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 |
|---|---|---|---|---|---|---|
50,801 | Forecasting demographic census | I don't know about the first point. But for the second one, autoregressive (AR) functions could be simple. I would really chose a parametric method against a non-parametric one. The forecasting in AR is straight forward. And consensus data has lots of samples for each period so you can get robust parameter estimates at... | Forecasting demographic census | I don't know about the first point. But for the second one, autoregressive (AR) functions could be simple. I would really chose a parametric method against a non-parametric one. The forecasting in AR | Forecasting demographic census
I don't know about the first point. But for the second one, autoregressive (AR) functions could be simple. I would really chose a parametric method against a non-parametric one. The forecasting in AR is straight forward. And consensus data has lots of samples for each period so you can ge... | Forecasting demographic census
I don't know about the first point. But for the second one, autoregressive (AR) functions could be simple. I would really chose a parametric method against a non-parametric one. The forecasting in AR |
50,802 | Prediction of the 1st stage in 2SLS not important? | Do we care how accurate the prediction of x^ actually is?
Yes, we definitely do. The instruments must be valid for the model to be considered acceptable. Any unnecessary instruments will not predict the x^ accurately. To check if the instruments are valid (predicting well), you can apply the Sargan Test. This test wil... | Prediction of the 1st stage in 2SLS not important? | Do we care how accurate the prediction of x^ actually is?
Yes, we definitely do. The instruments must be valid for the model to be considered acceptable. Any unnecessary instruments will not predict | Prediction of the 1st stage in 2SLS not important?
Do we care how accurate the prediction of x^ actually is?
Yes, we definitely do. The instruments must be valid for the model to be considered acceptable. Any unnecessary instruments will not predict the x^ accurately. To check if the instruments are valid (predicting ... | Prediction of the 1st stage in 2SLS not important?
Do we care how accurate the prediction of x^ actually is?
Yes, we definitely do. The instruments must be valid for the model to be considered acceptable. Any unnecessary instruments will not predict |
50,803 | Number of samples in scikit-Learn cost function for Ridge/Lasso regression | You are right that the standartization $\gamma = \frac{c}{n}$, where $n$ is the sample size, aims to make regularization term $\alpha$ invariant to different sample sizes. This makes sense for Lasso-like models that compute coefficients coordinate-wise via soft-thresholding:
$$
\mathbf{w}_j \leftarrow \mathcal{S}_{\alp... | Number of samples in scikit-Learn cost function for Ridge/Lasso regression | You are right that the standartization $\gamma = \frac{c}{n}$, where $n$ is the sample size, aims to make regularization term $\alpha$ invariant to different sample sizes. This makes sense for Lasso-l | Number of samples in scikit-Learn cost function for Ridge/Lasso regression
You are right that the standartization $\gamma = \frac{c}{n}$, where $n$ is the sample size, aims to make regularization term $\alpha$ invariant to different sample sizes. This makes sense for Lasso-like models that compute coefficients coordina... | Number of samples in scikit-Learn cost function for Ridge/Lasso regression
You are right that the standartization $\gamma = \frac{c}{n}$, where $n$ is the sample size, aims to make regularization term $\alpha$ invariant to different sample sizes. This makes sense for Lasso-l |
50,804 | Nuisance parameters and $o_p(n^{-1/4})$ convergence: citation | The paper I'm looking for appears to be
Newey, W. K. (1994). The Asymptotic Variance of Semiparametric Estimators. Econometrica, 62(6), 1349–1382. https://doi.org/10.2307/2951752
The fourth-root convergence assumption appears in the discussion following Assumption 5.1 | Nuisance parameters and $o_p(n^{-1/4})$ convergence: citation | The paper I'm looking for appears to be
Newey, W. K. (1994). The Asymptotic Variance of Semiparametric Estimators. Econometrica, 62(6), 1349–1382. https://doi.org/10.2307/2951752
The fourth-root conve | Nuisance parameters and $o_p(n^{-1/4})$ convergence: citation
The paper I'm looking for appears to be
Newey, W. K. (1994). The Asymptotic Variance of Semiparametric Estimators. Econometrica, 62(6), 1349–1382. https://doi.org/10.2307/2951752
The fourth-root convergence assumption appears in the discussion following Assu... | Nuisance parameters and $o_p(n^{-1/4})$ convergence: citation
The paper I'm looking for appears to be
Newey, W. K. (1994). The Asymptotic Variance of Semiparametric Estimators. Econometrica, 62(6), 1349–1382. https://doi.org/10.2307/2951752
The fourth-root conve |
50,805 | Statistical significance or Hypothesis testing? [duplicate] | Two questions on Cross Validated that contain answers:
What is the difference between "testing of hypothesis" and "test of significance"?
Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoherent mishmash"?
Papers that explain in depth with historical context:
Goodman, To... | Statistical significance or Hypothesis testing? [duplicate] | Two questions on Cross Validated that contain answers:
What is the difference between "testing of hypothesis" and "test of significance"?
Is the "hybrid" between Fisher and Neyman-Pearson approaches t | Statistical significance or Hypothesis testing? [duplicate]
Two questions on Cross Validated that contain answers:
What is the difference between "testing of hypothesis" and "test of significance"?
Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoherent mishmash"?
Paper... | Statistical significance or Hypothesis testing? [duplicate]
Two questions on Cross Validated that contain answers:
What is the difference between "testing of hypothesis" and "test of significance"?
Is the "hybrid" between Fisher and Neyman-Pearson approaches t |
50,806 | Wilcoxon–Mann–Whitney test sample size | Very roughly, suppose $\sigma/\Delta = 5,$ (where $\sigma$ is population standard deviation, $\Delta$ is effect size; maybe $\sigma=10, \Delta=2.)$ and desired power is 95%, then for a pooled t test $n \approx 650$ is required in each group (version), according to an on-line calculator here for pooled 2-sample t tests ... | Wilcoxon–Mann–Whitney test sample size | Very roughly, suppose $\sigma/\Delta = 5,$ (where $\sigma$ is population standard deviation, $\Delta$ is effect size; maybe $\sigma=10, \Delta=2.)$ and desired power is 95%, then for a pooled t test $ | Wilcoxon–Mann–Whitney test sample size
Very roughly, suppose $\sigma/\Delta = 5,$ (where $\sigma$ is population standard deviation, $\Delta$ is effect size; maybe $\sigma=10, \Delta=2.)$ and desired power is 95%, then for a pooled t test $n \approx 650$ is required in each group (version), according to an on-line calcu... | Wilcoxon–Mann–Whitney test sample size
Very roughly, suppose $\sigma/\Delta = 5,$ (where $\sigma$ is population standard deviation, $\Delta$ is effect size; maybe $\sigma=10, \Delta=2.)$ and desired power is 95%, then for a pooled t test $ |
50,807 | Decision Theory: Why is it called a "least favorable prior"? | I'm not sure how the name originates but here is my opinion on it.
The Bayes risk is some average of the risk function of the Bayes estimator, weighted by the prior. The least favorable prior only places weight on the part of the risk function that achieves the supremum. One example of such could be a Dirac delta at th... | Decision Theory: Why is it called a "least favorable prior"? | I'm not sure how the name originates but here is my opinion on it.
The Bayes risk is some average of the risk function of the Bayes estimator, weighted by the prior. The least favorable prior only pla | Decision Theory: Why is it called a "least favorable prior"?
I'm not sure how the name originates but here is my opinion on it.
The Bayes risk is some average of the risk function of the Bayes estimator, weighted by the prior. The least favorable prior only places weight on the part of the risk function that achieves t... | Decision Theory: Why is it called a "least favorable prior"?
I'm not sure how the name originates but here is my opinion on it.
The Bayes risk is some average of the risk function of the Bayes estimator, weighted by the prior. The least favorable prior only pla |
50,808 | When to care about FDR vs when to care about FWER | In the simplest possible terms, you control FWER when you care about the result of the specific hypotheses tested whereas you control FDR when you care about the number of significant results.
Here's my take on an example justifying FDR: suppose, for instance, you are exploring an in vitro or pharmacodynamic study of t... | When to care about FDR vs when to care about FWER | In the simplest possible terms, you control FWER when you care about the result of the specific hypotheses tested whereas you control FDR when you care about the number of significant results.
Here's | When to care about FDR vs when to care about FWER
In the simplest possible terms, you control FWER when you care about the result of the specific hypotheses tested whereas you control FDR when you care about the number of significant results.
Here's my take on an example justifying FDR: suppose, for instance, you are e... | When to care about FDR vs when to care about FWER
In the simplest possible terms, you control FWER when you care about the result of the specific hypotheses tested whereas you control FDR when you care about the number of significant results.
Here's |
50,809 | When to care about FDR vs when to care about FWER | Great question @Tobl, I had the same therefore I'm sharing the insights that I've been able to find hoping that they are enough or they can lead us to a constructive discussion.
I'm now wondering, from a very practical standpoint, when is it acceptable to use Benjamini-Hochberg to control FDR, and when must I strictly... | When to care about FDR vs when to care about FWER | Great question @Tobl, I had the same therefore I'm sharing the insights that I've been able to find hoping that they are enough or they can lead us to a constructive discussion.
I'm now wondering, fr | When to care about FDR vs when to care about FWER
Great question @Tobl, I had the same therefore I'm sharing the insights that I've been able to find hoping that they are enough or they can lead us to a constructive discussion.
I'm now wondering, from a very practical standpoint, when is it acceptable to use Benjamini... | When to care about FDR vs when to care about FWER
Great question @Tobl, I had the same therefore I'm sharing the insights that I've been able to find hoping that they are enough or they can lead us to a constructive discussion.
I'm now wondering, fr |
50,810 | Is there a formula for the determinant of the covariance matrix $\mathbf{X_n}^T \mathbf{X_n}$ in the case of multiple regression? | Just the 2) since I am not professor:
$\mathbf X^T \mathbf X$ is positive definite where $\mathsf {rk}(\mathbf X)=max(n,p+1)$ or maximum number of independent rows which leads the determinant you ask is positive since it is a product of $p+1$ eigenvalues of $\mathbf X^T \mathbf X$.
It's more fair to write $\mathbf X_{n... | Is there a formula for the determinant of the covariance matrix $\mathbf{X_n}^T \mathbf{X_n}$ in the | Just the 2) since I am not professor:
$\mathbf X^T \mathbf X$ is positive definite where $\mathsf {rk}(\mathbf X)=max(n,p+1)$ or maximum number of independent rows which leads the determinant you ask | Is there a formula for the determinant of the covariance matrix $\mathbf{X_n}^T \mathbf{X_n}$ in the case of multiple regression?
Just the 2) since I am not professor:
$\mathbf X^T \mathbf X$ is positive definite where $\mathsf {rk}(\mathbf X)=max(n,p+1)$ or maximum number of independent rows which leads the determinan... | Is there a formula for the determinant of the covariance matrix $\mathbf{X_n}^T \mathbf{X_n}$ in the
Just the 2) since I am not professor:
$\mathbf X^T \mathbf X$ is positive definite where $\mathsf {rk}(\mathbf X)=max(n,p+1)$ or maximum number of independent rows which leads the determinant you ask |
50,811 | $X\sim\frac{1}{b}\exp\{-\frac{1}{b}(x-a)\},x>a$. Find UMVUE of $\frac{a}{b}$ | Since nobody answered, I'll try to answer my own question. Please let me know if anything is not correct.
Denote $S=\frac{1}{n-1}\sum_{i=1}^n[X_i-X_{(1)}]$. We have $$S\sim \frac{b}{n-1}\text{Gamma}(n-2,1),$$
and
$$\frac{1}{S}\sim \frac{n-1}{b}\text{inv-Gamma}(n-2,1)$$
These implies $$\mathbb{E}\frac{1}{S}=\frac{n-1}{b... | $X\sim\frac{1}{b}\exp\{-\frac{1}{b}(x-a)\},x>a$. Find UMVUE of $\frac{a}{b}$ | Since nobody answered, I'll try to answer my own question. Please let me know if anything is not correct.
Denote $S=\frac{1}{n-1}\sum_{i=1}^n[X_i-X_{(1)}]$. We have $$S\sim \frac{b}{n-1}\text{Gamma}(n | $X\sim\frac{1}{b}\exp\{-\frac{1}{b}(x-a)\},x>a$. Find UMVUE of $\frac{a}{b}$
Since nobody answered, I'll try to answer my own question. Please let me know if anything is not correct.
Denote $S=\frac{1}{n-1}\sum_{i=1}^n[X_i-X_{(1)}]$. We have $$S\sim \frac{b}{n-1}\text{Gamma}(n-2,1),$$
and
$$\frac{1}{S}\sim \frac{n-1}{b... | $X\sim\frac{1}{b}\exp\{-\frac{1}{b}(x-a)\},x>a$. Find UMVUE of $\frac{a}{b}$
Since nobody answered, I'll try to answer my own question. Please let me know if anything is not correct.
Denote $S=\frac{1}{n-1}\sum_{i=1}^n[X_i-X_{(1)}]$. We have $$S\sim \frac{b}{n-1}\text{Gamma}(n |
50,812 | In linear regression, we have 0 training error if data dimension is high, but are there similar results for other supervised learning problems? | Let me start with the linear regression case. Consider:
$$
Xb = y
$$
where $X$ is a $n\times p$ matrix, $y$ is a $n$-vector, and $b$ is a $p$-vector. If and only if there exists $b$ that satisfies this equation, we can achieve the zero training error for the linear regression. "If" part is trivial. "Only if" part c... | In linear regression, we have 0 training error if data dimension is high, but are there similar resu | Let me start with the linear regression case. Consider:
$$
Xb = y
$$
where $X$ is a $n\times p$ matrix, $y$ is a $n$-vector, and $b$ is a $p$-vector. If and only if there exists $b$ that satisfies t | In linear regression, we have 0 training error if data dimension is high, but are there similar results for other supervised learning problems?
Let me start with the linear regression case. Consider:
$$
Xb = y
$$
where $X$ is a $n\times p$ matrix, $y$ is a $n$-vector, and $b$ is a $p$-vector. If and only if there exi... | In linear regression, we have 0 training error if data dimension is high, but are there similar resu
Let me start with the linear regression case. Consider:
$$
Xb = y
$$
where $X$ is a $n\times p$ matrix, $y$ is a $n$-vector, and $b$ is a $p$-vector. If and only if there exists $b$ that satisfies t |
50,813 | one example of LDA and max number of features | About linear discriminant analysis
A classical example of least discriminant analysis is R.A. Fisher's 1936 article "The use of multiple measurements in taxonomic problems". This is based on the iris dataset and easily plotted.
### load library
### with Edgar Anderson's Iris data set
### and the lda function
library(... | one example of LDA and max number of features | About linear discriminant analysis
A classical example of least discriminant analysis is R.A. Fisher's 1936 article "The use of multiple measurements in taxonomic problems". This is based on the iris | one example of LDA and max number of features
About linear discriminant analysis
A classical example of least discriminant analysis is R.A. Fisher's 1936 article "The use of multiple measurements in taxonomic problems". This is based on the iris dataset and easily plotted.
### load library
### with Edgar Anderson's Ir... | one example of LDA and max number of features
About linear discriminant analysis
A classical example of least discriminant analysis is R.A. Fisher's 1936 article "The use of multiple measurements in taxonomic problems". This is based on the iris |
50,814 | Expected squared distance between order statistics? | The terms of this sum are known exactly for some distributions, since
$$E[(X_{(i)}-Y_{(i)})^2]=E[X_{(i)}^2]-2E[X_{(i)}]E[Y_{(i)}]+E[Y_{(i)}^2]=2\text{Var}[X_{(i)}].$$
For those distributions, we can get some nice expressions for the limiting behavior.
In what follows, $\psi_1(z)$ is the trigamma function $d^2\log \Gamm... | Expected squared distance between order statistics? | The terms of this sum are known exactly for some distributions, since
$$E[(X_{(i)}-Y_{(i)})^2]=E[X_{(i)}^2]-2E[X_{(i)}]E[Y_{(i)}]+E[Y_{(i)}^2]=2\text{Var}[X_{(i)}].$$
For those distributions, we can g | Expected squared distance between order statistics?
The terms of this sum are known exactly for some distributions, since
$$E[(X_{(i)}-Y_{(i)})^2]=E[X_{(i)}^2]-2E[X_{(i)}]E[Y_{(i)}]+E[Y_{(i)}^2]=2\text{Var}[X_{(i)}].$$
For those distributions, we can get some nice expressions for the limiting behavior.
In what follows,... | Expected squared distance between order statistics?
The terms of this sum are known exactly for some distributions, since
$$E[(X_{(i)}-Y_{(i)})^2]=E[X_{(i)}^2]-2E[X_{(i)}]E[Y_{(i)}]+E[Y_{(i)}^2]=2\text{Var}[X_{(i)}].$$
For those distributions, we can g |
50,815 | Transfer Learning: data in the source domain and the target domain are required to be independent and identically distributed | I don't know what exactly was meant by the original statement, but it may include some or all of below statements
Source data generative process is i.i.d
Target data generative process is i.i.d
The processes are i.i.d with each other
All of these are very sensible standard assumptions, because if this is not the case... | Transfer Learning: data in the source domain and the target domain are required to be independent an | I don't know what exactly was meant by the original statement, but it may include some or all of below statements
Source data generative process is i.i.d
Target data generative process is i.i.d
The p | Transfer Learning: data in the source domain and the target domain are required to be independent and identically distributed
I don't know what exactly was meant by the original statement, but it may include some or all of below statements
Source data generative process is i.i.d
Target data generative process is i.i.d... | Transfer Learning: data in the source domain and the target domain are required to be independent an
I don't know what exactly was meant by the original statement, but it may include some or all of below statements
Source data generative process is i.i.d
Target data generative process is i.i.d
The p |
50,816 | Bias-Variance decomposition: Expectations over what? | The Bias-Variance Decomposition is done to the prediction error on a fixed observation in the test set.
We assume we resample our training set again and again and re-train the model with each of the resampled train sets.
For example, the estimation of the error goes in this way: After we get $N$ train sets by resampli... | Bias-Variance decomposition: Expectations over what? | The Bias-Variance Decomposition is done to the prediction error on a fixed observation in the test set.
We assume we resample our training set again and again and re-train the model with each of the | Bias-Variance decomposition: Expectations over what?
The Bias-Variance Decomposition is done to the prediction error on a fixed observation in the test set.
We assume we resample our training set again and again and re-train the model with each of the resampled train sets.
For example, the estimation of the error goes... | Bias-Variance decomposition: Expectations over what?
The Bias-Variance Decomposition is done to the prediction error on a fixed observation in the test set.
We assume we resample our training set again and again and re-train the model with each of the |
50,817 | Why aren't neural networks used with RBF activation functions (or other non-monotonic ones)? | Seems that some people are a bit confused by your question because of its title; indeed, RBF neural networks exist, but they are a different architecture than the traditional multi-layer NNs. The body of your question is complete and formulated well (apart from some ambiguity because of the use of MLP), so to get to th... | Why aren't neural networks used with RBF activation functions (or other non-monotonic ones)? | Seems that some people are a bit confused by your question because of its title; indeed, RBF neural networks exist, but they are a different architecture than the traditional multi-layer NNs. The body | Why aren't neural networks used with RBF activation functions (or other non-monotonic ones)?
Seems that some people are a bit confused by your question because of its title; indeed, RBF neural networks exist, but they are a different architecture than the traditional multi-layer NNs. The body of your question is comple... | Why aren't neural networks used with RBF activation functions (or other non-monotonic ones)?
Seems that some people are a bit confused by your question because of its title; indeed, RBF neural networks exist, but they are a different architecture than the traditional multi-layer NNs. The body |
50,818 | CDF that combines properties of Pareto and Exponential | The only possible distribution on $[1,\infty)$ satisfying the key equation above of
\begin{align}
P[&Y>ay+b]=z(a,b)\,P[Y>y]\\
&\text{ whenever } a>0, b\le 0, y\ge 1
\end{align}
is the distribution with $P[Y=1]=1$, concentrated entirely at $y=1$.
If the distribution is not concentrated entirely at $Y=1$, then:
Let $s$ ... | CDF that combines properties of Pareto and Exponential | The only possible distribution on $[1,\infty)$ satisfying the key equation above of
\begin{align}
P[&Y>ay+b]=z(a,b)\,P[Y>y]\\
&\text{ whenever } a>0, b\le 0, y\ge 1
\end{align}
is the distribution wit | CDF that combines properties of Pareto and Exponential
The only possible distribution on $[1,\infty)$ satisfying the key equation above of
\begin{align}
P[&Y>ay+b]=z(a,b)\,P[Y>y]\\
&\text{ whenever } a>0, b\le 0, y\ge 1
\end{align}
is the distribution with $P[Y=1]=1$, concentrated entirely at $y=1$.
If the distribution... | CDF that combines properties of Pareto and Exponential
The only possible distribution on $[1,\infty)$ satisfying the key equation above of
\begin{align}
P[&Y>ay+b]=z(a,b)\,P[Y>y]\\
&\text{ whenever } a>0, b\le 0, y\ge 1
\end{align}
is the distribution wit |
50,819 | Recover full covariance matrix from covariance diagonal and precision off-diagonals | This can be setup as a non-linear system of equations. Because of non-linearity, it is not obvious that the system has a unique solution, but I did for the $2\times 2$-case, where it is unique as far as I can see.
But the equations become unwieldy, so in practice it seems easier to formulate it as a minimization proble... | Recover full covariance matrix from covariance diagonal and precision off-diagonals | This can be setup as a non-linear system of equations. Because of non-linearity, it is not obvious that the system has a unique solution, but I did for the $2\times 2$-case, where it is unique as far | Recover full covariance matrix from covariance diagonal and precision off-diagonals
This can be setup as a non-linear system of equations. Because of non-linearity, it is not obvious that the system has a unique solution, but I did for the $2\times 2$-case, where it is unique as far as I can see.
But the equations beco... | Recover full covariance matrix from covariance diagonal and precision off-diagonals
This can be setup as a non-linear system of equations. Because of non-linearity, it is not obvious that the system has a unique solution, but I did for the $2\times 2$-case, where it is unique as far |
50,820 | In a paired test, what constitutes a valid pair? | Yes, the two measurement methods could constitute a "pair" in this example. More concerning (in my opinion) is that a t-test will only help you identify a constant bias between methods A and B. There could be a proportional (and/or constant) bias(es) between the methods which a t-test is not well suited to identify. Co... | In a paired test, what constitutes a valid pair? | Yes, the two measurement methods could constitute a "pair" in this example. More concerning (in my opinion) is that a t-test will only help you identify a constant bias between methods A and B. There | In a paired test, what constitutes a valid pair?
Yes, the two measurement methods could constitute a "pair" in this example. More concerning (in my opinion) is that a t-test will only help you identify a constant bias between methods A and B. There could be a proportional (and/or constant) bias(es) between the methods ... | In a paired test, what constitutes a valid pair?
Yes, the two measurement methods could constitute a "pair" in this example. More concerning (in my opinion) is that a t-test will only help you identify a constant bias between methods A and B. There |
50,821 | Visualizing the Coronavirus COVID-19 epidemic? | Representing population data on a map is difficult and implies applying simplifications to understand the data « at a glance ». One of these is to use a scatter plot which is exactly what is shown in this data:
For the different data points, the size of the area is shown as a disk whose surface increases linearly with ... | Visualizing the Coronavirus COVID-19 epidemic? | Representing population data on a map is difficult and implies applying simplifications to understand the data « at a glance ». One of these is to use a scatter plot which is exactly what is shown in | Visualizing the Coronavirus COVID-19 epidemic?
Representing population data on a map is difficult and implies applying simplifications to understand the data « at a glance ». One of these is to use a scatter plot which is exactly what is shown in this data:
For the different data points, the size of the area is shown a... | Visualizing the Coronavirus COVID-19 epidemic?
Representing population data on a map is difficult and implies applying simplifications to understand the data « at a glance ». One of these is to use a scatter plot which is exactly what is shown in |
50,822 | Notation and meaning of a general probability distribution | A "probability distribution" can be uniquely described either by its CDF or the corresponding probability measure. Contrarily, a density function is often not a unique description of a probability distribution, and so it would not usually be used for statements of the equality of distributions.$^\dagger$ Unfortunatel... | Notation and meaning of a general probability distribution | A "probability distribution" can be uniquely described either by its CDF or the corresponding probability measure. Contrarily, a density function is often not a unique description of a probability di | Notation and meaning of a general probability distribution
A "probability distribution" can be uniquely described either by its CDF or the corresponding probability measure. Contrarily, a density function is often not a unique description of a probability distribution, and so it would not usually be used for statement... | Notation and meaning of a general probability distribution
A "probability distribution" can be uniquely described either by its CDF or the corresponding probability measure. Contrarily, a density function is often not a unique description of a probability di |
50,823 | Differentiable programming for general Bayesian decision theory | TensorFlow Probability is a standalone probabilistic programming module for TensorFlow, numpyro package uses JAX, while Pyro is a PyTorch framework. All those frameworks enable you to do Variational Inference and Markov Chain Monte Carlo sampling.
The simplest way of computing the expected posterior loss, is using Mont... | Differentiable programming for general Bayesian decision theory | TensorFlow Probability is a standalone probabilistic programming module for TensorFlow, numpyro package uses JAX, while Pyro is a PyTorch framework. All those frameworks enable you to do Variational I | Differentiable programming for general Bayesian decision theory
TensorFlow Probability is a standalone probabilistic programming module for TensorFlow, numpyro package uses JAX, while Pyro is a PyTorch framework. All those frameworks enable you to do Variational Inference and Markov Chain Monte Carlo sampling.
The simp... | Differentiable programming for general Bayesian decision theory
TensorFlow Probability is a standalone probabilistic programming module for TensorFlow, numpyro package uses JAX, while Pyro is a PyTorch framework. All those frameworks enable you to do Variational I |
50,824 | What distribution should I fit to this data | I've plotted log(data) vs abscissa and dropped two last points, graph below
data going below x=500 would be good fitted with just a linear function - which means exponential distribution because we plotted log(data).
But from 0 to 500 things looks different, maybe power law? Thus, I don't know if data could be fitted ... | What distribution should I fit to this data | I've plotted log(data) vs abscissa and dropped two last points, graph below
data going below x=500 would be good fitted with just a linear function - which means exponential distribution because we p | What distribution should I fit to this data
I've plotted log(data) vs abscissa and dropped two last points, graph below
data going below x=500 would be good fitted with just a linear function - which means exponential distribution because we plotted log(data).
But from 0 to 500 things looks different, maybe power law?... | What distribution should I fit to this data
I've plotted log(data) vs abscissa and dropped two last points, graph below
data going below x=500 would be good fitted with just a linear function - which means exponential distribution because we p |
50,825 | Can you infer standard deviation/error from bootstrapped confidence intervals? | "is there any relationship between the size of confidence intervals calculated from bootstrapping and sd?"
Yes if the model residuals are perfectly normally distributed they would be identical ... non-normal residuals would lead to a mismatch.
I don't think that increasing the number of monte-carlo samples would reduc... | Can you infer standard deviation/error from bootstrapped confidence intervals? | "is there any relationship between the size of confidence intervals calculated from bootstrapping and sd?"
Yes if the model residuals are perfectly normally distributed they would be identical ... no | Can you infer standard deviation/error from bootstrapped confidence intervals?
"is there any relationship between the size of confidence intervals calculated from bootstrapping and sd?"
Yes if the model residuals are perfectly normally distributed they would be identical ... non-normal residuals would lead to a mismat... | Can you infer standard deviation/error from bootstrapped confidence intervals?
"is there any relationship between the size of confidence intervals calculated from bootstrapping and sd?"
Yes if the model residuals are perfectly normally distributed they would be identical ... no |
50,826 | Cross Validation and Multiple Imputation for Missing Data | I believe that your thinking is right.
The alternative is to perform multiple imputation on the entire dataset prior to splitting into train/test partitions. Doing so would mean that some information from the training sets is used to create/impute values in the test sets. In other words, there would be leakage from the... | Cross Validation and Multiple Imputation for Missing Data | I believe that your thinking is right.
The alternative is to perform multiple imputation on the entire dataset prior to splitting into train/test partitions. Doing so would mean that some information | Cross Validation and Multiple Imputation for Missing Data
I believe that your thinking is right.
The alternative is to perform multiple imputation on the entire dataset prior to splitting into train/test partitions. Doing so would mean that some information from the training sets is used to create/impute values in the ... | Cross Validation and Multiple Imputation for Missing Data
I believe that your thinking is right.
The alternative is to perform multiple imputation on the entire dataset prior to splitting into train/test partitions. Doing so would mean that some information |
50,827 | Treatment interference (causal analysis) | I would say this is indeed valid.
What you likely measure by comparing the control group
those who only see their actual grades in a course (as a percentage)
with the treatment group
who see both their actual grades in a course (as a percentage) and their percentile rank
is essentially the effect of presenting a... | Treatment interference (causal analysis) | I would say this is indeed valid.
What you likely measure by comparing the control group
those who only see their actual grades in a course (as a percentage)
with the treatment group
who see bot | Treatment interference (causal analysis)
I would say this is indeed valid.
What you likely measure by comparing the control group
those who only see their actual grades in a course (as a percentage)
with the treatment group
who see both their actual grades in a course (as a percentage) and their percentile rank
... | Treatment interference (causal analysis)
I would say this is indeed valid.
What you likely measure by comparing the control group
those who only see their actual grades in a course (as a percentage)
with the treatment group
who see bot |
50,828 | Kolmogorov Smirnov p-values not uniform under the null in R? | It is not surprising that when dealing with a two sample test with a fairly small sample size (100), the test statistic (and thus the p-value) takes on discrete values. Increasing n (and decreasing K to reduce computational time) leads to a less discontinuous distribution.
As whuber pointed out in the comments, the fac... | Kolmogorov Smirnov p-values not uniform under the null in R? | It is not surprising that when dealing with a two sample test with a fairly small sample size (100), the test statistic (and thus the p-value) takes on discrete values. Increasing n (and decreasing K | Kolmogorov Smirnov p-values not uniform under the null in R?
It is not surprising that when dealing with a two sample test with a fairly small sample size (100), the test statistic (and thus the p-value) takes on discrete values. Increasing n (and decreasing K to reduce computational time) leads to a less discontinuous... | Kolmogorov Smirnov p-values not uniform under the null in R?
It is not surprising that when dealing with a two sample test with a fairly small sample size (100), the test statistic (and thus the p-value) takes on discrete values. Increasing n (and decreasing K |
50,829 | Why construct statistics when you can never beat LRT? | Your question is very broad, so this is more of a comment. One possible problem is that the (generalized) likelihood ratio test might be suboptimal in some cases, this paper points to some such examples.
You say Indeed, many, if not all, of the above mentioned tests can be shown to be equivalent to a LRT, but I was re... | Why construct statistics when you can never beat LRT? | Your question is very broad, so this is more of a comment. One possible problem is that the (generalized) likelihood ratio test might be suboptimal in some cases, this paper points to some such examp | Why construct statistics when you can never beat LRT?
Your question is very broad, so this is more of a comment. One possible problem is that the (generalized) likelihood ratio test might be suboptimal in some cases, this paper points to some such examples.
You say Indeed, many, if not all, of the above mentioned test... | Why construct statistics when you can never beat LRT?
Your question is very broad, so this is more of a comment. One possible problem is that the (generalized) likelihood ratio test might be suboptimal in some cases, this paper points to some such examp |
50,830 | L1 and L2 regularization showing increased MSE with added vars (that eventually decreases) | This can be explained by the trade of between bias and variance. We know that mse = bias^2 + var, a sum of a decreasing function of the number of predictors involved (bias) and an increasing function (var).
The thing, we dont have a specific role about the behavior of mse (training mse), but generally it decreased wit... | L1 and L2 regularization showing increased MSE with added vars (that eventually decreases) | This can be explained by the trade of between bias and variance. We know that mse = bias^2 + var, a sum of a decreasing function of the number of predictors involved (bias) and an increasing function | L1 and L2 regularization showing increased MSE with added vars (that eventually decreases)
This can be explained by the trade of between bias and variance. We know that mse = bias^2 + var, a sum of a decreasing function of the number of predictors involved (bias) and an increasing function (var).
The thing, we dont ha... | L1 and L2 regularization showing increased MSE with added vars (that eventually decreases)
This can be explained by the trade of between bias and variance. We know that mse = bias^2 + var, a sum of a decreasing function of the number of predictors involved (bias) and an increasing function |
50,831 | Generalized Least Squares using Moore Penrose pseudo inverse | You can compute a solution using the Moore-Penrose inverse in place of the (non-existing) usual inverse. That is known to give a minimum-norm solution. That is, with the linear model in matrix form (assuming iid errors)
$$
Y = X\beta + \epsilon
$$ (you write generalized least square so presumably the covariance matr... | Generalized Least Squares using Moore Penrose pseudo inverse | You can compute a solution using the Moore-Penrose inverse in place of the (non-existing) usual inverse. That is known to give a minimum-norm solution. That is, with the linear model in matrix form (a | Generalized Least Squares using Moore Penrose pseudo inverse
You can compute a solution using the Moore-Penrose inverse in place of the (non-existing) usual inverse. That is known to give a minimum-norm solution. That is, with the linear model in matrix form (assuming iid errors)
$$
Y = X\beta + \epsilon
$$ (you wri... | Generalized Least Squares using Moore Penrose pseudo inverse
You can compute a solution using the Moore-Penrose inverse in place of the (non-existing) usual inverse. That is known to give a minimum-norm solution. That is, with the linear model in matrix form (a |
50,832 | When does the underfitted regression model have more precise coefficient estimates? | The sufficient condition mentioned in the book turns out to be necessary as well! I finally verified it using the two different formulas for the inverse of a block matrix.
Looking at the full model estimator
$$
\mathbf{X}^\intercal\mathbf{X} =
\begin{bmatrix}
\mathbf{X}_p^\intercal\mathbf{X}_p &\mathbf{X}_p^\intercal\m... | When does the underfitted regression model have more precise coefficient estimates? | The sufficient condition mentioned in the book turns out to be necessary as well! I finally verified it using the two different formulas for the inverse of a block matrix.
Looking at the full model es | When does the underfitted regression model have more precise coefficient estimates?
The sufficient condition mentioned in the book turns out to be necessary as well! I finally verified it using the two different formulas for the inverse of a block matrix.
Looking at the full model estimator
$$
\mathbf{X}^\intercal\math... | When does the underfitted regression model have more precise coefficient estimates?
The sufficient condition mentioned in the book turns out to be necessary as well! I finally verified it using the two different formulas for the inverse of a block matrix.
Looking at the full model es |
50,833 | Examples of "one to many" for RNN/LSTM | The most popular example is the decoder part of the seq2seq recurrent neural network (RNN). Such networks are one of the most basic examples of networks that can be used for machine translation. They consist of two sub-networks: encoder RNN network that takes as input sentence in one language and encodes using some vec... | Examples of "one to many" for RNN/LSTM | The most popular example is the decoder part of the seq2seq recurrent neural network (RNN). Such networks are one of the most basic examples of networks that can be used for machine translation. They | Examples of "one to many" for RNN/LSTM
The most popular example is the decoder part of the seq2seq recurrent neural network (RNN). Such networks are one of the most basic examples of networks that can be used for machine translation. They consist of two sub-networks: encoder RNN network that takes as input sentence in ... | Examples of "one to many" for RNN/LSTM
The most popular example is the decoder part of the seq2seq recurrent neural network (RNN). Such networks are one of the most basic examples of networks that can be used for machine translation. They |
50,834 | Bounding residual variance with distance from mean | I was able to come up with a bound although it's not very tight.
Let $X = UDV^T$ be the SVD of $X$, so that $H = UU^T$. Let $u_1,\dots,u_n \in \mathbb R^p$ be the rows of $U$ (as column vectors) which means that $h_i = \|u_i\|^2$.
Let $s_i^2 = \|x_i - \frac 1n X^T\mathbf 1\|^2$. If $e_i$ is the $i$th standard basis vec... | Bounding residual variance with distance from mean | I was able to come up with a bound although it's not very tight.
Let $X = UDV^T$ be the SVD of $X$, so that $H = UU^T$. Let $u_1,\dots,u_n \in \mathbb R^p$ be the rows of $U$ (as column vectors) which | Bounding residual variance with distance from mean
I was able to come up with a bound although it's not very tight.
Let $X = UDV^T$ be the SVD of $X$, so that $H = UU^T$. Let $u_1,\dots,u_n \in \mathbb R^p$ be the rows of $U$ (as column vectors) which means that $h_i = \|u_i\|^2$.
Let $s_i^2 = \|x_i - \frac 1n X^T\math... | Bounding residual variance with distance from mean
I was able to come up with a bound although it's not very tight.
Let $X = UDV^T$ be the SVD of $X$, so that $H = UU^T$. Let $u_1,\dots,u_n \in \mathbb R^p$ be the rows of $U$ (as column vectors) which |
50,835 | Approximate density from moments and quantiles, then sample from it | To quickly simulate based on moments, try rpearson() from library(PearsonDS).
library(PearsonDS)
target.moms <- c(1262.39, 9567670, 10.59025, 157.7004)
y <- rpearson(n=1000000, moments=target.moms)
rpearson() works well for matching the moments. However, the splines approach that you're already using will be better a... | Approximate density from moments and quantiles, then sample from it | To quickly simulate based on moments, try rpearson() from library(PearsonDS).
library(PearsonDS)
target.moms <- c(1262.39, 9567670, 10.59025, 157.7004)
y <- rpearson(n=1000000, moments=target.moms)
r | Approximate density from moments and quantiles, then sample from it
To quickly simulate based on moments, try rpearson() from library(PearsonDS).
library(PearsonDS)
target.moms <- c(1262.39, 9567670, 10.59025, 157.7004)
y <- rpearson(n=1000000, moments=target.moms)
rpearson() works well for matching the moments. Howe... | Approximate density from moments and quantiles, then sample from it
To quickly simulate based on moments, try rpearson() from library(PearsonDS).
library(PearsonDS)
target.moms <- c(1262.39, 9567670, 10.59025, 157.7004)
y <- rpearson(n=1000000, moments=target.moms)
r |
50,836 | Under what conditions does it make sense to fit random intercepts for an interaction, but not the main effects? | Using the notation dept:service you get the interaction and main effects. You can see this also in the output where the number of groups are specified as 28.
Loading required package: Matrix
Linear mixed model fit by maximum likelihood ['lmerMod']
Formula: y ~ 1 + (1 | s) + (1 | d) + (1 | dept:service)
Data: InstEv... | Under what conditions does it make sense to fit random intercepts for an interaction, but not the ma | Using the notation dept:service you get the interaction and main effects. You can see this also in the output where the number of groups are specified as 28.
Loading required package: Matrix
Linear mi | Under what conditions does it make sense to fit random intercepts for an interaction, but not the main effects?
Using the notation dept:service you get the interaction and main effects. You can see this also in the output where the number of groups are specified as 28.
Loading required package: Matrix
Linear mixed mode... | Under what conditions does it make sense to fit random intercepts for an interaction, but not the ma
Using the notation dept:service you get the interaction and main effects. You can see this also in the output where the number of groups are specified as 28.
Loading required package: Matrix
Linear mi |
50,837 | Which gamma regression model to use for extrapolation? | The OP has done a great job exploring a variety of different techniques. As commented, given that the response variable is Gamma-distributed it makes sense to consider a GLM and/or a GAM for Gamma distributed variables. Particularly for the use of GAMs, if the computation burden appears too much we might want to consid... | Which gamma regression model to use for extrapolation? | The OP has done a great job exploring a variety of different techniques. As commented, given that the response variable is Gamma-distributed it makes sense to consider a GLM and/or a GAM for Gamma dis | Which gamma regression model to use for extrapolation?
The OP has done a great job exploring a variety of different techniques. As commented, given that the response variable is Gamma-distributed it makes sense to consider a GLM and/or a GAM for Gamma distributed variables. Particularly for the use of GAMs, if the comp... | Which gamma regression model to use for extrapolation?
The OP has done a great job exploring a variety of different techniques. As commented, given that the response variable is Gamma-distributed it makes sense to consider a GLM and/or a GAM for Gamma dis |
50,838 | Which gamma regression model to use for extrapolation? | Linear models are great for extrapolation, since they don't make too complex assumptions which might not generalize outside of the training set. Unfortunately that also means that they are not able to use the full potential of other features which are not changed when extrapolating.
Since extrapolation is done only in ... | Which gamma regression model to use for extrapolation? | Linear models are great for extrapolation, since they don't make too complex assumptions which might not generalize outside of the training set. Unfortunately that also means that they are not able to | Which gamma regression model to use for extrapolation?
Linear models are great for extrapolation, since they don't make too complex assumptions which might not generalize outside of the training set. Unfortunately that also means that they are not able to use the full potential of other features which are not changed w... | Which gamma regression model to use for extrapolation?
Linear models are great for extrapolation, since they don't make too complex assumptions which might not generalize outside of the training set. Unfortunately that also means that they are not able to |
50,839 | Some questions about quarterly and monthly timeseries | I work with time series rather than being an expert in it and I have never seen this raised. I don't think, however, that you can go from data aggregated at the quarterly level to the monthly level. Why is it important to your company to answer the question at the monthly level if there are no patterns at the monthly l... | Some questions about quarterly and monthly timeseries | I work with time series rather than being an expert in it and I have never seen this raised. I don't think, however, that you can go from data aggregated at the quarterly level to the monthly level. W | Some questions about quarterly and monthly timeseries
I work with time series rather than being an expert in it and I have never seen this raised. I don't think, however, that you can go from data aggregated at the quarterly level to the monthly level. Why is it important to your company to answer the question at the m... | Some questions about quarterly and monthly timeseries
I work with time series rather than being an expert in it and I have never seen this raised. I don't think, however, that you can go from data aggregated at the quarterly level to the monthly level. W |
50,840 | Interrupted Time Series Analysis with multiple Intervention timepoints | A starting point for the concept of ITSA is Shadish, Cooke, & Campbell (2002) and a starting palce for the mathematical procedures for ITSA is Glass, Wilson, & Gottman (1975).
Some researchers may recommend a dummy code moderator in a multiple regression, where 0 represents no intervention and 1 represents intervention... | Interrupted Time Series Analysis with multiple Intervention timepoints | A starting point for the concept of ITSA is Shadish, Cooke, & Campbell (2002) and a starting palce for the mathematical procedures for ITSA is Glass, Wilson, & Gottman (1975).
Some researchers may rec | Interrupted Time Series Analysis with multiple Intervention timepoints
A starting point for the concept of ITSA is Shadish, Cooke, & Campbell (2002) and a starting palce for the mathematical procedures for ITSA is Glass, Wilson, & Gottman (1975).
Some researchers may recommend a dummy code moderator in a multiple regre... | Interrupted Time Series Analysis with multiple Intervention timepoints
A starting point for the concept of ITSA is Shadish, Cooke, & Campbell (2002) and a starting palce for the mathematical procedures for ITSA is Glass, Wilson, & Gottman (1975).
Some researchers may rec |
50,841 | Interrupted Time Series Analysis with multiple Intervention timepoints | I'd never heard of interrupted time series analysis before this question, and I can't really speak to how it's different from regular time series analysis that involves sophisticated-enough techniques to handle "outliers" and seasonality.
So I'd suggest looking more widely at time series literature in regards to season... | Interrupted Time Series Analysis with multiple Intervention timepoints | I'd never heard of interrupted time series analysis before this question, and I can't really speak to how it's different from regular time series analysis that involves sophisticated-enough techniques | Interrupted Time Series Analysis with multiple Intervention timepoints
I'd never heard of interrupted time series analysis before this question, and I can't really speak to how it's different from regular time series analysis that involves sophisticated-enough techniques to handle "outliers" and seasonality.
So I'd sug... | Interrupted Time Series Analysis with multiple Intervention timepoints
I'd never heard of interrupted time series analysis before this question, and I can't really speak to how it's different from regular time series analysis that involves sophisticated-enough techniques |
50,842 | Logistic Regression and Omitted Variable Bias | In practice this issue with omitted-variable bias in logistic regression might not be that much different from what is faced in ordinary least squares (OLS). The added problem in logistic regression is that, unlike OLS, omitting predictors associated with outcome but uncorrelated with the included predictors leads to b... | Logistic Regression and Omitted Variable Bias | In practice this issue with omitted-variable bias in logistic regression might not be that much different from what is faced in ordinary least squares (OLS). The added problem in logistic regression i | Logistic Regression and Omitted Variable Bias
In practice this issue with omitted-variable bias in logistic regression might not be that much different from what is faced in ordinary least squares (OLS). The added problem in logistic regression is that, unlike OLS, omitting predictors associated with outcome but uncorr... | Logistic Regression and Omitted Variable Bias
In practice this issue with omitted-variable bias in logistic regression might not be that much different from what is faced in ordinary least squares (OLS). The added problem in logistic regression i |
50,843 | Evaluating if time series need differencing | I'm a little confused about what your data is but, based on the above information, it does appear to be stationary. This is because there is relatively little persistence in the ACF, meaning that the autocorrelations do not consistently remain close to 1 (see here for a textbook example of a non-stationary ACF).
Howeve... | Evaluating if time series need differencing | I'm a little confused about what your data is but, based on the above information, it does appear to be stationary. This is because there is relatively little persistence in the ACF, meaning that the | Evaluating if time series need differencing
I'm a little confused about what your data is but, based on the above information, it does appear to be stationary. This is because there is relatively little persistence in the ACF, meaning that the autocorrelations do not consistently remain close to 1 (see here for a textb... | Evaluating if time series need differencing
I'm a little confused about what your data is but, based on the above information, it does appear to be stationary. This is because there is relatively little persistence in the ACF, meaning that the |
50,844 | Evaluating if time series need differencing | Unnecessary differencing or filtering can inject structure (see Slutsky Effect) . Sometimes a series can have a shift in the mean causing "non-statioanarity" ..the correct remedy is to neither difference or de-trend but to "de-mean" or use a Level Shift variable/filter to render the residual series stationary.
Sometime... | Evaluating if time series need differencing | Unnecessary differencing or filtering can inject structure (see Slutsky Effect) . Sometimes a series can have a shift in the mean causing "non-statioanarity" ..the correct remedy is to neither differe | Evaluating if time series need differencing
Unnecessary differencing or filtering can inject structure (see Slutsky Effect) . Sometimes a series can have a shift in the mean causing "non-statioanarity" ..the correct remedy is to neither difference or de-trend but to "de-mean" or use a Level Shift variable/filter to ren... | Evaluating if time series need differencing
Unnecessary differencing or filtering can inject structure (see Slutsky Effect) . Sometimes a series can have a shift in the mean causing "non-statioanarity" ..the correct remedy is to neither differe |
50,845 | What are some techniques to augment tabular data? | SMOTE has many variants. SMOTE should be treated as a conservative density estimation of the data, which makes the conservative assumption that the line segments between close neighbors of some class belong to the same class. Sampling from this rough, conservative density estimation absolutely makes sense, but does not... | What are some techniques to augment tabular data? | SMOTE has many variants. SMOTE should be treated as a conservative density estimation of the data, which makes the conservative assumption that the line segments between close neighbors of some class | What are some techniques to augment tabular data?
SMOTE has many variants. SMOTE should be treated as a conservative density estimation of the data, which makes the conservative assumption that the line segments between close neighbors of some class belong to the same class. Sampling from this rough, conservative densi... | What are some techniques to augment tabular data?
SMOTE has many variants. SMOTE should be treated as a conservative density estimation of the data, which makes the conservative assumption that the line segments between close neighbors of some class |
50,846 | Why there's never a good reason to use the Jarque-Bera test | I'm no expert on this subject, but there seems to be quite some blog posts and even publications on this subject.
I would suggest reading those, but in general it seems that the test might be biased and have low power when using small samples, and when the original distribution is short-tailed. | Why there's never a good reason to use the Jarque-Bera test | I'm no expert on this subject, but there seems to be quite some blog posts and even publications on this subject.
I would suggest reading those, but in general it seems that the test might be biased | Why there's never a good reason to use the Jarque-Bera test
I'm no expert on this subject, but there seems to be quite some blog posts and even publications on this subject.
I would suggest reading those, but in general it seems that the test might be biased and have low power when using small samples, and when the or... | Why there's never a good reason to use the Jarque-Bera test
I'm no expert on this subject, but there seems to be quite some blog posts and even publications on this subject.
I would suggest reading those, but in general it seems that the test might be biased |
50,847 | Why there's never a good reason to use the Jarque-Bera test | I would argue the opposite... and that as far as tests for Normal distributions are concerned, Jarque-Bera is the most transparent and explicit since it captures a combination of Skewness and Kurtosis which are the two dimensions that capture divergence from a Normal distribution. And, to my knowledge it does that bet... | Why there's never a good reason to use the Jarque-Bera test | I would argue the opposite... and that as far as tests for Normal distributions are concerned, Jarque-Bera is the most transparent and explicit since it captures a combination of Skewness and Kurtosis | Why there's never a good reason to use the Jarque-Bera test
I would argue the opposite... and that as far as tests for Normal distributions are concerned, Jarque-Bera is the most transparent and explicit since it captures a combination of Skewness and Kurtosis which are the two dimensions that capture divergence from a... | Why there's never a good reason to use the Jarque-Bera test
I would argue the opposite... and that as far as tests for Normal distributions are concerned, Jarque-Bera is the most transparent and explicit since it captures a combination of Skewness and Kurtosis |
50,848 | Is the use of loglik or AIC to compare logit/probit/cloglog models valid? | I would say yes, I can't see any reason why they wouldn't. We're talking about evaluating the log-likelihood for the same conditional probability distribution, with the same probability density (i.e. we don't have to account for changes in the scale due to transformation). So we're comparing the likelihoods for
$$
y_i... | Is the use of loglik or AIC to compare logit/probit/cloglog models valid? | I would say yes, I can't see any reason why they wouldn't. We're talking about evaluating the log-likelihood for the same conditional probability distribution, with the same probability density (i.e. | Is the use of loglik or AIC to compare logit/probit/cloglog models valid?
I would say yes, I can't see any reason why they wouldn't. We're talking about evaluating the log-likelihood for the same conditional probability distribution, with the same probability density (i.e. we don't have to account for changes in the s... | Is the use of loglik or AIC to compare logit/probit/cloglog models valid?
I would say yes, I can't see any reason why they wouldn't. We're talking about evaluating the log-likelihood for the same conditional probability distribution, with the same probability density (i.e. |
50,849 | Is the likelihood in Bayes theorem a probability? [duplicate] | The likelihood is a so-called conditional density. It is a probability density function on the data space (for $D$) given any parameter $\theta$ that we pass over to the function. When integrating over it with respect to $D$ we obtain the conditional distribution of the data given a certain parameter. This conditional ... | Is the likelihood in Bayes theorem a probability? [duplicate] | The likelihood is a so-called conditional density. It is a probability density function on the data space (for $D$) given any parameter $\theta$ that we pass over to the function. When integrating ove | Is the likelihood in Bayes theorem a probability? [duplicate]
The likelihood is a so-called conditional density. It is a probability density function on the data space (for $D$) given any parameter $\theta$ that we pass over to the function. When integrating over it with respect to $D$ we obtain the conditional distrib... | Is the likelihood in Bayes theorem a probability? [duplicate]
The likelihood is a so-called conditional density. It is a probability density function on the data space (for $D$) given any parameter $\theta$ that we pass over to the function. When integrating ove |
50,850 | Peanut butter jars full of river mud and bacteria? | You don't want a test, because you have no definite hypothesis to assess: you are exploring. This calls for graphical display of relationships among bacterial counts and the potential explanatory variables. It's likely you will need to re-express the grain size fractions, because basic science suggests many possible me... | Peanut butter jars full of river mud and bacteria? | You don't want a test, because you have no definite hypothesis to assess: you are exploring. This calls for graphical display of relationships among bacterial counts and the potential explanatory vari | Peanut butter jars full of river mud and bacteria?
You don't want a test, because you have no definite hypothesis to assess: you are exploring. This calls for graphical display of relationships among bacterial counts and the potential explanatory variables. It's likely you will need to re-express the grain size fractio... | Peanut butter jars full of river mud and bacteria?
You don't want a test, because you have no definite hypothesis to assess: you are exploring. This calls for graphical display of relationships among bacterial counts and the potential explanatory vari |
50,851 | Calculate binomial deviance (binomial log-likelihood) in the test dataset | I recommend against fudging these prediction values. The appropriate outcome here is that if the model predicts a thing with probability 1, and that thing doesn't happen, then its deviance is infinite. Similarly, if the model predicts a thing with probability 0, and that thing happens, then its deviance is infinite. ... | Calculate binomial deviance (binomial log-likelihood) in the test dataset | I recommend against fudging these prediction values. The appropriate outcome here is that if the model predicts a thing with probability 1, and that thing doesn't happen, then its deviance is infinit | Calculate binomial deviance (binomial log-likelihood) in the test dataset
I recommend against fudging these prediction values. The appropriate outcome here is that if the model predicts a thing with probability 1, and that thing doesn't happen, then its deviance is infinite. Similarly, if the model predicts a thing w... | Calculate binomial deviance (binomial log-likelihood) in the test dataset
I recommend against fudging these prediction values. The appropriate outcome here is that if the model predicts a thing with probability 1, and that thing doesn't happen, then its deviance is infinit |
50,852 | Calculate binomial deviance (binomial log-likelihood) in the test dataset | You can clip the probabilities to guarantee that will they will never be 0 or 1. For example as per sklearn docs, set up a small value named eps and use max(eps, min(1 - eps, p) where p is the classifier's probability.
sklearn docs for logloss | Calculate binomial deviance (binomial log-likelihood) in the test dataset | You can clip the probabilities to guarantee that will they will never be 0 or 1. For example as per sklearn docs, set up a small value named eps and use max(eps, min(1 - eps, p) where p is the classif | Calculate binomial deviance (binomial log-likelihood) in the test dataset
You can clip the probabilities to guarantee that will they will never be 0 or 1. For example as per sklearn docs, set up a small value named eps and use max(eps, min(1 - eps, p) where p is the classifier's probability.
sklearn docs for logloss | Calculate binomial deviance (binomial log-likelihood) in the test dataset
You can clip the probabilities to guarantee that will they will never be 0 or 1. For example as per sklearn docs, set up a small value named eps and use max(eps, min(1 - eps, p) where p is the classif |
50,853 | Partial Effects Plots vs. Partial Dependence Plots for Random Forests | For linear models without categorical variables, if you are using the mean when computing the PE plot, then the PE plot is the same as the PDP. Intuitively, the PE plot is to take the average for other variables first and then plot a curve, where the slope is the beta. The PDP is to compute the values for every instanc... | Partial Effects Plots vs. Partial Dependence Plots for Random Forests | For linear models without categorical variables, if you are using the mean when computing the PE plot, then the PE plot is the same as the PDP. Intuitively, the PE plot is to take the average for othe | Partial Effects Plots vs. Partial Dependence Plots for Random Forests
For linear models without categorical variables, if you are using the mean when computing the PE plot, then the PE plot is the same as the PDP. Intuitively, the PE plot is to take the average for other variables first and then plot a curve, where the... | Partial Effects Plots vs. Partial Dependence Plots for Random Forests
For linear models without categorical variables, if you are using the mean when computing the PE plot, then the PE plot is the same as the PDP. Intuitively, the PE plot is to take the average for othe |
50,854 | Which method to use when calculating the confidence interval of GLMM Gamma Regression with the lme4 package in R | I found this blog to be helpful RE finding CI's for estimates of a GLM(M):
https://fromthebottomoftheheap.net/2018/12/10/confidence-intervals-for-glms/ | Which method to use when calculating the confidence interval of GLMM Gamma Regression with the lme4 | I found this blog to be helpful RE finding CI's for estimates of a GLM(M):
https://fromthebottomoftheheap.net/2018/12/10/confidence-intervals-for-glms/ | Which method to use when calculating the confidence interval of GLMM Gamma Regression with the lme4 package in R
I found this blog to be helpful RE finding CI's for estimates of a GLM(M):
https://fromthebottomoftheheap.net/2018/12/10/confidence-intervals-for-glms/ | Which method to use when calculating the confidence interval of GLMM Gamma Regression with the lme4
I found this blog to be helpful RE finding CI's for estimates of a GLM(M):
https://fromthebottomoftheheap.net/2018/12/10/confidence-intervals-for-glms/ |
50,855 | Notation question based on 1950s typesetting | From @whuber's answer in the comments:
I looked at the paper on JSTOR. The typesetting looks clear to me:
what you haven't reproduced here is the spacing used there to clarify
the meaning. For instance, look closely at this:
$$D = 1 + 2e^{\gamma/\delta}\ \cos \sqrt{}2\ \pi/\delta h +
e^{2\gamma/\delta}.$$ | Notation question based on 1950s typesetting | From @whuber's answer in the comments:
I looked at the paper on JSTOR. The typesetting looks clear to me:
what you haven't reproduced here is the spacing used there to clarify
the meaning. For in | Notation question based on 1950s typesetting
From @whuber's answer in the comments:
I looked at the paper on JSTOR. The typesetting looks clear to me:
what you haven't reproduced here is the spacing used there to clarify
the meaning. For instance, look closely at this:
$$D = 1 + 2e^{\gamma/\delta}\ \cos \sqrt{}2\... | Notation question based on 1950s typesetting
From @whuber's answer in the comments:
I looked at the paper on JSTOR. The typesetting looks clear to me:
what you haven't reproduced here is the spacing used there to clarify
the meaning. For in |
50,856 | What's the definition of "Dynamic Regression Models"? | No problem but I'd definitely try to get my hands on some kind of textbook or lecture notes. The following is not a formal definition but here goes my attempt: To me, a DRM is any model which is time dependent, in the sense that, the next value of an observation (on the right hand side of the model ), at the next poi... | What's the definition of "Dynamic Regression Models"? | No problem but I'd definitely try to get my hands on some kind of textbook or lecture notes. The following is not a formal definition but here goes my attempt: To me, a DRM is any model which is tim | What's the definition of "Dynamic Regression Models"?
No problem but I'd definitely try to get my hands on some kind of textbook or lecture notes. The following is not a formal definition but here goes my attempt: To me, a DRM is any model which is time dependent, in the sense that, the next value of an observation (... | What's the definition of "Dynamic Regression Models"?
No problem but I'd definitely try to get my hands on some kind of textbook or lecture notes. The following is not a formal definition but here goes my attempt: To me, a DRM is any model which is tim |
50,857 | Which approach based on the LASSO yields more biologically relevant results for gene data-sets? | Since you're only interested in the influence of the genes, you should "force keep" the non-gene variables in the model (for example in R with glmnet package and option penalty.factor equal to zero for the corresponding variables). Or you could first do a model with the confounding variables only and identify the ones ... | Which approach based on the LASSO yields more biologically relevant results for gene data-sets? | Since you're only interested in the influence of the genes, you should "force keep" the non-gene variables in the model (for example in R with glmnet package and option penalty.factor equal to zero fo | Which approach based on the LASSO yields more biologically relevant results for gene data-sets?
Since you're only interested in the influence of the genes, you should "force keep" the non-gene variables in the model (for example in R with glmnet package and option penalty.factor equal to zero for the corresponding vari... | Which approach based on the LASSO yields more biologically relevant results for gene data-sets?
Since you're only interested in the influence of the genes, you should "force keep" the non-gene variables in the model (for example in R with glmnet package and option penalty.factor equal to zero fo |
50,858 | How to improve forecast accuray of bsts model | Clean out the outlier instead of using a dummy variable (use tsclean()).
Try AddTrig instead of AddSeasonal for there seasonal component, since your data seems to have multiple seasonalities.
What other methods are you using that are giving better results than BSTS? | How to improve forecast accuray of bsts model | Clean out the outlier instead of using a dummy variable (use tsclean()).
Try AddTrig instead of AddSeasonal for there seasonal component, since your data seems to have multiple seasonalities.
What o | How to improve forecast accuray of bsts model
Clean out the outlier instead of using a dummy variable (use tsclean()).
Try AddTrig instead of AddSeasonal for there seasonal component, since your data seems to have multiple seasonalities.
What other methods are you using that are giving better results than BSTS? | How to improve forecast accuray of bsts model
Clean out the outlier instead of using a dummy variable (use tsclean()).
Try AddTrig instead of AddSeasonal for there seasonal component, since your data seems to have multiple seasonalities.
What o |
50,859 | How to improve forecast accuray of bsts model | Your approach is feasible but you need to accommodate many more columns (i.e. predictor series) than you have. I took your data into a comprehensive time series package that simultaneously deals with i.e. identifies 1) lead and lag effects around holidays 2) day-of-the-week effects and changes in day-of-the-week effect... | How to improve forecast accuray of bsts model | Your approach is feasible but you need to accommodate many more columns (i.e. predictor series) than you have. I took your data into a comprehensive time series package that simultaneously deals with | How to improve forecast accuray of bsts model
Your approach is feasible but you need to accommodate many more columns (i.e. predictor series) than you have. I took your data into a comprehensive time series package that simultaneously deals with i.e. identifies 1) lead and lag effects around holidays 2) day-of-the-week... | How to improve forecast accuray of bsts model
Your approach is feasible but you need to accommodate many more columns (i.e. predictor series) than you have. I took your data into a comprehensive time series package that simultaneously deals with |
50,860 | Finding most similar training samples for a given ML model output | Found a recent paper that presents a similar approach to the one I described in the question: "Consistent Individualized Feature Attribution for Tree Ensembles", Lundberg et.al., KDD 2018.
They use Shapley values to explain the model prediction for each sample as a sum of contributions from each feature, and then compa... | Finding most similar training samples for a given ML model output | Found a recent paper that presents a similar approach to the one I described in the question: "Consistent Individualized Feature Attribution for Tree Ensembles", Lundberg et.al., KDD 2018.
They use Sh | Finding most similar training samples for a given ML model output
Found a recent paper that presents a similar approach to the one I described in the question: "Consistent Individualized Feature Attribution for Tree Ensembles", Lundberg et.al., KDD 2018.
They use Shapley values to explain the model prediction for each ... | Finding most similar training samples for a given ML model output
Found a recent paper that presents a similar approach to the one I described in the question: "Consistent Individualized Feature Attribution for Tree Ensembles", Lundberg et.al., KDD 2018.
They use Sh |
50,861 | Finding most similar training samples for a given ML model output | If you are looking to pick 'n' closest samples from the training data set that is similar to an out-of-sample observation, why not simply use the features you have to get a distance with each training observation - euclidean, manhattan or whatever (depends on the feature types)? The training sample with the smallest d... | Finding most similar training samples for a given ML model output | If you are looking to pick 'n' closest samples from the training data set that is similar to an out-of-sample observation, why not simply use the features you have to get a distance with each trainin | Finding most similar training samples for a given ML model output
If you are looking to pick 'n' closest samples from the training data set that is similar to an out-of-sample observation, why not simply use the features you have to get a distance with each training observation - euclidean, manhattan or whatever (depe... | Finding most similar training samples for a given ML model output
If you are looking to pick 'n' closest samples from the training data set that is similar to an out-of-sample observation, why not simply use the features you have to get a distance with each trainin |
50,862 | When to stop training of neural network when validation loss is still decreasing but gap with training loss is increasing? | As long as your validation loss is continuing to decrease, your model is continuing to perform better in a generalized setting.
A growing gap between training and validation performance does mean that your model is treating more and more of the noise in your training set as real signal. However, the fact that your vali... | When to stop training of neural network when validation loss is still decreasing but gap with traini | As long as your validation loss is continuing to decrease, your model is continuing to perform better in a generalized setting.
A growing gap between training and validation performance does mean that | When to stop training of neural network when validation loss is still decreasing but gap with training loss is increasing?
As long as your validation loss is continuing to decrease, your model is continuing to perform better in a generalized setting.
A growing gap between training and validation performance does mean t... | When to stop training of neural network when validation loss is still decreasing but gap with traini
As long as your validation loss is continuing to decrease, your model is continuing to perform better in a generalized setting.
A growing gap between training and validation performance does mean that |
50,863 | How to index rater agreement: multiple raters identify strenghts/weaknesses from 30 traits? | You can think about the raters as points that occupy a 35 dimensional space (one dimension for each trait) for each person.
Then, you can measure their degree of agreement by measuring how far apart they are from each other in that space. The distance can be measured using the Euclidean distance (Pythagorean) formula.... | How to index rater agreement: multiple raters identify strenghts/weaknesses from 30 traits? | You can think about the raters as points that occupy a 35 dimensional space (one dimension for each trait) for each person.
Then, you can measure their degree of agreement by measuring how far apart | How to index rater agreement: multiple raters identify strenghts/weaknesses from 30 traits?
You can think about the raters as points that occupy a 35 dimensional space (one dimension for each trait) for each person.
Then, you can measure their degree of agreement by measuring how far apart they are from each other in ... | How to index rater agreement: multiple raters identify strenghts/weaknesses from 30 traits?
You can think about the raters as points that occupy a 35 dimensional space (one dimension for each trait) for each person.
Then, you can measure their degree of agreement by measuring how far apart |
50,864 | How to index rater agreement: multiple raters identify strenghts/weaknesses from 30 traits? | I think you are on the right track. Below are some thoughts that may be of help.
ad A. The non-standardized Rater Agreement measure that you suggest is called Hamming distance.
The traits ($1 \le k \le 35$) assigned to individual $i$ by rater $j$ can be represented as a binary vector, $v_{ij}$, of length $35$.
Say tr... | How to index rater agreement: multiple raters identify strenghts/weaknesses from 30 traits? | I think you are on the right track. Below are some thoughts that may be of help.
ad A. The non-standardized Rater Agreement measure that you suggest is called Hamming distance.
The traits ($1 \le k \ | How to index rater agreement: multiple raters identify strenghts/weaknesses from 30 traits?
I think you are on the right track. Below are some thoughts that may be of help.
ad A. The non-standardized Rater Agreement measure that you suggest is called Hamming distance.
The traits ($1 \le k \le 35$) assigned to individu... | How to index rater agreement: multiple raters identify strenghts/weaknesses from 30 traits?
I think you are on the right track. Below are some thoughts that may be of help.
ad A. The non-standardized Rater Agreement measure that you suggest is called Hamming distance.
The traits ($1 \le k \ |
50,865 | Is 'poisson-izing' a feature a useful method? | Technically, it sounds like your method is trying to "unpoisson" the data.
You don't typically see changes-of-variable for a regressor along the lines of what you propose. That's for a couple reasons: 1) You don't need normally distributed regressors, you just want centered/scaled regressors so the L1-penalty is compar... | Is 'poisson-izing' a feature a useful method? | Technically, it sounds like your method is trying to "unpoisson" the data.
You don't typically see changes-of-variable for a regressor along the lines of what you propose. That's for a couple reasons: | Is 'poisson-izing' a feature a useful method?
Technically, it sounds like your method is trying to "unpoisson" the data.
You don't typically see changes-of-variable for a regressor along the lines of what you propose. That's for a couple reasons: 1) You don't need normally distributed regressors, you just want centered... | Is 'poisson-izing' a feature a useful method?
Technically, it sounds like your method is trying to "unpoisson" the data.
You don't typically see changes-of-variable for a regressor along the lines of what you propose. That's for a couple reasons: |
50,866 | Ridge regression: penalizing weights corresponding to larger-scale features | If the columns of $X$ have mean zero, then their variances are $\sigma^2 = \text{diag}(X^TX)$. Then if $X_s$ is the scaled version of $X$ so that $X = X_s \cdot \text{diag}(\sigma)$, the standard ridge loss can be written as
$$
\begin{align}
\|y - X_s\beta_s\|^2 + \lambda \|\beta_s\|^2
&= \|y - X_s \cdot \text{diag}(... | Ridge regression: penalizing weights corresponding to larger-scale features | If the columns of $X$ have mean zero, then their variances are $\sigma^2 = \text{diag}(X^TX)$. Then if $X_s$ is the scaled version of $X$ so that $X = X_s \cdot \text{diag}(\sigma)$, the standard ridg | Ridge regression: penalizing weights corresponding to larger-scale features
If the columns of $X$ have mean zero, then their variances are $\sigma^2 = \text{diag}(X^TX)$. Then if $X_s$ is the scaled version of $X$ so that $X = X_s \cdot \text{diag}(\sigma)$, the standard ridge loss can be written as
$$
\begin{align}
\... | Ridge regression: penalizing weights corresponding to larger-scale features
If the columns of $X$ have mean zero, then their variances are $\sigma^2 = \text{diag}(X^TX)$. Then if $X_s$ is the scaled version of $X$ so that $X = X_s \cdot \text{diag}(\sigma)$, the standard ridg |
50,867 | Generate Beta distribution from Uniform random variables | I just had the same problem with the distribution creation, thanks for the latest reply to the original post.
Please find below a viable solution to create one RV in Python:
def beta(a,b):
rv1 = np.random.rand()**(1/a)
rv2 = np.random.rand()**(1/b)
while (rv1+rv2) > 1:
rv1 = np.random.rand()**(1/a)... | Generate Beta distribution from Uniform random variables | I just had the same problem with the distribution creation, thanks for the latest reply to the original post.
Please find below a viable solution to create one RV in Python:
def beta(a,b):
rv1 = n | Generate Beta distribution from Uniform random variables
I just had the same problem with the distribution creation, thanks for the latest reply to the original post.
Please find below a viable solution to create one RV in Python:
def beta(a,b):
rv1 = np.random.rand()**(1/a)
rv2 = np.random.rand()**(1/b)
w... | Generate Beta distribution from Uniform random variables
I just had the same problem with the distribution creation, thanks for the latest reply to the original post.
Please find below a viable solution to create one RV in Python:
def beta(a,b):
rv1 = n |
50,868 | effect of class 0,1 proportion on logistic regression estimated probability | As Tim wrote above the logistic regression gives you a prediction of the probability of each class. Concretely, you will get
$$P(C_a|D)$$ and $$P(C_n|D)$$
where $C_a$ and $C_n$ are the anomaly class and normal class and $D$ is your data.
According to Baye's Theorem:
$$P(C_a|D)= \frac{P(D|C_a) P(C_a)}{P(D)}$$
$$P(C_n|D)... | effect of class 0,1 proportion on logistic regression estimated probability | As Tim wrote above the logistic regression gives you a prediction of the probability of each class. Concretely, you will get
$$P(C_a|D)$$ and $$P(C_n|D)$$
where $C_a$ and $C_n$ are the anomaly class a | effect of class 0,1 proportion on logistic regression estimated probability
As Tim wrote above the logistic regression gives you a prediction of the probability of each class. Concretely, you will get
$$P(C_a|D)$$ and $$P(C_n|D)$$
where $C_a$ and $C_n$ are the anomaly class and normal class and $D$ is your data.
Accord... | effect of class 0,1 proportion on logistic regression estimated probability
As Tim wrote above the logistic regression gives you a prediction of the probability of each class. Concretely, you will get
$$P(C_a|D)$$ and $$P(C_n|D)$$
where $C_a$ and $C_n$ are the anomaly class a |
50,869 | effect of class 0,1 proportion on logistic regression estimated probability | Logistic regression is a model that estimates probabilities. For the first dataset, it will predict the probability of "success", on average, to be $\tfrac{200}{20+200}$, in the second $\tfrac{20\,000}{20+20\,000}$. The predicted conditional probabilities will differ depending on how exactly the datasets differ.
It is ... | effect of class 0,1 proportion on logistic regression estimated probability | Logistic regression is a model that estimates probabilities. For the first dataset, it will predict the probability of "success", on average, to be $\tfrac{200}{20+200}$, in the second $\tfrac{20\,000 | effect of class 0,1 proportion on logistic regression estimated probability
Logistic regression is a model that estimates probabilities. For the first dataset, it will predict the probability of "success", on average, to be $\tfrac{200}{20+200}$, in the second $\tfrac{20\,000}{20+20\,000}$. The predicted conditional pr... | effect of class 0,1 proportion on logistic regression estimated probability
Logistic regression is a model that estimates probabilities. For the first dataset, it will predict the probability of "success", on average, to be $\tfrac{200}{20+200}$, in the second $\tfrac{20\,000 |
50,870 | Neural Networks - Strategies for problems with high Bayes error rate | You might find focal loss interesting. This is a reshaped standard cross entropy loss that down-weights the loss assigned to well-classified examples. It motivates a classifier to show more confidence where appropriate instead of only fearing a huge penalty for misclassification and hiding behind the base rate.
It is... | Neural Networks - Strategies for problems with high Bayes error rate | You might find focal loss interesting. This is a reshaped standard cross entropy loss that down-weights the loss assigned to well-classified examples. It motivates a classifier to show more confidence | Neural Networks - Strategies for problems with high Bayes error rate
You might find focal loss interesting. This is a reshaped standard cross entropy loss that down-weights the loss assigned to well-classified examples. It motivates a classifier to show more confidence where appropriate instead of only fearing a huge p... | Neural Networks - Strategies for problems with high Bayes error rate
You might find focal loss interesting. This is a reshaped standard cross entropy loss that down-weights the loss assigned to well-classified examples. It motivates a classifier to show more confidence |
50,871 | Comparing two models with statistical testing | This sounds like a great application for the $k$-fold cross-validated paired $t$ test (Dietterich, 1998). However, you need the accuracies per fold of both your model and the model from the other paper. Having only the mean accuracies over all folds is not sufficient (see alternative below).
The $k$-fold cross-validate... | Comparing two models with statistical testing | This sounds like a great application for the $k$-fold cross-validated paired $t$ test (Dietterich, 1998). However, you need the accuracies per fold of both your model and the model from the other pape | Comparing two models with statistical testing
This sounds like a great application for the $k$-fold cross-validated paired $t$ test (Dietterich, 1998). However, you need the accuracies per fold of both your model and the model from the other paper. Having only the mean accuracies over all folds is not sufficient (see a... | Comparing two models with statistical testing
This sounds like a great application for the $k$-fold cross-validated paired $t$ test (Dietterich, 1998). However, you need the accuracies per fold of both your model and the model from the other pape |
50,872 | About the variance of a weighted sum | It turns out that for large $n$, the above estimator can be written in the form $\mathbb E_X [(h(X) - b) g(X)]$ where $h(x) := f(x) / \int f(y) d\mu_X(y)$ , and by direct computation, has variance $\mathbb E_X [h(X)g(X)] - b\mathbb E_X[g(X)^2]$ which is of course minimized by taking
$$b = b^* := \frac{\operatorname{cov... | About the variance of a weighted sum | It turns out that for large $n$, the above estimator can be written in the form $\mathbb E_X [(h(X) - b) g(X)]$ where $h(x) := f(x) / \int f(y) d\mu_X(y)$ , and by direct computation, has variance $\m | About the variance of a weighted sum
It turns out that for large $n$, the above estimator can be written in the form $\mathbb E_X [(h(X) - b) g(X)]$ where $h(x) := f(x) / \int f(y) d\mu_X(y)$ , and by direct computation, has variance $\mathbb E_X [h(X)g(X)] - b\mathbb E_X[g(X)^2]$ which is of course minimized by taking... | About the variance of a weighted sum
It turns out that for large $n$, the above estimator can be written in the form $\mathbb E_X [(h(X) - b) g(X)]$ where $h(x) := f(x) / \int f(y) d\mu_X(y)$ , and by direct computation, has variance $\m |
50,873 | Keras difference between GRU and GRUCell | In GRU/LSTM Cell, there is no option of return_sequences. That means it is just a cell of an unfolded GRU/LSTM unit.
The argument of GRU/LSTM i.e. return_sequences, if return_sequences=True, then returns all the output state of the GRU/LSTM.
GRU/LSTM Cell computes and returns only one timestamp.
But, GRU/LSTM can retur... | Keras difference between GRU and GRUCell | In GRU/LSTM Cell, there is no option of return_sequences. That means it is just a cell of an unfolded GRU/LSTM unit.
The argument of GRU/LSTM i.e. return_sequences, if return_sequences=True, then retu | Keras difference between GRU and GRUCell
In GRU/LSTM Cell, there is no option of return_sequences. That means it is just a cell of an unfolded GRU/LSTM unit.
The argument of GRU/LSTM i.e. return_sequences, if return_sequences=True, then returns all the output state of the GRU/LSTM.
GRU/LSTM Cell computes and returns on... | Keras difference between GRU and GRUCell
In GRU/LSTM Cell, there is no option of return_sequences. That means it is just a cell of an unfolded GRU/LSTM unit.
The argument of GRU/LSTM i.e. return_sequences, if return_sequences=True, then retu |
50,874 | How would I use the largest expected effect size to determine a prior? | A good way to set priors is using prior predictive checks - basically you simulate new datasets from your model. If the simulated datasets are unrealistic in any way, it means your priors have problems.
Prior predictive checks have the advantage that they take complete structure of the model into account. If you howev... | How would I use the largest expected effect size to determine a prior? | A good way to set priors is using prior predictive checks - basically you simulate new datasets from your model. If the simulated datasets are unrealistic in any way, it means your priors have problem | How would I use the largest expected effect size to determine a prior?
A good way to set priors is using prior predictive checks - basically you simulate new datasets from your model. If the simulated datasets are unrealistic in any way, it means your priors have problems.
Prior predictive checks have the advantage th... | How would I use the largest expected effect size to determine a prior?
A good way to set priors is using prior predictive checks - basically you simulate new datasets from your model. If the simulated datasets are unrealistic in any way, it means your priors have problem |
50,875 | Feature Importance for Breast Cancer: Random Forests vs Logistic Regression | From your comments, it seems like what you are really after is feature selection - you want a set of models that use variable numbers of features (1, 2, 3, ..., N), such that incrementally adding a new feature yields as great an increase in model performance as possible. Then the decision makers can assess whether they... | Feature Importance for Breast Cancer: Random Forests vs Logistic Regression | From your comments, it seems like what you are really after is feature selection - you want a set of models that use variable numbers of features (1, 2, 3, ..., N), such that incrementally adding a ne | Feature Importance for Breast Cancer: Random Forests vs Logistic Regression
From your comments, it seems like what you are really after is feature selection - you want a set of models that use variable numbers of features (1, 2, 3, ..., N), such that incrementally adding a new feature yields as great an increase in mod... | Feature Importance for Breast Cancer: Random Forests vs Logistic Regression
From your comments, it seems like what you are really after is feature selection - you want a set of models that use variable numbers of features (1, 2, 3, ..., N), such that incrementally adding a ne |
50,876 | Feature Importance for Breast Cancer: Random Forests vs Logistic Regression | The question is ill-posed. We cannot advise the doctor that, for example, inspecting feature $X_a$ is more worthwhile than inspecting feature $X_b$, since how "important" a feature is only makes sense in the context of a specific model being used, and not the real world.
Logistic Regression and Random Forests are two ... | Feature Importance for Breast Cancer: Random Forests vs Logistic Regression | The question is ill-posed. We cannot advise the doctor that, for example, inspecting feature $X_a$ is more worthwhile than inspecting feature $X_b$, since how "important" a feature is only makes sense | Feature Importance for Breast Cancer: Random Forests vs Logistic Regression
The question is ill-posed. We cannot advise the doctor that, for example, inspecting feature $X_a$ is more worthwhile than inspecting feature $X_b$, since how "important" a feature is only makes sense in the context of a specific model being us... | Feature Importance for Breast Cancer: Random Forests vs Logistic Regression
The question is ill-posed. We cannot advise the doctor that, for example, inspecting feature $X_a$ is more worthwhile than inspecting feature $X_b$, since how "important" a feature is only makes sense |
50,877 | Zero-mean RV $X$, probability of being positive using moments | We can find find in literature (F.D. Lesley and V. Rotar) that:
$$P (X \geq 0) \geq \frac{2 \sqrt {3}-3}{E (X^4)}$$
if X has variance equal to 1. What is left for you to do is find out how this inequality scales when that condition is not true, and maybe see whether the $X\geq0$ instead of $X>0$ is not troubling. | Zero-mean RV $X$, probability of being positive using moments | We can find find in literature (F.D. Lesley and V. Rotar) that:
$$P (X \geq 0) \geq \frac{2 \sqrt {3}-3}{E (X^4)}$$
if X has variance equal to 1. What is left for you to do is find out how this inequa | Zero-mean RV $X$, probability of being positive using moments
We can find find in literature (F.D. Lesley and V. Rotar) that:
$$P (X \geq 0) \geq \frac{2 \sqrt {3}-3}{E (X^4)}$$
if X has variance equal to 1. What is left for you to do is find out how this inequality scales when that condition is not true, and maybe see... | Zero-mean RV $X$, probability of being positive using moments
We can find find in literature (F.D. Lesley and V. Rotar) that:
$$P (X \geq 0) \geq \frac{2 \sqrt {3}-3}{E (X^4)}$$
if X has variance equal to 1. What is left for you to do is find out how this inequa |
50,878 | Equivalent Gradients in Kernelized SVM | The second method is valid. It will converge because like you said, the problem is convex in terms of $\alpha$. However the two methods will not follow the same trajectory.
The two methods are related via preconditioning. Section 4 of the Pegasos paper has some commentary on this. I give an explicit description of thi... | Equivalent Gradients in Kernelized SVM | The second method is valid. It will converge because like you said, the problem is convex in terms of $\alpha$. However the two methods will not follow the same trajectory.
The two methods are relate | Equivalent Gradients in Kernelized SVM
The second method is valid. It will converge because like you said, the problem is convex in terms of $\alpha$. However the two methods will not follow the same trajectory.
The two methods are related via preconditioning. Section 4 of the Pegasos paper has some commentary on this... | Equivalent Gradients in Kernelized SVM
The second method is valid. It will converge because like you said, the problem is convex in terms of $\alpha$. However the two methods will not follow the same trajectory.
The two methods are relate |
50,879 | Interpretation of Constraint in Maximum Entropy Derivation of Cauchy distribution | I would say the result has been found backward, namely that, using the general property that the maximum entropy distribution under the constraint
$\mathbb{E}[f(X)]=\alpha$ is given by the density
$$\pi(x)=C\,\exp\{\lambda f(x)\}$$
when $C$ and $\lambda$ are determined by the conditions
$$\int_\mathcal{X} \exp\{\lambda... | Interpretation of Constraint in Maximum Entropy Derivation of Cauchy distribution | I would say the result has been found backward, namely that, using the general property that the maximum entropy distribution under the constraint
$\mathbb{E}[f(X)]=\alpha$ is given by the density
$$\ | Interpretation of Constraint in Maximum Entropy Derivation of Cauchy distribution
I would say the result has been found backward, namely that, using the general property that the maximum entropy distribution under the constraint
$\mathbb{E}[f(X)]=\alpha$ is given by the density
$$\pi(x)=C\,\exp\{\lambda f(x)\}$$
when $... | Interpretation of Constraint in Maximum Entropy Derivation of Cauchy distribution
I would say the result has been found backward, namely that, using the general property that the maximum entropy distribution under the constraint
$\mathbb{E}[f(X)]=\alpha$ is given by the density
$$\ |
50,880 | Number of components for Gaussian mixture model? | An alternative strategy is to test for Normality. If your data comes from a single Gaussian, you should fail to reject the null hypothesis. Conversely, if you get a statistically significant p-value for rejecting the null hypothesis, then you know that k > 1. This strategy can be easily generalized to the multi-variate... | Number of components for Gaussian mixture model? | An alternative strategy is to test for Normality. If your data comes from a single Gaussian, you should fail to reject the null hypothesis. Conversely, if you get a statistically significant p-value f | Number of components for Gaussian mixture model?
An alternative strategy is to test for Normality. If your data comes from a single Gaussian, you should fail to reject the null hypothesis. Conversely, if you get a statistically significant p-value for rejecting the null hypothesis, then you know that k > 1. This strate... | Number of components for Gaussian mixture model?
An alternative strategy is to test for Normality. If your data comes from a single Gaussian, you should fail to reject the null hypothesis. Conversely, if you get a statistically significant p-value f |
50,881 | Unbiased estimator of distribution function in two-stage randomization design | This question contains a lot of background material, but most of it is not relevant for answering the questions you pose.
This is a two stage trial. The initial treatment $A$ has two levels $A_1$ and $A_2$. However, as explained in the paper, patients randomized to $A_1$ and $A_2$ form two independent samples, so I'm ... | Unbiased estimator of distribution function in two-stage randomization design | This question contains a lot of background material, but most of it is not relevant for answering the questions you pose.
This is a two stage trial. The initial treatment $A$ has two levels $A_1$ and | Unbiased estimator of distribution function in two-stage randomization design
This question contains a lot of background material, but most of it is not relevant for answering the questions you pose.
This is a two stage trial. The initial treatment $A$ has two levels $A_1$ and $A_2$. However, as explained in the paper... | Unbiased estimator of distribution function in two-stage randomization design
This question contains a lot of background material, but most of it is not relevant for answering the questions you pose.
This is a two stage trial. The initial treatment $A$ has two levels $A_1$ and |
50,882 | Autocorrelation and heteroskedasticity in time series data | We have seen residual plots such as yours when untreated deterministic effects are present. These might include hourly or daily effects. Care should be taken to identify and incorporate any needed effects like Pulses,Level Shifts,Seasonal Pulses and/or Local Time Trends . Needed ARIMA Structure suggested by model diagn... | Autocorrelation and heteroskedasticity in time series data | We have seen residual plots such as yours when untreated deterministic effects are present. These might include hourly or daily effects. Care should be taken to identify and incorporate any needed eff | Autocorrelation and heteroskedasticity in time series data
We have seen residual plots such as yours when untreated deterministic effects are present. These might include hourly or daily effects. Care should be taken to identify and incorporate any needed effects like Pulses,Level Shifts,Seasonal Pulses and/or Local Ti... | Autocorrelation and heteroskedasticity in time series data
We have seen residual plots such as yours when untreated deterministic effects are present. These might include hourly or daily effects. Care should be taken to identify and incorporate any needed eff |
50,883 | Dependent count variable with negative values | While the number of managers before and after are count variables, your dependent variable no longer is: Counts can't be negative, after all. So you don't need to use either poisson or negative binomial. | Dependent count variable with negative values | While the number of managers before and after are count variables, your dependent variable no longer is: Counts can't be negative, after all. So you don't need to use either poisson or negative binomi | Dependent count variable with negative values
While the number of managers before and after are count variables, your dependent variable no longer is: Counts can't be negative, after all. So you don't need to use either poisson or negative binomial. | Dependent count variable with negative values
While the number of managers before and after are count variables, your dependent variable no longer is: Counts can't be negative, after all. So you don't need to use either poisson or negative binomi |
50,884 | Dependent count variable with negative values | For this kind of analysis I would suggest that you follow whuber's advice in his comment, and track the individual counts of the number of managers before and after each change. It should not be too hard to create a GLM that uses the non-negative count variable managers as the response variable and uses a binary indic... | Dependent count variable with negative values | For this kind of analysis I would suggest that you follow whuber's advice in his comment, and track the individual counts of the number of managers before and after each change. It should not be too | Dependent count variable with negative values
For this kind of analysis I would suggest that you follow whuber's advice in his comment, and track the individual counts of the number of managers before and after each change. It should not be too hard to create a GLM that uses the non-negative count variable managers as... | Dependent count variable with negative values
For this kind of analysis I would suggest that you follow whuber's advice in his comment, and track the individual counts of the number of managers before and after each change. It should not be too |
50,885 | Dependent count variable with negative values | Y is not actually a count - counts can only have positive values. It's a difference, which is, well, different.
One option would be to treat Y as a continuous variable and use ordinary least squares regression. Another would be to add 5 to Y and use a count regression model. You could try both and see if the results ... | Dependent count variable with negative values | Y is not actually a count - counts can only have positive values. It's a difference, which is, well, different.
One option would be to treat Y as a continuous variable and use ordinary least squares | Dependent count variable with negative values
Y is not actually a count - counts can only have positive values. It's a difference, which is, well, different.
One option would be to treat Y as a continuous variable and use ordinary least squares regression. Another would be to add 5 to Y and use a count regression mode... | Dependent count variable with negative values
Y is not actually a count - counts can only have positive values. It's a difference, which is, well, different.
One option would be to treat Y as a continuous variable and use ordinary least squares |
50,886 | Batch normalization: How to update gamma and beta during backpropagation training step? | Your intuition is correct. You can use gradient descent to update any parameter in your network. So as long as you can compute the gradient of the loss function with respect to that parameter (using backpropagation). Gamma and Beta of batch normalization layers are no exceptions. | Batch normalization: How to update gamma and beta during backpropagation training step? | Your intuition is correct. You can use gradient descent to update any parameter in your network. So as long as you can compute the gradient of the loss function with respect to that parameter (using b | Batch normalization: How to update gamma and beta during backpropagation training step?
Your intuition is correct. You can use gradient descent to update any parameter in your network. So as long as you can compute the gradient of the loss function with respect to that parameter (using backpropagation). Gamma and Beta ... | Batch normalization: How to update gamma and beta during backpropagation training step?
Your intuition is correct. You can use gradient descent to update any parameter in your network. So as long as you can compute the gradient of the loss function with respect to that parameter (using b |
50,887 | Functions of continuous random variables | First of all,
$$ P[W \le w] = P[Y^3 \le w] = P[Y \le w^{1/3}] = 1- e^\frac{-w^{1/3} }{t}$$
ie. this is a function of W not Y.
Second, as said in the comments your logic is right but your integral is wrong.
We have the expression
$$ \int_0^{w^{1/3}} \frac{1}{t} e^{-y/t} dy $$
Let $$u = \frac{-y}{t} $$
and you get the ... | Functions of continuous random variables | First of all,
$$ P[W \le w] = P[Y^3 \le w] = P[Y \le w^{1/3}] = 1- e^\frac{-w^{1/3} }{t}$$
ie. this is a function of W not Y.
Second, as said in the comments your logic is right but your integral is w | Functions of continuous random variables
First of all,
$$ P[W \le w] = P[Y^3 \le w] = P[Y \le w^{1/3}] = 1- e^\frac{-w^{1/3} }{t}$$
ie. this is a function of W not Y.
Second, as said in the comments your logic is right but your integral is wrong.
We have the expression
$$ \int_0^{w^{1/3}} \frac{1}{t} e^{-y/t} dy $$
L... | Functions of continuous random variables
First of all,
$$ P[W \le w] = P[Y^3 \le w] = P[Y \le w^{1/3}] = 1- e^\frac{-w^{1/3} }{t}$$
ie. this is a function of W not Y.
Second, as said in the comments your logic is right but your integral is w |
50,888 | HMM for multichannel - multivariate data | One option:
I worked on this exact same problem couple of years ago. The mixed data I was working with were multivariate with some of the dimensions being categorical and some other continuous.
The trick has been to modify the equations of the Baum-Welch approach so it can handle both types of data. For instance, the r... | HMM for multichannel - multivariate data | One option:
I worked on this exact same problem couple of years ago. The mixed data I was working with were multivariate with some of the dimensions being categorical and some other continuous.
The tr | HMM for multichannel - multivariate data
One option:
I worked on this exact same problem couple of years ago. The mixed data I was working with were multivariate with some of the dimensions being categorical and some other continuous.
The trick has been to modify the equations of the Baum-Welch approach so it can handl... | HMM for multichannel - multivariate data
One option:
I worked on this exact same problem couple of years ago. The mixed data I was working with were multivariate with some of the dimensions being categorical and some other continuous.
The tr |
50,889 | What is the point of putting two lstm cells one after another? [duplicate] | One layer only has one cell. For more information read this. And the stacked multi-layer LSTM model is for extracting more abstract information. I think this question and this answer have explained this issue in detail. | What is the point of putting two lstm cells one after another? [duplicate] | One layer only has one cell. For more information read this. And the stacked multi-layer LSTM model is for extracting more abstract information. I think this question and this answer have explained th | What is the point of putting two lstm cells one after another? [duplicate]
One layer only has one cell. For more information read this. And the stacked multi-layer LSTM model is for extracting more abstract information. I think this question and this answer have explained this issue in detail. | What is the point of putting two lstm cells one after another? [duplicate]
One layer only has one cell. For more information read this. And the stacked multi-layer LSTM model is for extracting more abstract information. I think this question and this answer have explained th |
50,890 | mean and variance of norm of normal random variables | The distribution you are looking for relates to the convolution of two non-central chi-squared distributions each with one degree-of-freedom (which is a nasty one). Squaring the norm gives you:
$$\begin{align}
R^2
&= X^2 + Y^2 \\[6pt]
&= \sigma_x^2 \Big( \frac{X}{\sigma_x} \Big)^2 + \sigma_y^2 \Big( \frac{Y}{\sigma_y... | mean and variance of norm of normal random variables | The distribution you are looking for relates to the convolution of two non-central chi-squared distributions each with one degree-of-freedom (which is a nasty one). Squaring the norm gives you:
$$\be | mean and variance of norm of normal random variables
The distribution you are looking for relates to the convolution of two non-central chi-squared distributions each with one degree-of-freedom (which is a nasty one). Squaring the norm gives you:
$$\begin{align}
R^2
&= X^2 + Y^2 \\[6pt]
&= \sigma_x^2 \Big( \frac{X}{\... | mean and variance of norm of normal random variables
The distribution you are looking for relates to the convolution of two non-central chi-squared distributions each with one degree-of-freedom (which is a nasty one). Squaring the norm gives you:
$$\be |
50,891 | mean and variance of norm of normal random variables | If $x$ and $y$ are independent, $\mu_x=\mu_y=0$ and $\sigma_x=\sigma_y=\sigma$, $r$ follows a Rayleigh distribution, thus:
$$ \begin{align}
& E[r] = \sigma \sqrt{\frac{\pi}{2}}
\\[6pt]
& V[r] = \frac{4-\pi}{2}\sigma^2
\end{align} $$ | mean and variance of norm of normal random variables | If $x$ and $y$ are independent, $\mu_x=\mu_y=0$ and $\sigma_x=\sigma_y=\sigma$, $r$ follows a Rayleigh distribution, thus:
$$ \begin{align}
& E[r] = \sigma \sqrt{\frac{\pi}{2}}
\\[6pt]
& V[r] = \frac{ | mean and variance of norm of normal random variables
If $x$ and $y$ are independent, $\mu_x=\mu_y=0$ and $\sigma_x=\sigma_y=\sigma$, $r$ follows a Rayleigh distribution, thus:
$$ \begin{align}
& E[r] = \sigma \sqrt{\frac{\pi}{2}}
\\[6pt]
& V[r] = \frac{4-\pi}{2}\sigma^2
\end{align} $$ | mean and variance of norm of normal random variables
If $x$ and $y$ are independent, $\mu_x=\mu_y=0$ and $\sigma_x=\sigma_y=\sigma$, $r$ follows a Rayleigh distribution, thus:
$$ \begin{align}
& E[r] = \sigma \sqrt{\frac{\pi}{2}}
\\[6pt]
& V[r] = \frac{ |
50,892 | mean and variance of norm of normal random variables | Use the polar coordinates transformation if you're good at integrating.
Define
$$
\left[\begin{array}{c}
R \\
\theta
\end{array} \right]
=
\left[\begin{array}{c}
\sqrt{X^2 + Y^2} \\
\text{arctan}(\theta)
\end{array} \right],
$$
which means
$$
\left[\begin{array}{c}
X \\
Y
\end{array} \right]
=
\left[\begin{array}{c}
R... | mean and variance of norm of normal random variables | Use the polar coordinates transformation if you're good at integrating.
Define
$$
\left[\begin{array}{c}
R \\
\theta
\end{array} \right]
=
\left[\begin{array}{c}
\sqrt{X^2 + Y^2} \\
\text{arctan}(\th | mean and variance of norm of normal random variables
Use the polar coordinates transformation if you're good at integrating.
Define
$$
\left[\begin{array}{c}
R \\
\theta
\end{array} \right]
=
\left[\begin{array}{c}
\sqrt{X^2 + Y^2} \\
\text{arctan}(\theta)
\end{array} \right],
$$
which means
$$
\left[\begin{array}{c}
... | mean and variance of norm of normal random variables
Use the polar coordinates transformation if you're good at integrating.
Define
$$
\left[\begin{array}{c}
R \\
\theta
\end{array} \right]
=
\left[\begin{array}{c}
\sqrt{X^2 + Y^2} \\
\text{arctan}(\th |
50,893 | t test p value vs randomization-inference p value: What can we learn from comparison? | I think your statement of the randomization inference null hypothesis is incorrect. Or at least, you're confusing two methods to test hypotheses versus two different hypotheses. The randomization test aka the permutation test considers the exact or approximation distribution of test statistics obtained when "labels" ar... | t test p value vs randomization-inference p value: What can we learn from comparison? | I think your statement of the randomization inference null hypothesis is incorrect. Or at least, you're confusing two methods to test hypotheses versus two different hypotheses. The randomization test | t test p value vs randomization-inference p value: What can we learn from comparison?
I think your statement of the randomization inference null hypothesis is incorrect. Or at least, you're confusing two methods to test hypotheses versus two different hypotheses. The randomization test aka the permutation test consider... | t test p value vs randomization-inference p value: What can we learn from comparison?
I think your statement of the randomization inference null hypothesis is incorrect. Or at least, you're confusing two methods to test hypotheses versus two different hypotheses. The randomization test |
50,894 | t test p value vs randomization-inference p value: What can we learn from comparison? | I found this discussion of the difference between t-test p values and RI p values helpful, and it speaks to the question I ask above.
Author: Don Green
Source: https://egap.org/resource/10-things-to-know-about-randomization-inference/
Randomization inference may give different p-values from conventional tests when the ... | t test p value vs randomization-inference p value: What can we learn from comparison? | I found this discussion of the difference between t-test p values and RI p values helpful, and it speaks to the question I ask above.
Author: Don Green
Source: https://egap.org/resource/10-things-to-k | t test p value vs randomization-inference p value: What can we learn from comparison?
I found this discussion of the difference between t-test p values and RI p values helpful, and it speaks to the question I ask above.
Author: Don Green
Source: https://egap.org/resource/10-things-to-know-about-randomization-inference/... | t test p value vs randomization-inference p value: What can we learn from comparison?
I found this discussion of the difference between t-test p values and RI p values helpful, and it speaks to the question I ask above.
Author: Don Green
Source: https://egap.org/resource/10-things-to-k |
50,895 | Regression Trees' greedy algorithm in Hastie et al. (2009) | This simple example might illustrate why the 'greedy algorithm' is quicker than 'finding the best partition', but also why it can be less good.
Imagine a binary outcome with two features that follows the following rule: the outcome is A if feature 1 is non-negative and feature 2 is negative or feature 1 is negative and... | Regression Trees' greedy algorithm in Hastie et al. (2009) | This simple example might illustrate why the 'greedy algorithm' is quicker than 'finding the best partition', but also why it can be less good.
Imagine a binary outcome with two features that follows | Regression Trees' greedy algorithm in Hastie et al. (2009)
This simple example might illustrate why the 'greedy algorithm' is quicker than 'finding the best partition', but also why it can be less good.
Imagine a binary outcome with two features that follows the following rule: the outcome is A if feature 1 is non-nega... | Regression Trees' greedy algorithm in Hastie et al. (2009)
This simple example might illustrate why the 'greedy algorithm' is quicker than 'finding the best partition', but also why it can be less good.
Imagine a binary outcome with two features that follows |
50,896 | Regression Trees' greedy algorithm in Hastie et al. (2009) | The difference between the squared error minimization that is done for each split in a decision tree and that is done for a typical $L_2$ loss optimization has 1 subtle distinction:
The decision tree splitting problem must search across possible partitions of the data into 2 groups and then find the optimal means with... | Regression Trees' greedy algorithm in Hastie et al. (2009) | The difference between the squared error minimization that is done for each split in a decision tree and that is done for a typical $L_2$ loss optimization has 1 subtle distinction:
The decision tree | Regression Trees' greedy algorithm in Hastie et al. (2009)
The difference between the squared error minimization that is done for each split in a decision tree and that is done for a typical $L_2$ loss optimization has 1 subtle distinction:
The decision tree splitting problem must search across possible partitions of ... | Regression Trees' greedy algorithm in Hastie et al. (2009)
The difference between the squared error minimization that is done for each split in a decision tree and that is done for a typical $L_2$ loss optimization has 1 subtle distinction:
The decision tree |
50,897 | Different estimates for over dispersion using Pearson or Deviance statistics in Poisson model | What about the descriptive statistics to confirm those results? Is the variance of your dependent variable higher than the mean? Here is the reference:
Ryan, W. H., Evers, E. R. K., & Moore, D. A. (2021). Poisson regressions: A little fishy. Collabra: Psychology, 7(1), 27242. https://doi.org/10.1525/collabra.27242
I ... | Different estimates for over dispersion using Pearson or Deviance statistics in Poisson model | What about the descriptive statistics to confirm those results? Is the variance of your dependent variable higher than the mean? Here is the reference:
Ryan, W. H., Evers, E. R. K., & Moore, D. A. (2 | Different estimates for over dispersion using Pearson or Deviance statistics in Poisson model
What about the descriptive statistics to confirm those results? Is the variance of your dependent variable higher than the mean? Here is the reference:
Ryan, W. H., Evers, E. R. K., & Moore, D. A. (2021). Poisson regressions:... | Different estimates for over dispersion using Pearson or Deviance statistics in Poisson model
What about the descriptive statistics to confirm those results? Is the variance of your dependent variable higher than the mean? Here is the reference:
Ryan, W. H., Evers, E. R. K., & Moore, D. A. (2 |
50,898 | XGBoost feature subsampling | You seem to fine-tune the wrong things.
On your feature selection:
I don't think that this is done properly:
You remove the good feature and all linearly correlated features. That's nice, but higher order correlated features are still there. On the other hand, strong correlation does not always mean that the feature i... | XGBoost feature subsampling | You seem to fine-tune the wrong things.
On your feature selection:
I don't think that this is done properly:
You remove the good feature and all linearly correlated features. That's nice, but higher | XGBoost feature subsampling
You seem to fine-tune the wrong things.
On your feature selection:
I don't think that this is done properly:
You remove the good feature and all linearly correlated features. That's nice, but higher order correlated features are still there. On the other hand, strong correlation does not al... | XGBoost feature subsampling
You seem to fine-tune the wrong things.
On your feature selection:
I don't think that this is done properly:
You remove the good feature and all linearly correlated features. That's nice, but higher |
50,899 | How to understand "factor loadings" in PCA? [duplicate] | I believe your two plots are factor loadings given by PCA for the first two principal components.
The bar represents the magnitude for each variable "loaded" on the latent component
The bar also represent whether the loading is positive or negative
Based on the plots, I can see variable 4 and 6 are highly loaded on P... | How to understand "factor loadings" in PCA? [duplicate] | I believe your two plots are factor loadings given by PCA for the first two principal components.
The bar represents the magnitude for each variable "loaded" on the latent component
The bar also repr | How to understand "factor loadings" in PCA? [duplicate]
I believe your two plots are factor loadings given by PCA for the first two principal components.
The bar represents the magnitude for each variable "loaded" on the latent component
The bar also represent whether the loading is positive or negative
Based on the ... | How to understand "factor loadings" in PCA? [duplicate]
I believe your two plots are factor loadings given by PCA for the first two principal components.
The bar represents the magnitude for each variable "loaded" on the latent component
The bar also repr |
50,900 | Opinion polls during which voters are allowed to see accumulated intermediate result | There is some research in betting markets which are a form of opinion poll with money attached. See Soccermatics by David Sumpter, p229. The wisdom of crowds polling is based on each individual making an independent choice. If they see what others have done then the "wisdom" of the crowd is lost - they become a dumb he... | Opinion polls during which voters are allowed to see accumulated intermediate result | There is some research in betting markets which are a form of opinion poll with money attached. See Soccermatics by David Sumpter, p229. The wisdom of crowds polling is based on each individual making | Opinion polls during which voters are allowed to see accumulated intermediate result
There is some research in betting markets which are a form of opinion poll with money attached. See Soccermatics by David Sumpter, p229. The wisdom of crowds polling is based on each individual making an independent choice. If they see... | Opinion polls during which voters are allowed to see accumulated intermediate result
There is some research in betting markets which are a form of opinion poll with money attached. See Soccermatics by David Sumpter, p229. The wisdom of crowds polling is based on each individual making |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.