts.obj %>%
aggts() %>%
get_groups()
x=0 | Combinef in R HTS package- constrain to keep forecasts positive?
Some code based on Rob's workaround of setting the negatives to zero and reconcile
# Re-reconciliate when zero values present
# Extract groups
groups <- hts.obj %>%
aggts() %>%
get_groups()
x=0 #Counter
# Loop until all positive
while(sum(hts.obj[[... | Combinef in R HTS package- constrain to keep forecasts positive?
Some code based on Rob's workaround of setting the negatives to zero and reconcile
# Re-reconciliate when zero values present
# Extract groups
groups <- hts.obj %>%
aggts() %>%
get_groups()
x=0 |
42,073 | What to Do When a Log-binomial Model's Convergence Fails | The Poisson approximation to the relative risk is a very good approach with two small limitations: it is easily possible to overpredict the risk, and the mean-variance assumption may be unreasonable in moderately high risks. Together these do not invalidate the estimates (when using robust standard errors) but they and... | What to Do When a Log-binomial Model's Convergence Fails | The Poisson approximation to the relative risk is a very good approach with two small limitations: it is easily possible to overpredict the risk, and the mean-variance assumption may be unreasonable i | What to Do When a Log-binomial Model's Convergence Fails
The Poisson approximation to the relative risk is a very good approach with two small limitations: it is easily possible to overpredict the risk, and the mean-variance assumption may be unreasonable in moderately high risks. Together these do not invalidate the e... | What to Do When a Log-binomial Model's Convergence Fails
The Poisson approximation to the relative risk is a very good approach with two small limitations: it is easily possible to overpredict the risk, and the mean-variance assumption may be unreasonable i |
42,074 | Is there a name for this process/ distribution? | I gather all these r.v.'s are independent.
This is a Markov process, because the past is fully encapsulated in $S_{t-1}$, and so current probabilities conditional in its whole past are equivalent to current probabilities conditional only on the previous period.
It is also a martingale process because a) it is absolut... | Is there a name for this process/ distribution? | I gather all these r.v.'s are independent.
This is a Markov process, because the past is fully encapsulated in $S_{t-1}$, and so current probabilities conditional in its whole past are equivalent to | Is there a name for this process/ distribution?
I gather all these r.v.'s are independent.
This is a Markov process, because the past is fully encapsulated in $S_{t-1}$, and so current probabilities conditional in its whole past are equivalent to current probabilities conditional only on the previous period.
It is al... | Is there a name for this process/ distribution?
I gather all these r.v.'s are independent.
This is a Markov process, because the past is fully encapsulated in $S_{t-1}$, and so current probabilities conditional in its whole past are equivalent to |
42,075 | Random Forest - how to know if variables affect positively or negatively | As the answers at the linked question by @Simone show, it is entirely possible to quantify the partial effect of a predictor/independent variable on the target/dependent variable. This is a very useful way to derive understanding from a random forest (or machine learning model in general).
However, this is not exactly... | Random Forest - how to know if variables affect positively or negatively | As the answers at the linked question by @Simone show, it is entirely possible to quantify the partial effect of a predictor/independent variable on the target/dependent variable. This is a very usefu | Random Forest - how to know if variables affect positively or negatively
As the answers at the linked question by @Simone show, it is entirely possible to quantify the partial effect of a predictor/independent variable on the target/dependent variable. This is a very useful way to derive understanding from a random for... | Random Forest - how to know if variables affect positively or negatively
As the answers at the linked question by @Simone show, it is entirely possible to quantify the partial effect of a predictor/independent variable on the target/dependent variable. This is a very usefu |
42,076 | Introduction to recurrent neural networks? | The major applications of Recurrent Neural Network (RNN) is sequence modelling. Applications like Machine Translation, Named Entity Recognition, Part-of-Speech Tagging etc.(since, i work in NLP, all the examples are from NLP)
Some of the resources which I found helpful for a beginner are:
Supervised Sequence Labelling... | Introduction to recurrent neural networks? | The major applications of Recurrent Neural Network (RNN) is sequence modelling. Applications like Machine Translation, Named Entity Recognition, Part-of-Speech Tagging etc.(since, i work in NLP, all t | Introduction to recurrent neural networks?
The major applications of Recurrent Neural Network (RNN) is sequence modelling. Applications like Machine Translation, Named Entity Recognition, Part-of-Speech Tagging etc.(since, i work in NLP, all the examples are from NLP)
Some of the resources which I found helpful for a b... | Introduction to recurrent neural networks?
The major applications of Recurrent Neural Network (RNN) is sequence modelling. Applications like Machine Translation, Named Entity Recognition, Part-of-Speech Tagging etc.(since, i work in NLP, all t |
42,077 | How do Restricted Boltzmann Machines work? | While it seems that the OP is not interested in this question anymore (and, based on the profile information, in Cross Validated, for that matter), I've decided to add some additional information, which is IMHO relevant and hopefully will be useful for the community.
First and foremost, I would like to share an excelle... | How do Restricted Boltzmann Machines work? | While it seems that the OP is not interested in this question anymore (and, based on the profile information, in Cross Validated, for that matter), I've decided to add some additional information, whi | How do Restricted Boltzmann Machines work?
While it seems that the OP is not interested in this question anymore (and, based on the profile information, in Cross Validated, for that matter), I've decided to add some additional information, which is IMHO relevant and hopefully will be useful for the community.
First and... | How do Restricted Boltzmann Machines work?
While it seems that the OP is not interested in this question anymore (and, based on the profile information, in Cross Validated, for that matter), I've decided to add some additional information, whi |
42,078 | How do Restricted Boltzmann Machines work? | First look into this paper in deep.
A. Fischer and C. Igel, "An Introduction to Restricted Boltzmann machines," in Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications, ed: Springer, 2012, pp. 14-36.
Then, You may look into Hinton's coursera course website. You will understand proper.
I... | How do Restricted Boltzmann Machines work? | First look into this paper in deep.
A. Fischer and C. Igel, "An Introduction to Restricted Boltzmann machines," in Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications, | How do Restricted Boltzmann Machines work?
First look into this paper in deep.
A. Fischer and C. Igel, "An Introduction to Restricted Boltzmann machines," in Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications, ed: Springer, 2012, pp. 14-36.
Then, You may look into Hinton's coursera cou... | How do Restricted Boltzmann Machines work?
First look into this paper in deep.
A. Fischer and C. Igel, "An Introduction to Restricted Boltzmann machines," in Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications, |
42,079 | Treatment Effect Bounds | Let $R_i$ be a dummy which equals one for respondents and zero for non-respondents, $Y_i$ the outcome and $D_i$ the treatment variable from your randomized experiment. You cannot observe the counterfactual quantities that you want to compare, i.e. $E[Y_{i1}|R_i = 0|D_i = 1]$ and $E[Y_{i0}|R_i = 0, D_i = 0]$, due to non... | Treatment Effect Bounds | Let $R_i$ be a dummy which equals one for respondents and zero for non-respondents, $Y_i$ the outcome and $D_i$ the treatment variable from your randomized experiment. You cannot observe the counterfa | Treatment Effect Bounds
Let $R_i$ be a dummy which equals one for respondents and zero for non-respondents, $Y_i$ the outcome and $D_i$ the treatment variable from your randomized experiment. You cannot observe the counterfactual quantities that you want to compare, i.e. $E[Y_{i1}|R_i = 0|D_i = 1]$ and $E[Y_{i0}|R_i = ... | Treatment Effect Bounds
Let $R_i$ be a dummy which equals one for respondents and zero for non-respondents, $Y_i$ the outcome and $D_i$ the treatment variable from your randomized experiment. You cannot observe the counterfa |
42,080 | Theil-Sen estimation, more than one independent variable | There have been a number of proposals for extending Theil-Sen estimation to multiple regression contexts.
I'll point to a couple:
1)
Zhou, W. and R. Serfling (2007),
Multivariate Spatial U-Quantiles: a Bahadur-Kiefer
Representation, a Theil-Sen Estimator for Multiple
Regression, and a Robust Dispersion Estimator,
Jo... | Theil-Sen estimation, more than one independent variable | There have been a number of proposals for extending Theil-Sen estimation to multiple regression contexts.
I'll point to a couple:
1)
Zhou, W. and R. Serfling (2007),
Multivariate Spatial U-Quantiles: | Theil-Sen estimation, more than one independent variable
There have been a number of proposals for extending Theil-Sen estimation to multiple regression contexts.
I'll point to a couple:
1)
Zhou, W. and R. Serfling (2007),
Multivariate Spatial U-Quantiles: a Bahadur-Kiefer
Representation, a Theil-Sen Estimator for Mu... | Theil-Sen estimation, more than one independent variable
There have been a number of proposals for extending Theil-Sen estimation to multiple regression contexts.
I'll point to a couple:
1)
Zhou, W. and R. Serfling (2007),
Multivariate Spatial U-Quantiles: |
42,081 | PCA: 91% of explained variance on one principal component | I am (very) new to this, but I'll do my best to help. The answers to your questions are
Am I justified in removing the other 8 principal components?
I do not think you are "justified". But if you want to make a first coarse assessment of the data you can concentrate on the first PC, just bear in mind that you neglect... | PCA: 91% of explained variance on one principal component | I am (very) new to this, but I'll do my best to help. The answers to your questions are
Am I justified in removing the other 8 principal components?
I do not think you are "justified". But if you wa | PCA: 91% of explained variance on one principal component
I am (very) new to this, but I'll do my best to help. The answers to your questions are
Am I justified in removing the other 8 principal components?
I do not think you are "justified". But if you want to make a first coarse assessment of the data you can conce... | PCA: 91% of explained variance on one principal component
I am (very) new to this, but I'll do my best to help. The answers to your questions are
Am I justified in removing the other 8 principal components?
I do not think you are "justified". But if you wa |
42,082 | PCA: 91% of explained variance on one principal component | Going by your plotting the first 2 components, I would definitely say keep the second one, and maybe the third one too.
Drawing cumulative information gain graphs also help a lot in deciding about PCA.
If you are using R, there are simple methods to do that. You could look up R labs in standard data mining books like ... | PCA: 91% of explained variance on one principal component | Going by your plotting the first 2 components, I would definitely say keep the second one, and maybe the third one too.
Drawing cumulative information gain graphs also help a lot in deciding about PC | PCA: 91% of explained variance on one principal component
Going by your plotting the first 2 components, I would definitely say keep the second one, and maybe the third one too.
Drawing cumulative information gain graphs also help a lot in deciding about PCA.
If you are using R, there are simple methods to do that. Yo... | PCA: 91% of explained variance on one principal component
Going by your plotting the first 2 components, I would definitely say keep the second one, and maybe the third one too.
Drawing cumulative information gain graphs also help a lot in deciding about PC |
42,083 | Is there an advantage to squaring dissimilarities when using Ward clustering? | From the Conclusion of Murtaugh, F. & Legendre, P. (2011). Ward's Hierarchical Clustering Method: Clustering Criterion and Agglomerative Algorithm, ArXive:1111.6285v2 (pdf):
Two algorithms, Ward1 and Ward2...When applied to the same distance matrix D, they produce different results. This article has shown that when t... | Is there an advantage to squaring dissimilarities when using Ward clustering? | From the Conclusion of Murtaugh, F. & Legendre, P. (2011). Ward's Hierarchical Clustering Method: Clustering Criterion and Agglomerative Algorithm, ArXive:1111.6285v2 (pdf):
Two algorithms, Ward1 an | Is there an advantage to squaring dissimilarities when using Ward clustering?
From the Conclusion of Murtaugh, F. & Legendre, P. (2011). Ward's Hierarchical Clustering Method: Clustering Criterion and Agglomerative Algorithm, ArXive:1111.6285v2 (pdf):
Two algorithms, Ward1 and Ward2...When applied to the same distanc... | Is there an advantage to squaring dissimilarities when using Ward clustering?
From the Conclusion of Murtaugh, F. & Legendre, P. (2011). Ward's Hierarchical Clustering Method: Clustering Criterion and Agglomerative Algorithm, ArXive:1111.6285v2 (pdf):
Two algorithms, Ward1 an |
42,084 | Is there an advantage to squaring dissimilarities when using Ward clustering? | Judging from the explanation, ward in R was first implemented incorrectly.
Only in recent versions, a corrected version of ward linkage was added, as ward.D2. So if you want to use ward linkage, use ward.D2. | Is there an advantage to squaring dissimilarities when using Ward clustering? | Judging from the explanation, ward in R was first implemented incorrectly.
Only in recent versions, a corrected version of ward linkage was added, as ward.D2. So if you want to use ward linkage, use w | Is there an advantage to squaring dissimilarities when using Ward clustering?
Judging from the explanation, ward in R was first implemented incorrectly.
Only in recent versions, a corrected version of ward linkage was added, as ward.D2. So if you want to use ward linkage, use ward.D2. | Is there an advantage to squaring dissimilarities when using Ward clustering?
Judging from the explanation, ward in R was first implemented incorrectly.
Only in recent versions, a corrected version of ward linkage was added, as ward.D2. So if you want to use ward linkage, use w |
42,085 | Bayesian inferencing: how iterative parameter updates work? | The problem of finding the hyperparameters is called evidence approximation. It is nicely explained in Bishop's book (page 166), or else in this paper, in great detail.
The idea is that your problem has the canonical form (the predictive distribution for a new sample),
$$
p(t|\mathbf{t}) = \int p(t|\mathbf{w},\alpha) p... | Bayesian inferencing: how iterative parameter updates work? | The problem of finding the hyperparameters is called evidence approximation. It is nicely explained in Bishop's book (page 166), or else in this paper, in great detail.
The idea is that your problem h | Bayesian inferencing: how iterative parameter updates work?
The problem of finding the hyperparameters is called evidence approximation. It is nicely explained in Bishop's book (page 166), or else in this paper, in great detail.
The idea is that your problem has the canonical form (the predictive distribution for a new... | Bayesian inferencing: how iterative parameter updates work?
The problem of finding the hyperparameters is called evidence approximation. It is nicely explained in Bishop's book (page 166), or else in this paper, in great detail.
The idea is that your problem h |
42,086 | Bayesian inferencing: how iterative parameter updates work? | Ok, I finally figured out the intuitive reason or this. Thanks to @juampa for the tip. The thing in Bishop's book that brought home the point for me was figure 3.13. The thing is that we need to think what happens to the model evidence with relation to model complexity.
So, in my example when the regularisation term $... | Bayesian inferencing: how iterative parameter updates work? | Ok, I finally figured out the intuitive reason or this. Thanks to @juampa for the tip. The thing in Bishop's book that brought home the point for me was figure 3.13. The thing is that we need to thin | Bayesian inferencing: how iterative parameter updates work?
Ok, I finally figured out the intuitive reason or this. Thanks to @juampa for the tip. The thing in Bishop's book that brought home the point for me was figure 3.13. The thing is that we need to think what happens to the model evidence with relation to model ... | Bayesian inferencing: how iterative parameter updates work?
Ok, I finally figured out the intuitive reason or this. Thanks to @juampa for the tip. The thing in Bishop's book that brought home the point for me was figure 3.13. The thing is that we need to thin |
42,087 | What does "PCA (Principal Component Analysis) spheres the data" mean? | Your understanding is right. Have a look at this figure which represents various possibilities of your data points: http://shapeofdata.files.wordpress.com/2013/02/pca22.png
They look ellipsoidal. If you do what you've described above i.e. compress the points in the direction in which they are spread the most (approx th... | What does "PCA (Principal Component Analysis) spheres the data" mean? | Your understanding is right. Have a look at this figure which represents various possibilities of your data points: http://shapeofdata.files.wordpress.com/2013/02/pca22.png
They look ellipsoidal. If y | What does "PCA (Principal Component Analysis) spheres the data" mean?
Your understanding is right. Have a look at this figure which represents various possibilities of your data points: http://shapeofdata.files.wordpress.com/2013/02/pca22.png
They look ellipsoidal. If you do what you've described above i.e. compress th... | What does "PCA (Principal Component Analysis) spheres the data" mean?
Your understanding is right. Have a look at this figure which represents various possibilities of your data points: http://shapeofdata.files.wordpress.com/2013/02/pca22.png
They look ellipsoidal. If y |
42,088 | Statistics for Area under the ROC curve | An alternative given by [1] is to compute the interval for the logit AUC:
$ log \left( \frac{AUC}{1-AUC} \right) \pm \phi ^{-1} \left( 1 - \frac{\alpha}{2} \right) \frac{\sqrt{AUC}}{AUC(1 - AUC)} $
so that you get an asymmetric interval. In your case, you would get a 95% CI $(0.38, 0.81)$.
If you are frequently dealing... | Statistics for Area under the ROC curve | An alternative given by [1] is to compute the interval for the logit AUC:
$ log \left( \frac{AUC}{1-AUC} \right) \pm \phi ^{-1} \left( 1 - \frac{\alpha}{2} \right) \frac{\sqrt{AUC}}{AUC(1 - AUC)} $
so | Statistics for Area under the ROC curve
An alternative given by [1] is to compute the interval for the logit AUC:
$ log \left( \frac{AUC}{1-AUC} \right) \pm \phi ^{-1} \left( 1 - \frac{\alpha}{2} \right) \frac{\sqrt{AUC}}{AUC(1 - AUC)} $
so that you get an asymmetric interval. In your case, you would get a 95% CI $(0.3... | Statistics for Area under the ROC curve
An alternative given by [1] is to compute the interval for the logit AUC:
$ log \left( \frac{AUC}{1-AUC} \right) \pm \phi ^{-1} \left( 1 - \frac{\alpha}{2} \right) \frac{\sqrt{AUC}}{AUC(1 - AUC)} $
so |
42,089 | Zero-inflated two-part models for semi-continuous data | Not sure about Stata, but R can run zero-inflated models with fixed effects. Check out, for example, the gamlss package and zeroinfl() from the pscl package. | Zero-inflated two-part models for semi-continuous data | Not sure about Stata, but R can run zero-inflated models with fixed effects. Check out, for example, the gamlss package and zeroinfl() from the pscl package. | Zero-inflated two-part models for semi-continuous data
Not sure about Stata, but R can run zero-inflated models with fixed effects. Check out, for example, the gamlss package and zeroinfl() from the pscl package. | Zero-inflated two-part models for semi-continuous data
Not sure about Stata, but R can run zero-inflated models with fixed effects. Check out, for example, the gamlss package and zeroinfl() from the pscl package. |
42,090 | Zero-inflated two-part models for semi-continuous data | Disadvantages of $\ln(0+c)$:
$c=1$ is arbitrary. Often the value of $c$ changes estimates, so you need to conduct a grid search for the "optimal" result and justify
that choice in the end
Zero mass may respond differently to covariates (extensive vs. intensive margin may have different DGPs)
Retransformation back to n... | Zero-inflated two-part models for semi-continuous data | Disadvantages of $\ln(0+c)$:
$c=1$ is arbitrary. Often the value of $c$ changes estimates, so you need to conduct a grid search for the "optimal" result and justify
that choice in the end
Zero mass m | Zero-inflated two-part models for semi-continuous data
Disadvantages of $\ln(0+c)$:
$c=1$ is arbitrary. Often the value of $c$ changes estimates, so you need to conduct a grid search for the "optimal" result and justify
that choice in the end
Zero mass may respond differently to covariates (extensive vs. intensive mar... | Zero-inflated two-part models for semi-continuous data
Disadvantages of $\ln(0+c)$:
$c=1$ is arbitrary. Often the value of $c$ changes estimates, so you need to conduct a grid search for the "optimal" result and justify
that choice in the end
Zero mass m |
42,091 | Regression in $p\gg N$ setting (predicting drug efficiency from gene expression with 30k predictors and ~30 samples) | Most of the 31000 genes are unlikely to differ much in expression among the cell lines (at least when appropriately normalized), so they add no information to the problem.
For a practical biological problem like this, it may help to concentrate on genes whose expression levels are relatively high on an absolute basis. ... | Regression in $p\gg N$ setting (predicting drug efficiency from gene expression with 30k predictors | Most of the 31000 genes are unlikely to differ much in expression among the cell lines (at least when appropriately normalized), so they add no information to the problem.
For a practical biological p | Regression in $p\gg N$ setting (predicting drug efficiency from gene expression with 30k predictors and ~30 samples)
Most of the 31000 genes are unlikely to differ much in expression among the cell lines (at least when appropriately normalized), so they add no information to the problem.
For a practical biological prob... | Regression in $p\gg N$ setting (predicting drug efficiency from gene expression with 30k predictors
Most of the 31000 genes are unlikely to differ much in expression among the cell lines (at least when appropriately normalized), so they add no information to the problem.
For a practical biological p |
42,092 | Regression in $p\gg N$ setting (predicting drug efficiency from gene expression with 30k predictors and ~30 samples) | I believe the reason you will be getting varying answers is because you have $p>>n$, i.e more variables than samples. In this situation the LASSO can only selected $n$ variable and I assume will have problems with convergence. While having no experience with dealing with this, the Elastic Net supposedly overcomes some ... | Regression in $p\gg N$ setting (predicting drug efficiency from gene expression with 30k predictors | I believe the reason you will be getting varying answers is because you have $p>>n$, i.e more variables than samples. In this situation the LASSO can only selected $n$ variable and I assume will have | Regression in $p\gg N$ setting (predicting drug efficiency from gene expression with 30k predictors and ~30 samples)
I believe the reason you will be getting varying answers is because you have $p>>n$, i.e more variables than samples. In this situation the LASSO can only selected $n$ variable and I assume will have pro... | Regression in $p\gg N$ setting (predicting drug efficiency from gene expression with 30k predictors
I believe the reason you will be getting varying answers is because you have $p>>n$, i.e more variables than samples. In this situation the LASSO can only selected $n$ variable and I assume will have |
42,093 | Regression in $p\gg N$ setting (predicting drug efficiency from gene expression with 30k predictors and ~30 samples) | Can I suggest you the paper robustness of lasso solutions under cross-validation variability and Stability selection (Meinshausen and Bruhlman, 2009)?
They propose stable version of the lasso estimator. | Regression in $p\gg N$ setting (predicting drug efficiency from gene expression with 30k predictors | Can I suggest you the paper robustness of lasso solutions under cross-validation variability and Stability selection (Meinshausen and Bruhlman, 2009)?
They propose stable version of the lasso estimato | Regression in $p\gg N$ setting (predicting drug efficiency from gene expression with 30k predictors and ~30 samples)
Can I suggest you the paper robustness of lasso solutions under cross-validation variability and Stability selection (Meinshausen and Bruhlman, 2009)?
They propose stable version of the lasso estimator. | Regression in $p\gg N$ setting (predicting drug efficiency from gene expression with 30k predictors
Can I suggest you the paper robustness of lasso solutions under cross-validation variability and Stability selection (Meinshausen and Bruhlman, 2009)?
They propose stable version of the lasso estimato |
42,094 | Estimated variance using linear factor models | There exists a basic result in least squares algebra that says that, in a linear regression and using OLS estimation, regressing a variable on a set of regressors plus a constant, is equivalent (in a mathematically exact way) to estimating using the dependent variable and the regressors as deviations from their respect... | Estimated variance using linear factor models | There exists a basic result in least squares algebra that says that, in a linear regression and using OLS estimation, regressing a variable on a set of regressors plus a constant, is equivalent (in a | Estimated variance using linear factor models
There exists a basic result in least squares algebra that says that, in a linear regression and using OLS estimation, regressing a variable on a set of regressors plus a constant, is equivalent (in a mathematically exact way) to estimating using the dependent variable and t... | Estimated variance using linear factor models
There exists a basic result in least squares algebra that says that, in a linear regression and using OLS estimation, regressing a variable on a set of regressors plus a constant, is equivalent (in a |
42,095 | Estimated variance using linear factor models | The values are not exactly the same, but are very close. This appears to be purely accidental when we look at what goes into them:
Model beta'*Sigma*beta Deviance DF Deviance/DF "est.var"
1 0.0001504468 0.0005199823 1256 4.139987e-07 0.0001508608
2 9.168255e-08 0.1896668 1256 ... | Estimated variance using linear factor models | The values are not exactly the same, but are very close. This appears to be purely accidental when we look at what goes into them:
Model beta'*Sigma*beta Deviance DF Deviance/DF "est.var | Estimated variance using linear factor models
The values are not exactly the same, but are very close. This appears to be purely accidental when we look at what goes into them:
Model beta'*Sigma*beta Deviance DF Deviance/DF "est.var"
1 0.0001504468 0.0005199823 1256 4.139987e-07 0.0001508608... | Estimated variance using linear factor models
The values are not exactly the same, but are very close. This appears to be purely accidental when we look at what goes into them:
Model beta'*Sigma*beta Deviance DF Deviance/DF "est.var |
42,096 | Prove that distribution of sample median (for even sample) is symmetric | To those comfortable with the mathematics of probability and random variables the following argument is a one-liner, because you will take for granted most of the manipulation (and will find it obvious). To cover all bases, though, I provide the details.
The setting--and a generalization
Let $X = (X_1, X_2, \ldots, X_... | Prove that distribution of sample median (for even sample) is symmetric | To those comfortable with the mathematics of probability and random variables the following argument is a one-liner, because you will take for granted most of the manipulation (and will find it obviou | Prove that distribution of sample median (for even sample) is symmetric
To those comfortable with the mathematics of probability and random variables the following argument is a one-liner, because you will take for granted most of the manipulation (and will find it obvious). To cover all bases, though, I provide the d... | Prove that distribution of sample median (for even sample) is symmetric
To those comfortable with the mathematics of probability and random variables the following argument is a one-liner, because you will take for granted most of the manipulation (and will find it obviou |
42,097 | Covariance pattern models versus generalized estimating equation models | Actually you have correctly listed the major differences between the covariance pattern models and GEE models. One thing I would like to add is that, for the Section 6.2.5 "Random Effects Structure" of Hedeker and Gibbons (2006), the two models would be characterized as subject-specific (conditional) models and populat... | Covariance pattern models versus generalized estimating equation models | Actually you have correctly listed the major differences between the covariance pattern models and GEE models. One thing I would like to add is that, for the Section 6.2.5 "Random Effects Structure" o | Covariance pattern models versus generalized estimating equation models
Actually you have correctly listed the major differences between the covariance pattern models and GEE models. One thing I would like to add is that, for the Section 6.2.5 "Random Effects Structure" of Hedeker and Gibbons (2006), the two models wou... | Covariance pattern models versus generalized estimating equation models
Actually you have correctly listed the major differences between the covariance pattern models and GEE models. One thing I would like to add is that, for the Section 6.2.5 "Random Effects Structure" o |
42,098 | Could prior elicitation by actually drawing the density of the prior be sensible? Has it been done/discussed? | The TeachingDemos package for R has the TkBuildDist and TkBuildDist2 functions that provide interactive ways to draw a histogram and/or log density plot for creating a histogram. The first one uses left clicks to add points and right clicks to remove points and the second allows you to click on the tops of bars and dr... | Could prior elicitation by actually drawing the density of the prior be sensible? Has it been done/d | The TeachingDemos package for R has the TkBuildDist and TkBuildDist2 functions that provide interactive ways to draw a histogram and/or log density plot for creating a histogram. The first one uses l | Could prior elicitation by actually drawing the density of the prior be sensible? Has it been done/discussed?
The TeachingDemos package for R has the TkBuildDist and TkBuildDist2 functions that provide interactive ways to draw a histogram and/or log density plot for creating a histogram. The first one uses left clicks... | Could prior elicitation by actually drawing the density of the prior be sensible? Has it been done/d
The TeachingDemos package for R has the TkBuildDist and TkBuildDist2 functions that provide interactive ways to draw a histogram and/or log density plot for creating a histogram. The first one uses l |
42,099 | Could prior elicitation by actually drawing the density of the prior be sensible? Has it been done/discussed? | So, I found the "trial roulette method" described here which is I guess could be considered as drawing with chips. More info in the picture below: | Could prior elicitation by actually drawing the density of the prior be sensible? Has it been done/d | So, I found the "trial roulette method" described here which is I guess could be considered as drawing with chips. More info in the picture below: | Could prior elicitation by actually drawing the density of the prior be sensible? Has it been done/discussed?
So, I found the "trial roulette method" described here which is I guess could be considered as drawing with chips. More info in the picture below: | Could prior elicitation by actually drawing the density of the prior be sensible? Has it been done/d
So, I found the "trial roulette method" described here which is I guess could be considered as drawing with chips. More info in the picture below: |
42,100 | Quantile regression power analysis | For general linear quantile models of the form
$$F^{-1}_{Y|X}(\tau) = X'\beta_n(\tau)$$
where $\beta_n$ is allowed to depend on the sample size, Chernozhukov and Fernandez-Val (2005) construct a power analysis for conditional quantile regression models as in your case. They consider the general null hypothesis
$$R(\tau... | Quantile regression power analysis | For general linear quantile models of the form
$$F^{-1}_{Y|X}(\tau) = X'\beta_n(\tau)$$
where $\beta_n$ is allowed to depend on the sample size, Chernozhukov and Fernandez-Val (2005) construct a power | Quantile regression power analysis
For general linear quantile models of the form
$$F^{-1}_{Y|X}(\tau) = X'\beta_n(\tau)$$
where $\beta_n$ is allowed to depend on the sample size, Chernozhukov and Fernandez-Val (2005) construct a power analysis for conditional quantile regression models as in your case. They consider t... | Quantile regression power analysis
For general linear quantile models of the form
$$F^{-1}_{Y|X}(\tau) = X'\beta_n(\tau)$$
where $\beta_n$ is allowed to depend on the sample size, Chernozhukov and Fernandez-Val (2005) construct a power |
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