idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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43,101 | Is the inductive bias a prior? | Prior is a prior knowledge that can help us learn new concepts from the available data.
Prior or inductive prior is also known as inductive bias.
In here, the word inductive does not hold the strict mathematical meaning of induction, but rather the fact that we will make some inference based on the previous knowledge.
... | Is the inductive bias a prior? | Prior is a prior knowledge that can help us learn new concepts from the available data.
Prior or inductive prior is also known as inductive bias.
In here, the word inductive does not hold the strict m | Is the inductive bias a prior?
Prior is a prior knowledge that can help us learn new concepts from the available data.
Prior or inductive prior is also known as inductive bias.
In here, the word inductive does not hold the strict mathematical meaning of induction, but rather the fact that we will make some inference ba... | Is the inductive bias a prior?
Prior is a prior knowledge that can help us learn new concepts from the available data.
Prior or inductive prior is also known as inductive bias.
In here, the word inductive does not hold the strict m |
43,102 | Is the inductive bias a prior? | No. This is the likelihood as evident from the defintion. You introduce inductive bias in linear regression by making assumption that the data follows linear model. Even in Bayesian approaches you're introducing some inductive bias by assuming that data follows a model from a certain family. | Is the inductive bias a prior? | No. This is the likelihood as evident from the defintion. You introduce inductive bias in linear regression by making assumption that the data follows linear model. Even in Bayesian approaches you're | Is the inductive bias a prior?
No. This is the likelihood as evident from the defintion. You introduce inductive bias in linear regression by making assumption that the data follows linear model. Even in Bayesian approaches you're introducing some inductive bias by assuming that data follows a model from a certain fami... | Is the inductive bias a prior?
No. This is the likelihood as evident from the defintion. You introduce inductive bias in linear regression by making assumption that the data follows linear model. Even in Bayesian approaches you're |
43,103 | Computing cross-validated $R^2$ from mean cross-validation error | The confusion was caused by a one-symbol typo in the originally posted code (see comments above).
The answers are:
Yes.
Yes, but only for Gaussian GLM (as far as I understand from the glmnet package description).
Depends on how you define $R^2$ for the weighted regression. Deviance ratio will take weights into account... | Computing cross-validated $R^2$ from mean cross-validation error | The confusion was caused by a one-symbol typo in the originally posted code (see comments above).
The answers are:
Yes.
Yes, but only for Gaussian GLM (as far as I understand from the glmnet package | Computing cross-validated $R^2$ from mean cross-validation error
The confusion was caused by a one-symbol typo in the originally posted code (see comments above).
The answers are:
Yes.
Yes, but only for Gaussian GLM (as far as I understand from the glmnet package description).
Depends on how you define $R^2$ for the w... | Computing cross-validated $R^2$ from mean cross-validation error
The confusion was caused by a one-symbol typo in the originally posted code (see comments above).
The answers are:
Yes.
Yes, but only for Gaussian GLM (as far as I understand from the glmnet package |
43,104 | What is the objective of maximum likelihood estimation? | The objective is to estimate the parameters or, more precisely, to get a method for their estimation (since the same form of likelihood can be applied to different data sets).
There are different ways to choose parameter estimators - maximum likelihood is just one of them, which uses as the criteria for choosing the es... | What is the objective of maximum likelihood estimation? | The objective is to estimate the parameters or, more precisely, to get a method for their estimation (since the same form of likelihood can be applied to different data sets).
There are different ways | What is the objective of maximum likelihood estimation?
The objective is to estimate the parameters or, more precisely, to get a method for their estimation (since the same form of likelihood can be applied to different data sets).
There are different ways to choose parameter estimators - maximum likelihood is just one... | What is the objective of maximum likelihood estimation?
The objective is to estimate the parameters or, more precisely, to get a method for their estimation (since the same form of likelihood can be applied to different data sets).
There are different ways |
43,105 | What is the objective of maximum likelihood estimation? | Oh, I think I understand a bit better now. The objective is to find parameters that maximize the likelihood that our observations will be similar if we take another, similar, sample. For example, let's say that we draw 5 marbles from a bag and 3 of them are black. We then place them back in the bag. Our objective, then... | What is the objective of maximum likelihood estimation? | Oh, I think I understand a bit better now. The objective is to find parameters that maximize the likelihood that our observations will be similar if we take another, similar, sample. For example, let' | What is the objective of maximum likelihood estimation?
Oh, I think I understand a bit better now. The objective is to find parameters that maximize the likelihood that our observations will be similar if we take another, similar, sample. For example, let's say that we draw 5 marbles from a bag and 3 of them are black.... | What is the objective of maximum likelihood estimation?
Oh, I think I understand a bit better now. The objective is to find parameters that maximize the likelihood that our observations will be similar if we take another, similar, sample. For example, let' |
43,106 | Kolmogorov-Smirnov test with dependent data | the Kolmogorov-Smirnov test is only to be used if the samples are independent. However, here you can find a script that does the job in form of a permutation test (in R). | Kolmogorov-Smirnov test with dependent data | the Kolmogorov-Smirnov test is only to be used if the samples are independent. However, here you can find a script that does the job in form of a permutation test (in R). | Kolmogorov-Smirnov test with dependent data
the Kolmogorov-Smirnov test is only to be used if the samples are independent. However, here you can find a script that does the job in form of a permutation test (in R). | Kolmogorov-Smirnov test with dependent data
the Kolmogorov-Smirnov test is only to be used if the samples are independent. However, here you can find a script that does the job in form of a permutation test (in R). |
43,107 | Kolmogorov-Smirnov test with dependent data | The Kolmogorov-Smirnov test is designed for two independent samples. You need a test for paired observations. I do not think anyone has ever proposed a KS test analog for paired observations. Also, it is a very cautious test, that is, it has low power in many circumstances.
I suggest a paired nonparametric test, either... | Kolmogorov-Smirnov test with dependent data | The Kolmogorov-Smirnov test is designed for two independent samples. You need a test for paired observations. I do not think anyone has ever proposed a KS test analog for paired observations. Also, it | Kolmogorov-Smirnov test with dependent data
The Kolmogorov-Smirnov test is designed for two independent samples. You need a test for paired observations. I do not think anyone has ever proposed a KS test analog for paired observations. Also, it is a very cautious test, that is, it has low power in many circumstances.
I... | Kolmogorov-Smirnov test with dependent data
The Kolmogorov-Smirnov test is designed for two independent samples. You need a test for paired observations. I do not think anyone has ever proposed a KS test analog for paired observations. Also, it |
43,108 | Kolmogorov-Smirnov test with dependent data | I believe what you need is a (Related-Samples) Friedman's Two-way Analysis of Variance by Ranks (see this).
It comes with the a pair of null hypotheses about the distributions you are comparing that you can reject/retain depending on the p value:
H0(a): "The populations represented by the k conditions have the same di... | Kolmogorov-Smirnov test with dependent data | I believe what you need is a (Related-Samples) Friedman's Two-way Analysis of Variance by Ranks (see this).
It comes with the a pair of null hypotheses about the distributions you are comparing that y | Kolmogorov-Smirnov test with dependent data
I believe what you need is a (Related-Samples) Friedman's Two-way Analysis of Variance by Ranks (see this).
It comes with the a pair of null hypotheses about the distributions you are comparing that you can reject/retain depending on the p value:
H0(a): "The populations repr... | Kolmogorov-Smirnov test with dependent data
I believe what you need is a (Related-Samples) Friedman's Two-way Analysis of Variance by Ranks (see this).
It comes with the a pair of null hypotheses about the distributions you are comparing that y |
43,109 | How to use LDA results for feature selection? | If it doesn't need to be vanilla LDA (which is not supposed to select from input features), there's e.g. Sparse Discriminant Analysis, which is a LASSO penalized LDA:
Line Clemmensen, Trevor Hastie, Daniela Witten, Bjarne Ersbøll: Sparse Discriminant Analysis (2011)
This uses a discrete subset of the input features vi... | How to use LDA results for feature selection? | If it doesn't need to be vanilla LDA (which is not supposed to select from input features), there's e.g. Sparse Discriminant Analysis, which is a LASSO penalized LDA:
Line Clemmensen, Trevor Hastie, | How to use LDA results for feature selection?
If it doesn't need to be vanilla LDA (which is not supposed to select from input features), there's e.g. Sparse Discriminant Analysis, which is a LASSO penalized LDA:
Line Clemmensen, Trevor Hastie, Daniela Witten, Bjarne Ersbøll: Sparse Discriminant Analysis (2011)
This u... | How to use LDA results for feature selection?
If it doesn't need to be vanilla LDA (which is not supposed to select from input features), there's e.g. Sparse Discriminant Analysis, which is a LASSO penalized LDA:
Line Clemmensen, Trevor Hastie, |
43,110 | How to use LDA results for feature selection? | Lda models are used to predict a categorical variable (factor) using one or several continuous (numerical) features. So given some measurements about a forest, you will be able to predict which type of forest a given observation belongs to. Before applying a lda model, you have to determine which features are relevant ... | How to use LDA results for feature selection? | Lda models are used to predict a categorical variable (factor) using one or several continuous (numerical) features. So given some measurements about a forest, you will be able to predict which type o | How to use LDA results for feature selection?
Lda models are used to predict a categorical variable (factor) using one or several continuous (numerical) features. So given some measurements about a forest, you will be able to predict which type of forest a given observation belongs to. Before applying a lda model, you ... | How to use LDA results for feature selection?
Lda models are used to predict a categorical variable (factor) using one or several continuous (numerical) features. So given some measurements about a forest, you will be able to predict which type o |
43,111 | How to use LDA results for feature selection? | I don't know if this may be of any use, but I wanted to mention the idea of using LDA to give an "importance value" to each features (for selection), by computing the correlation of each features to each components (LD1, LD2, LD3,...) and selecting the features that are highly correlated to some important components.
P... | How to use LDA results for feature selection? | I don't know if this may be of any use, but I wanted to mention the idea of using LDA to give an "importance value" to each features (for selection), by computing the correlation of each features to e | How to use LDA results for feature selection?
I don't know if this may be of any use, but I wanted to mention the idea of using LDA to give an "importance value" to each features (for selection), by computing the correlation of each features to each components (LD1, LD2, LD3,...) and selecting the features that are hig... | How to use LDA results for feature selection?
I don't know if this may be of any use, but I wanted to mention the idea of using LDA to give an "importance value" to each features (for selection), by computing the correlation of each features to e |
43,112 | multi-class classification with word2vec | It is always hard to assess a priori the performance of a pre-treatment on the data. Even something as simple as normalizing the data does not have an obvious influence on the performance on the later trained classifiers (see per example this post : Normalizing data worsens the performance of CNN?).
However the follow... | multi-class classification with word2vec | It is always hard to assess a priori the performance of a pre-treatment on the data. Even something as simple as normalizing the data does not have an obvious influence on the performance on the later | multi-class classification with word2vec
It is always hard to assess a priori the performance of a pre-treatment on the data. Even something as simple as normalizing the data does not have an obvious influence on the performance on the later trained classifiers (see per example this post : Normalizing data worsens the ... | multi-class classification with word2vec
It is always hard to assess a priori the performance of a pre-treatment on the data. Even something as simple as normalizing the data does not have an obvious influence on the performance on the later |
43,113 | multi-class classification with word2vec | The best place to start is with a linear kernel, since this is a) the simplest and b) often works well with text data. You could then try nonlinear kernels such as the popular RBF kernel. | multi-class classification with word2vec | The best place to start is with a linear kernel, since this is a) the simplest and b) often works well with text data. You could then try nonlinear kernels such as the popular RBF kernel. | multi-class classification with word2vec
The best place to start is with a linear kernel, since this is a) the simplest and b) often works well with text data. You could then try nonlinear kernels such as the popular RBF kernel. | multi-class classification with word2vec
The best place to start is with a linear kernel, since this is a) the simplest and b) often works well with text data. You could then try nonlinear kernels such as the popular RBF kernel. |
43,114 | Closed form function relating $\mu$ to the natural parameter for the logarithmic series distribution? | You have the answer in your question: Lambert-W.
In R you can use
# Load library
library(LambertW)
# Define function to obtain p from mu
p <- function(mu) {1 - exp((1/mu) + W(-1/(mu*exp(1/mu)),-1))}
# Show (visually) that the function provides the correct values
mu <- 1 + 10*c(0:100)/100
plot(p(mu), mu, xlab... | Closed form function relating $\mu$ to the natural parameter for the logarithmic series distribution | You have the answer in your question: Lambert-W.
In R you can use
# Load library
library(LambertW)
# Define function to obtain p from mu
p <- function(mu) {1 - exp((1/mu) + W(-1/(mu*exp(1/mu)),- | Closed form function relating $\mu$ to the natural parameter for the logarithmic series distribution?
You have the answer in your question: Lambert-W.
In R you can use
# Load library
library(LambertW)
# Define function to obtain p from mu
p <- function(mu) {1 - exp((1/mu) + W(-1/(mu*exp(1/mu)),-1))}
# Show (visu... | Closed form function relating $\mu$ to the natural parameter for the logarithmic series distribution
You have the answer in your question: Lambert-W.
In R you can use
# Load library
library(LambertW)
# Define function to obtain p from mu
p <- function(mu) {1 - exp((1/mu) + W(-1/(mu*exp(1/mu)),- |
43,115 | ARMA-GARCH model selection / fit evaluation | In short, you should select models using AIC and/or out-of-sample fit criteria and view the rejected hypothesis as a suggestion to consider other types of models.
When using this class of time series models researchers are usually interested in accurate prediction\forecasting. Since AIC measures how well a model pre... | ARMA-GARCH model selection / fit evaluation | In short, you should select models using AIC and/or out-of-sample fit criteria and view the rejected hypothesis as a suggestion to consider other types of models.
When using this class of time serie | ARMA-GARCH model selection / fit evaluation
In short, you should select models using AIC and/or out-of-sample fit criteria and view the rejected hypothesis as a suggestion to consider other types of models.
When using this class of time series models researchers are usually interested in accurate prediction\forecasti... | ARMA-GARCH model selection / fit evaluation
In short, you should select models using AIC and/or out-of-sample fit criteria and view the rejected hypothesis as a suggestion to consider other types of models.
When using this class of time serie |
43,116 | How to standardize proportions from US Census data | After talking to local statisticians and not seeing any other answers, I can provide some answer. I'm also happy to remove the question if commentators think it is too narrow.
The number of respondents is the right sample size for the score computations. I was using 1%, and I've since learned that 2/3 of 1% is a better... | How to standardize proportions from US Census data | After talking to local statisticians and not seeing any other answers, I can provide some answer. I'm also happy to remove the question if commentators think it is too narrow.
The number of respondent | How to standardize proportions from US Census data
After talking to local statisticians and not seeing any other answers, I can provide some answer. I'm also happy to remove the question if commentators think it is too narrow.
The number of respondents is the right sample size for the score computations. I was using 1%... | How to standardize proportions from US Census data
After talking to local statisticians and not seeing any other answers, I can provide some answer. I'm also happy to remove the question if commentators think it is too narrow.
The number of respondent |
43,117 | Time varying coefficient in Cox model | Just answered my own question with the same problem. Basically you need to do a time-split as you describe and then add an interaction term for the time. As you suggested it sounds like a good idea to perhaps split the time more fine grained in the beginning and then increase the intervals. Using my Greg package you ca... | Time varying coefficient in Cox model | Just answered my own question with the same problem. Basically you need to do a time-split as you describe and then add an interaction term for the time. As you suggested it sounds like a good idea to | Time varying coefficient in Cox model
Just answered my own question with the same problem. Basically you need to do a time-split as you describe and then add an interaction term for the time. As you suggested it sounds like a good idea to perhaps split the time more fine grained in the beginning and then increase the i... | Time varying coefficient in Cox model
Just answered my own question with the same problem. Basically you need to do a time-split as you describe and then add an interaction term for the time. As you suggested it sounds like a good idea to |
43,118 | Conditional Expected Value of Product of Normal and Log-Normal Distribution | What is the intended use of the result? That bears on what form of answer is needed, to include whether a stochastic (Monte Carlo) simulation approach might be adequate, And even the bigger picture matter of is this problem necessary to solve, and did someone come up with this problem as a way of solving a higher lev... | Conditional Expected Value of Product of Normal and Log-Normal Distribution | What is the intended use of the result? That bears on what form of answer is needed, to include whether a stochastic (Monte Carlo) simulation approach might be adequate, And even the bigger picture | Conditional Expected Value of Product of Normal and Log-Normal Distribution
What is the intended use of the result? That bears on what form of answer is needed, to include whether a stochastic (Monte Carlo) simulation approach might be adequate, And even the bigger picture matter of is this problem necessary to solve... | Conditional Expected Value of Product of Normal and Log-Normal Distribution
What is the intended use of the result? That bears on what form of answer is needed, to include whether a stochastic (Monte Carlo) simulation approach might be adequate, And even the bigger picture |
43,119 | Conditional Expected Value of Product of Normal and Log-Normal Distribution | Comments:
The joint density is given by multiplying the densities since they are idp. One variable is just a paramater to the other.
$Ye^X$ is not normally distributed so approach (4) wont work.
The expressions below might allow you to find some approximation. If not they are relatively easy to evaluate with a compute... | Conditional Expected Value of Product of Normal and Log-Normal Distribution | Comments:
The joint density is given by multiplying the densities since they are idp. One variable is just a paramater to the other.
$Ye^X$ is not normally distributed so approach (4) wont work.
The | Conditional Expected Value of Product of Normal and Log-Normal Distribution
Comments:
The joint density is given by multiplying the densities since they are idp. One variable is just a paramater to the other.
$Ye^X$ is not normally distributed so approach (4) wont work.
The expressions below might allow you to find so... | Conditional Expected Value of Product of Normal and Log-Normal Distribution
Comments:
The joint density is given by multiplying the densities since they are idp. One variable is just a paramater to the other.
$Ye^X$ is not normally distributed so approach (4) wont work.
The |
43,120 | Conditional Expected Value of Product of Normal and Log-Normal Distribution | This solution is due to the suggestions and corrections from @Hunaphu, @whuber, and others. Could someone please verify if all the steps make sense?
ANSWER STEPS START
Using some notational shortcuts,
Consider,
\begin{eqnarray*}
E\left[\left.\left(e^{X}Y+k\right)\right|\left(e^{X}Y+k\right)>0\right] & = & E\left[k\left... | Conditional Expected Value of Product of Normal and Log-Normal Distribution | This solution is due to the suggestions and corrections from @Hunaphu, @whuber, and others. Could someone please verify if all the steps make sense?
ANSWER STEPS START
Using some notational shortcuts, | Conditional Expected Value of Product of Normal and Log-Normal Distribution
This solution is due to the suggestions and corrections from @Hunaphu, @whuber, and others. Could someone please verify if all the steps make sense?
ANSWER STEPS START
Using some notational shortcuts,
Consider,
\begin{eqnarray*}
E\left[\left.\l... | Conditional Expected Value of Product of Normal and Log-Normal Distribution
This solution is due to the suggestions and corrections from @Hunaphu, @whuber, and others. Could someone please verify if all the steps make sense?
ANSWER STEPS START
Using some notational shortcuts, |
43,121 | Examples of Non-Linear Time Series? | Contrived financial example:
Lets say you put away amount $M$ into your savings account every month. You also put $\frac{1}{2}$ of the total money you have in the bank into a 2 month CD each month. The CD pays interest into your main account, and the interest rate for it is some step function $q(D)$, where $D$ is the a... | Examples of Non-Linear Time Series? | Contrived financial example:
Lets say you put away amount $M$ into your savings account every month. You also put $\frac{1}{2}$ of the total money you have in the bank into a 2 month CD each month. Th | Examples of Non-Linear Time Series?
Contrived financial example:
Lets say you put away amount $M$ into your savings account every month. You also put $\frac{1}{2}$ of the total money you have in the bank into a 2 month CD each month. The CD pays interest into your main account, and the interest rate for it is some step... | Examples of Non-Linear Time Series?
Contrived financial example:
Lets say you put away amount $M$ into your savings account every month. You also put $\frac{1}{2}$ of the total money you have in the bank into a 2 month CD each month. Th |
43,122 | Is it possible to parallelize a matching method? | Nearest neighbor matching without replacement cannot be parallelized in a straightforward way. Each match depends on the matches that occurred before it (i.e., the matching must be performed sequentially). This means one could not perform the matching on independent cores that do not communicate with each other. An exc... | Is it possible to parallelize a matching method? | Nearest neighbor matching without replacement cannot be parallelized in a straightforward way. Each match depends on the matches that occurred before it (i.e., the matching must be performed sequentia | Is it possible to parallelize a matching method?
Nearest neighbor matching without replacement cannot be parallelized in a straightforward way. Each match depends on the matches that occurred before it (i.e., the matching must be performed sequentially). This means one could not perform the matching on independent core... | Is it possible to parallelize a matching method?
Nearest neighbor matching without replacement cannot be parallelized in a straightforward way. Each match depends on the matches that occurred before it (i.e., the matching must be performed sequentia |
43,123 | Shrinkage of the eigenvalues | First of all, I don't know anything about Stein-Haff estimator other than what I saw from a few seconds of Googling in https://stat.duke.edu/~berger/papers/yang.pdf , which contains the quote "This estimator has two problems. First, the intuitively compatible ordering $\phi_1 \geq \phi_2 \geq \dots \geq \phi_p$ is freq... | Shrinkage of the eigenvalues | First of all, I don't know anything about Stein-Haff estimator other than what I saw from a few seconds of Googling in https://stat.duke.edu/~berger/papers/yang.pdf , which contains the quote "This es | Shrinkage of the eigenvalues
First of all, I don't know anything about Stein-Haff estimator other than what I saw from a few seconds of Googling in https://stat.duke.edu/~berger/papers/yang.pdf , which contains the quote "This estimator has two problems. First, the intuitively compatible ordering $\phi_1 \geq \phi_2 \g... | Shrinkage of the eigenvalues
First of all, I don't know anything about Stein-Haff estimator other than what I saw from a few seconds of Googling in https://stat.duke.edu/~berger/papers/yang.pdf , which contains the quote "This es |
43,124 | Any significance of area under curves in lasso plot? | A couple things that immediately occur to me about this.
I think spdrnl's right, due to the standardization, the effect sizes should be comparable. It looks like it may be the case that the plot is on the scale of the original variables though, I'd check which is true and work with a plot of the coefficients of the st... | Any significance of area under curves in lasso plot? | A couple things that immediately occur to me about this.
I think spdrnl's right, due to the standardization, the effect sizes should be comparable. It looks like it may be the case that the plot is o | Any significance of area under curves in lasso plot?
A couple things that immediately occur to me about this.
I think spdrnl's right, due to the standardization, the effect sizes should be comparable. It looks like it may be the case that the plot is on the scale of the original variables though, I'd check which is tr... | Any significance of area under curves in lasso plot?
A couple things that immediately occur to me about this.
I think spdrnl's right, due to the standardization, the effect sizes should be comparable. It looks like it may be the case that the plot is o |
43,125 | Clustering from similarity/distance matrix [duplicate] | If you have a similarity matrix, try to use Spectral methods for clustering. Take a look at Laplacian Eigenmaps for example. The idea is to compute eigenvectors from the Laplacian matrix (computed from the similarity matrix) and then come up with the feature vectors (one for each element) that respect the similarities.... | Clustering from similarity/distance matrix [duplicate] | If you have a similarity matrix, try to use Spectral methods for clustering. Take a look at Laplacian Eigenmaps for example. The idea is to compute eigenvectors from the Laplacian matrix (computed fro | Clustering from similarity/distance matrix [duplicate]
If you have a similarity matrix, try to use Spectral methods for clustering. Take a look at Laplacian Eigenmaps for example. The idea is to compute eigenvectors from the Laplacian matrix (computed from the similarity matrix) and then come up with the feature vector... | Clustering from similarity/distance matrix [duplicate]
If you have a similarity matrix, try to use Spectral methods for clustering. Take a look at Laplacian Eigenmaps for example. The idea is to compute eigenvectors from the Laplacian matrix (computed fro |
43,126 | Clustering from similarity/distance matrix [duplicate] | Two ideas immediately come to mind:
The simpler is hierarchical clustering http://en.wikipedia.org/wiki/Hierarchical_clustering which only requires distances between points.
The other is much more complicated. There are techniques which, given distances between points, provides a distance preserving embedding into a E... | Clustering from similarity/distance matrix [duplicate] | Two ideas immediately come to mind:
The simpler is hierarchical clustering http://en.wikipedia.org/wiki/Hierarchical_clustering which only requires distances between points.
The other is much more com | Clustering from similarity/distance matrix [duplicate]
Two ideas immediately come to mind:
The simpler is hierarchical clustering http://en.wikipedia.org/wiki/Hierarchical_clustering which only requires distances between points.
The other is much more complicated. There are techniques which, given distances between po... | Clustering from similarity/distance matrix [duplicate]
Two ideas immediately come to mind:
The simpler is hierarchical clustering http://en.wikipedia.org/wiki/Hierarchical_clustering which only requires distances between points.
The other is much more com |
43,127 | The correct use of tensor product in gam (mgcv) function | Before answering both of your questions, it's important to address the purpose of using ti() (and te() for that matter). Both smoothing functions are used when you're including interaction terms with different scales or units in your model.
On that note, whenever you're trying to examine the effects of an explanatory v... | The correct use of tensor product in gam (mgcv) function | Before answering both of your questions, it's important to address the purpose of using ti() (and te() for that matter). Both smoothing functions are used when you're including interaction terms with | The correct use of tensor product in gam (mgcv) function
Before answering both of your questions, it's important to address the purpose of using ti() (and te() for that matter). Both smoothing functions are used when you're including interaction terms with different scales or units in your model.
On that note, whenever... | The correct use of tensor product in gam (mgcv) function
Before answering both of your questions, it's important to address the purpose of using ti() (and te() for that matter). Both smoothing functions are used when you're including interaction terms with |
43,128 | GradientBoostClassifier(sklearn) takes very long time to train [closed] | Might be a bit late... But.
1 - sklearn's Random Forest supports multithreading. GradientBoostingClassifier does not. This can be responsible for a 8 times speed up.
2 - sklearn's Random Forest works on a subset of the total number of features (at least, by default) whereas GradientBoostingClassifier uses all the featu... | GradientBoostClassifier(sklearn) takes very long time to train [closed] | Might be a bit late... But.
1 - sklearn's Random Forest supports multithreading. GradientBoostingClassifier does not. This can be responsible for a 8 times speed up.
2 - sklearn's Random Forest works | GradientBoostClassifier(sklearn) takes very long time to train [closed]
Might be a bit late... But.
1 - sklearn's Random Forest supports multithreading. GradientBoostingClassifier does not. This can be responsible for a 8 times speed up.
2 - sklearn's Random Forest works on a subset of the total number of features (at ... | GradientBoostClassifier(sklearn) takes very long time to train [closed]
Might be a bit late... But.
1 - sklearn's Random Forest supports multithreading. GradientBoostingClassifier does not. This can be responsible for a 8 times speed up.
2 - sklearn's Random Forest works |
43,129 | Nested linear mixed-effects model | I think the models you wrote are not incorrect, although I do wonder why you chose to treat Sites as fixed effects rather than random effects. There is nothing special about these sites, right? For example, you don't care about any differences among these particular 9 sites? If not, they are probably best considered ra... | Nested linear mixed-effects model | I think the models you wrote are not incorrect, although I do wonder why you chose to treat Sites as fixed effects rather than random effects. There is nothing special about these sites, right? For ex | Nested linear mixed-effects model
I think the models you wrote are not incorrect, although I do wonder why you chose to treat Sites as fixed effects rather than random effects. There is nothing special about these sites, right? For example, you don't care about any differences among these particular 9 sites? If not, th... | Nested linear mixed-effects model
I think the models you wrote are not incorrect, although I do wonder why you chose to treat Sites as fixed effects rather than random effects. There is nothing special about these sites, right? For ex |
43,130 | What are the disadvantages of using Lasso for feature selection in classification problems? [duplicate] | Lasso doesn't just do feature selection. It's trying to minimise the sum of squared errors subject penalised by the magnitude of the regression coefficients. This will often lead to a lower mean square error compared to an OLS procedure.
The nature of the $l_1$ penalty pushes many regression coefficients to zero; induc... | What are the disadvantages of using Lasso for feature selection in classification problems? [duplica | Lasso doesn't just do feature selection. It's trying to minimise the sum of squared errors subject penalised by the magnitude of the regression coefficients. This will often lead to a lower mean squar | What are the disadvantages of using Lasso for feature selection in classification problems? [duplicate]
Lasso doesn't just do feature selection. It's trying to minimise the sum of squared errors subject penalised by the magnitude of the regression coefficients. This will often lead to a lower mean square error compared... | What are the disadvantages of using Lasso for feature selection in classification problems? [duplica
Lasso doesn't just do feature selection. It's trying to minimise the sum of squared errors subject penalised by the magnitude of the regression coefficients. This will often lead to a lower mean squar |
43,131 | How is ABC more computationally efficient than exact Bayesian Computation for parameter estimation in dynamical systems (ODE) models? | It looks like it is similar to HMC in that it uses a type of stochastic gradient instead of a random walk. I didn't see anywhere that they say they could do the estimate based on a single simulation. Instead, it looks like you can simply get good values much faster. It really looks very similar to HMC as it's implement... | How is ABC more computationally efficient than exact Bayesian Computation for parameter estimation i | It looks like it is similar to HMC in that it uses a type of stochastic gradient instead of a random walk. I didn't see anywhere that they say they could do the estimate based on a single simulation. | How is ABC more computationally efficient than exact Bayesian Computation for parameter estimation in dynamical systems (ODE) models?
It looks like it is similar to HMC in that it uses a type of stochastic gradient instead of a random walk. I didn't see anywhere that they say they could do the estimate based on a singl... | How is ABC more computationally efficient than exact Bayesian Computation for parameter estimation i
It looks like it is similar to HMC in that it uses a type of stochastic gradient instead of a random walk. I didn't see anywhere that they say they could do the estimate based on a single simulation. |
43,132 | Can a labeled LDA (Latent Dirichlet Allocation) dataset have just one label per document? | There's nothing stopping you, but this essentially reduces to learning a bag of words model for each label, albeit with a shared prior in the form of $\eta$. The new model would look like this:
To see why these are equivalent, see this snippet from the labelled LDA paper:
The traditional LDA model then draws a multin... | Can a labeled LDA (Latent Dirichlet Allocation) dataset have just one label per document? | There's nothing stopping you, but this essentially reduces to learning a bag of words model for each label, albeit with a shared prior in the form of $\eta$. The new model would look like this:
To se | Can a labeled LDA (Latent Dirichlet Allocation) dataset have just one label per document?
There's nothing stopping you, but this essentially reduces to learning a bag of words model for each label, albeit with a shared prior in the form of $\eta$. The new model would look like this:
To see why these are equivalent, se... | Can a labeled LDA (Latent Dirichlet Allocation) dataset have just one label per document?
There's nothing stopping you, but this essentially reduces to learning a bag of words model for each label, albeit with a shared prior in the form of $\eta$. The new model would look like this:
To se |
43,133 | Can a labeled LDA (Latent Dirichlet Allocation) dataset have just one label per document? | In supervised LDA a single label is added for each document (in addition to topic labels for each word). This label known as response variable reflects some quantity of interest associated with a document: this could be the quality score of a report, or a star rating of a movie review, or the number of downloads of an ... | Can a labeled LDA (Latent Dirichlet Allocation) dataset have just one label per document? | In supervised LDA a single label is added for each document (in addition to topic labels for each word). This label known as response variable reflects some quantity of interest associated with a docu | Can a labeled LDA (Latent Dirichlet Allocation) dataset have just one label per document?
In supervised LDA a single label is added for each document (in addition to topic labels for each word). This label known as response variable reflects some quantity of interest associated with a document: this could be the qualit... | Can a labeled LDA (Latent Dirichlet Allocation) dataset have just one label per document?
In supervised LDA a single label is added for each document (in addition to topic labels for each word). This label known as response variable reflects some quantity of interest associated with a docu |
43,134 | DNA exoneration: what are the chances? | Are there any studies that have investigated this FRR for DNA?
Yes, what you are refering to is also called a type II error or a false negative. People have investigated this and also for lab work in general:
Koehler et al.
Kloosterman et al.
Lapworth & Teal
NFI
A very broad range of error values, with Koehler repor... | DNA exoneration: what are the chances? | Are there any studies that have investigated this FRR for DNA?
Yes, what you are refering to is also called a type II error or a false negative. People have investigated this and also for lab work in | DNA exoneration: what are the chances?
Are there any studies that have investigated this FRR for DNA?
Yes, what you are refering to is also called a type II error or a false negative. People have investigated this and also for lab work in general:
Koehler et al.
Kloosterman et al.
Lapworth & Teal
NFI
A very broad ra... | DNA exoneration: what are the chances?
Are there any studies that have investigated this FRR for DNA?
Yes, what you are refering to is also called a type II error or a false negative. People have investigated this and also for lab work in |
43,135 | How can I derive confidence intervals from the confusion matrix for a classifier? | The question makes good sense. It is specifically noted that the contingency table is a result of cross-validation. Witten et al's Data Mining book (based around Weka) discusses a modified T-Test for (Repeated) Cross-Validation. A T-Test implicitly defines a confidence interval. Given we have a CV and each cell is an ... | How can I derive confidence intervals from the confusion matrix for a classifier? | The question makes good sense. It is specifically noted that the contingency table is a result of cross-validation. Witten et al's Data Mining book (based around Weka) discusses a modified T-Test for | How can I derive confidence intervals from the confusion matrix for a classifier?
The question makes good sense. It is specifically noted that the contingency table is a result of cross-validation. Witten et al's Data Mining book (based around Weka) discusses a modified T-Test for (Repeated) Cross-Validation. A T-Test... | How can I derive confidence intervals from the confusion matrix for a classifier?
The question makes good sense. It is specifically noted that the contingency table is a result of cross-validation. Witten et al's Data Mining book (based around Weka) discusses a modified T-Test for |
43,136 | How can I derive confidence intervals from the confusion matrix for a classifier? | I don't see the value in confidence intervals on (elements of) a contingency table. I suggest to consider ROC curves instead, because the confidence depends per prediction, not per class. That is assuming you have a model that is more informative than simply positive/negative.
Consider logistic regression at the standa... | How can I derive confidence intervals from the confusion matrix for a classifier? | I don't see the value in confidence intervals on (elements of) a contingency table. I suggest to consider ROC curves instead, because the confidence depends per prediction, not per class. That is assu | How can I derive confidence intervals from the confusion matrix for a classifier?
I don't see the value in confidence intervals on (elements of) a contingency table. I suggest to consider ROC curves instead, because the confidence depends per prediction, not per class. That is assuming you have a model that is more inf... | How can I derive confidence intervals from the confusion matrix for a classifier?
I don't see the value in confidence intervals on (elements of) a contingency table. I suggest to consider ROC curves instead, because the confidence depends per prediction, not per class. That is assu |
43,137 | How can I derive confidence intervals from the confusion matrix for a classifier? | I agree with the others. If you want it to make sense you'd have to give the "interval" for a particular individual. You could give for example a list of the most probable classes as a "CI" instead of just the most likely one for that observation. If you don't have the information per observation though, what's the poi... | How can I derive confidence intervals from the confusion matrix for a classifier? | I agree with the others. If you want it to make sense you'd have to give the "interval" for a particular individual. You could give for example a list of the most probable classes as a "CI" instead of | How can I derive confidence intervals from the confusion matrix for a classifier?
I agree with the others. If you want it to make sense you'd have to give the "interval" for a particular individual. You could give for example a list of the most probable classes as a "CI" instead of just the most likely one for that obs... | How can I derive confidence intervals from the confusion matrix for a classifier?
I agree with the others. If you want it to make sense you'd have to give the "interval" for a particular individual. You could give for example a list of the most probable classes as a "CI" instead of |
43,138 | First remove seasonal trend or long-term trend in time series? | As you suggested you one can observe non-stationarity (symptom) but the correct remedy (medicine) is unclear. The correct remedy could be multiple level shifts , multiple trends , seasonal pulses too name a few. Assuming any one approach is both simple and potentially damaging to good statistical analysis.. The high ro... | First remove seasonal trend or long-term trend in time series? | As you suggested you one can observe non-stationarity (symptom) but the correct remedy (medicine) is unclear. The correct remedy could be multiple level shifts , multiple trends , seasonal pulses too | First remove seasonal trend or long-term trend in time series?
As you suggested you one can observe non-stationarity (symptom) but the correct remedy (medicine) is unclear. The correct remedy could be multiple level shifts , multiple trends , seasonal pulses too name a few. Assuming any one approach is both simple and ... | First remove seasonal trend or long-term trend in time series?
As you suggested you one can observe non-stationarity (symptom) but the correct remedy (medicine) is unclear. The correct remedy could be multiple level shifts , multiple trends , seasonal pulses too |
43,139 | First remove seasonal trend or long-term trend in time series? | Remove them simultaneously. This example shows you how to do it. Henderson filter extracts the trend while S(3,3) filter extracts the seasonality. In fact all de-seasonalizing software will do this, I think. | First remove seasonal trend or long-term trend in time series? | Remove them simultaneously. This example shows you how to do it. Henderson filter extracts the trend while S(3,3) filter extracts the seasonality. In fact all de-seasonalizing software will do this, I | First remove seasonal trend or long-term trend in time series?
Remove them simultaneously. This example shows you how to do it. Henderson filter extracts the trend while S(3,3) filter extracts the seasonality. In fact all de-seasonalizing software will do this, I think. | First remove seasonal trend or long-term trend in time series?
Remove them simultaneously. This example shows you how to do it. Henderson filter extracts the trend while S(3,3) filter extracts the seasonality. In fact all de-seasonalizing software will do this, I |
43,140 | How to tell that a reciprocal relationship exists by a residual plot? | To address your question directly, the key is in the increasing scatter to the right in your first image. This essentially showing you that as fitted values increase the spread of residuals also increase. This means your data is heteroscedastic. As a rule-of-thumb, a cone opening to the right, you transform with a ... | How to tell that a reciprocal relationship exists by a residual plot? | To address your question directly, the key is in the increasing scatter to the right in your first image. This essentially showing you that as fitted values increase the spread of residuals also incr | How to tell that a reciprocal relationship exists by a residual plot?
To address your question directly, the key is in the increasing scatter to the right in your first image. This essentially showing you that as fitted values increase the spread of residuals also increase. This means your data is heteroscedastic. ... | How to tell that a reciprocal relationship exists by a residual plot?
To address your question directly, the key is in the increasing scatter to the right in your first image. This essentially showing you that as fitted values increase the spread of residuals also incr |
43,141 | How to decide the p and q for GARCH model? | As the commenters point out, increasing ARCH/GARCH orders amounts to including additional degrees of freedom, so the (log) likelihood is guaranteed to increase. If you simply follow this increase in (log) likelihood, you will overfit.
One possibility would be to balance the gain in (log) likelihood against model comple... | How to decide the p and q for GARCH model? | As the commenters point out, increasing ARCH/GARCH orders amounts to including additional degrees of freedom, so the (log) likelihood is guaranteed to increase. If you simply follow this increase in ( | How to decide the p and q for GARCH model?
As the commenters point out, increasing ARCH/GARCH orders amounts to including additional degrees of freedom, so the (log) likelihood is guaranteed to increase. If you simply follow this increase in (log) likelihood, you will overfit.
One possibility would be to balance the ga... | How to decide the p and q for GARCH model?
As the commenters point out, increasing ARCH/GARCH orders amounts to including additional degrees of freedom, so the (log) likelihood is guaranteed to increase. If you simply follow this increase in ( |
43,142 | Choice of grouping in Chi-Squared test | This procedure is basically the idea behind "CHi-squared Automated Interaction Detection", or "CHAID" described by G.V. Kass in 1980. The general setting is very similar to your television watching prediction example: You want to best predict the occurrence of a categorical variable by a combination of other categor... | Choice of grouping in Chi-Squared test | This procedure is basically the idea behind "CHi-squared Automated Interaction Detection", or "CHAID" described by G.V. Kass in 1980. The general setting is very similar to your television watching | Choice of grouping in Chi-Squared test
This procedure is basically the idea behind "CHi-squared Automated Interaction Detection", or "CHAID" described by G.V. Kass in 1980. The general setting is very similar to your television watching prediction example: You want to best predict the occurrence of a categorical var... | Choice of grouping in Chi-Squared test
This procedure is basically the idea behind "CHi-squared Automated Interaction Detection", or "CHAID" described by G.V. Kass in 1980. The general setting is very similar to your television watching |
43,143 | How to account for overdispersion in a glm with negative binomial distribution? | I'm not sure how to correct the p-values. However you can typically examine the mean-variance assumption in a negative binomial regression by looking at the residuals versus fitted values plot.
If this plot of residuals versus fitted values is not (roughly) an amorphous, random cloud of data points, then you can try us... | How to account for overdispersion in a glm with negative binomial distribution? | I'm not sure how to correct the p-values. However you can typically examine the mean-variance assumption in a negative binomial regression by looking at the residuals versus fitted values plot.
If thi | How to account for overdispersion in a glm with negative binomial distribution?
I'm not sure how to correct the p-values. However you can typically examine the mean-variance assumption in a negative binomial regression by looking at the residuals versus fitted values plot.
If this plot of residuals versus fitted values... | How to account for overdispersion in a glm with negative binomial distribution?
I'm not sure how to correct the p-values. However you can typically examine the mean-variance assumption in a negative binomial regression by looking at the residuals versus fitted values plot.
If thi |
43,144 | How to formulate linear mixed model to find out effects of continuous variables? | An idea for improvement of the marginal $R^2$ calculation used would be to assess this with the other predictors included in the model. As it stands here, the marginal $R^2$ calculation only takes into account one predictor at a time.
An alternative is to fit two models. One model contains all predictors, the other ha... | How to formulate linear mixed model to find out effects of continuous variables? | An idea for improvement of the marginal $R^2$ calculation used would be to assess this with the other predictors included in the model. As it stands here, the marginal $R^2$ calculation only takes int | How to formulate linear mixed model to find out effects of continuous variables?
An idea for improvement of the marginal $R^2$ calculation used would be to assess this with the other predictors included in the model. As it stands here, the marginal $R^2$ calculation only takes into account one predictor at a time.
An ... | How to formulate linear mixed model to find out effects of continuous variables?
An idea for improvement of the marginal $R^2$ calculation used would be to assess this with the other predictors included in the model. As it stands here, the marginal $R^2$ calculation only takes int |
43,145 | Linear regression or mixed effects models for data with two time points? | If you limit yourself to a frequentist framework for the change analysis, then study participants with only 1 observation will be eliminated. An alternative might be to switch to a Bayesian framework where individuals with only a single observed period in a multiperiod model do not represent a limitation. See chapter 1... | Linear regression or mixed effects models for data with two time points? | If you limit yourself to a frequentist framework for the change analysis, then study participants with only 1 observation will be eliminated. An alternative might be to switch to a Bayesian framework | Linear regression or mixed effects models for data with two time points?
If you limit yourself to a frequentist framework for the change analysis, then study participants with only 1 observation will be eliminated. An alternative might be to switch to a Bayesian framework where individuals with only a single observed p... | Linear regression or mixed effects models for data with two time points?
If you limit yourself to a frequentist framework for the change analysis, then study participants with only 1 observation will be eliminated. An alternative might be to switch to a Bayesian framework |
43,146 | Linear regression or mixed effects models for data with two time points? | I recommend to perform multiple imputation (eg with mice in R), and then use a mixed model or generalizing estimating equations, explicitly recognizing the clustering features.
Reliance on multiple imputation according to Rubin approach will force you to recognize the uncertainty due to missingness without discarding p... | Linear regression or mixed effects models for data with two time points? | I recommend to perform multiple imputation (eg with mice in R), and then use a mixed model or generalizing estimating equations, explicitly recognizing the clustering features.
Reliance on multiple im | Linear regression or mixed effects models for data with two time points?
I recommend to perform multiple imputation (eg with mice in R), and then use a mixed model or generalizing estimating equations, explicitly recognizing the clustering features.
Reliance on multiple imputation according to Rubin approach will force... | Linear regression or mixed effects models for data with two time points?
I recommend to perform multiple imputation (eg with mice in R), and then use a mixed model or generalizing estimating equations, explicitly recognizing the clustering features.
Reliance on multiple im |
43,147 | Linear regression or mixed effects models for data with two time points? | After reviewing this paper
Peugh, J. L. (2010). A practical guide to multilevel modeling. Journal of School Psychology. Retrieved from http://www.sciencedirect.com/science/article/pii/S0022440509000545
A potential answer for this question can be obtained by calculating the ICC and design effect (DE), which can be us... | Linear regression or mixed effects models for data with two time points? | After reviewing this paper
Peugh, J. L. (2010). A practical guide to multilevel modeling. Journal of School Psychology. Retrieved from http://www.sciencedirect.com/science/article/pii/S0022440509000 | Linear regression or mixed effects models for data with two time points?
After reviewing this paper
Peugh, J. L. (2010). A practical guide to multilevel modeling. Journal of School Psychology. Retrieved from http://www.sciencedirect.com/science/article/pii/S0022440509000545
A potential answer for this question can b... | Linear regression or mixed effects models for data with two time points?
After reviewing this paper
Peugh, J. L. (2010). A practical guide to multilevel modeling. Journal of School Psychology. Retrieved from http://www.sciencedirect.com/science/article/pii/S0022440509000 |
43,148 | Logistic regression gives very different result to Fisher's exact test - why? | I think the problem is that you are trying to answer two questions with the same model. The Fisher test is for the crude odds ratio, collapsing across experimental levels. The logistic model does not test the crude OR. We do not want to conduct a crude or stratified analysis if the homogeneity of the odds ratio is not ... | Logistic regression gives very different result to Fisher's exact test - why? | I think the problem is that you are trying to answer two questions with the same model. The Fisher test is for the crude odds ratio, collapsing across experimental levels. The logistic model does not | Logistic regression gives very different result to Fisher's exact test - why?
I think the problem is that you are trying to answer two questions with the same model. The Fisher test is for the crude odds ratio, collapsing across experimental levels. The logistic model does not test the crude OR. We do not want to condu... | Logistic regression gives very different result to Fisher's exact test - why?
I think the problem is that you are trying to answer two questions with the same model. The Fisher test is for the crude odds ratio, collapsing across experimental levels. The logistic model does not |
43,149 | Why and how does the inclusion of random effects in mixed models influence the fixed-effect intercept term? | You have to consider that you are not predicting a single intercept, but a distribution (random intercepts) across a nonlinear link function. Remember http://en.wikipedia.org/wiki/Jensen%27s_inequality , which basically tells you that in general f(mean(x) != mean(f(x))
If I look at the values in your example and rough... | Why and how does the inclusion of random effects in mixed models influence the fixed-effect intercep | You have to consider that you are not predicting a single intercept, but a distribution (random intercepts) across a nonlinear link function. Remember http://en.wikipedia.org/wiki/Jensen%27s_inequalit | Why and how does the inclusion of random effects in mixed models influence the fixed-effect intercept term?
You have to consider that you are not predicting a single intercept, but a distribution (random intercepts) across a nonlinear link function. Remember http://en.wikipedia.org/wiki/Jensen%27s_inequality , which ba... | Why and how does the inclusion of random effects in mixed models influence the fixed-effect intercep
You have to consider that you are not predicting a single intercept, but a distribution (random intercepts) across a nonlinear link function. Remember http://en.wikipedia.org/wiki/Jensen%27s_inequalit |
43,150 | Why is the restricted boltzmann machine both unsupervised and generative? | The definition of generative model as learning the joint probability $P(X,Y)$ is given in the context of supervised learning.
In a more general setting, the process of learning the joint probability is "generative" because knowing the joint probability allows the generation of new data - in the supervised context, ha... | Why is the restricted boltzmann machine both unsupervised and generative? | The definition of generative model as learning the joint probability $P(X,Y)$ is given in the context of supervised learning.
In a more general setting, the process of learning the joint probability | Why is the restricted boltzmann machine both unsupervised and generative?
The definition of generative model as learning the joint probability $P(X,Y)$ is given in the context of supervised learning.
In a more general setting, the process of learning the joint probability is "generative" because knowing the joint pro... | Why is the restricted boltzmann machine both unsupervised and generative?
The definition of generative model as learning the joint probability $P(X,Y)$ is given in the context of supervised learning.
In a more general setting, the process of learning the joint probability |
43,151 | Why is the restricted boltzmann machine both unsupervised and generative? | Lets X=(x1,x2,x3,x4,x5) and let the target variable Y=(y1,y2). Generative model learns a joint probability distribution P(X,Y)=P(x1,x2,x3,x4,x5,y1,y2).
So now think of this P(X,Y) in the form of a table with all these variables and with another column appended to it as the probability of the particular configuration ... | Why is the restricted boltzmann machine both unsupervised and generative? | Lets X=(x1,x2,x3,x4,x5) and let the target variable Y=(y1,y2). Generative model learns a joint probability distribution P(X,Y)=P(x1,x2,x3,x4,x5,y1,y2).
So now think of this P(X,Y) in the form of a t | Why is the restricted boltzmann machine both unsupervised and generative?
Lets X=(x1,x2,x3,x4,x5) and let the target variable Y=(y1,y2). Generative model learns a joint probability distribution P(X,Y)=P(x1,x2,x3,x4,x5,y1,y2).
So now think of this P(X,Y) in the form of a table with all these variables and with another... | Why is the restricted boltzmann machine both unsupervised and generative?
Lets X=(x1,x2,x3,x4,x5) and let the target variable Y=(y1,y2). Generative model learns a joint probability distribution P(X,Y)=P(x1,x2,x3,x4,x5,y1,y2).
So now think of this P(X,Y) in the form of a t |
43,152 | Is it necessary to do $k$-fold cross validation for decision trees in random forests? | I can recommend this article dicussing good CV practice.
(A) When simply running one RF model: Yes OOB-CV is a fine estimate of your future prediction performance, given i.i.d. sampling. For many practical instances you don't have time nor need for anything more. A default RF model is simply good enough, you will firs... | Is it necessary to do $k$-fold cross validation for decision trees in random forests? | I can recommend this article dicussing good CV practice.
(A) When simply running one RF model: Yes OOB-CV is a fine estimate of your future prediction performance, given i.i.d. sampling. For many pra | Is it necessary to do $k$-fold cross validation for decision trees in random forests?
I can recommend this article dicussing good CV practice.
(A) When simply running one RF model: Yes OOB-CV is a fine estimate of your future prediction performance, given i.i.d. sampling. For many practical instances you don't have ti... | Is it necessary to do $k$-fold cross validation for decision trees in random forests?
I can recommend this article dicussing good CV practice.
(A) When simply running one RF model: Yes OOB-CV is a fine estimate of your future prediction performance, given i.i.d. sampling. For many pra |
43,153 | Is it necessary to do $k$-fold cross validation for decision trees in random forests? | For decision trees, is it better to use the full train data set to construct the tree?
It is always better to have more data to train your model. But if you use all data that you have in hand, then you have no idea about your test error (of course you can indirectly estimate it but estimations remain estimations), and ... | Is it necessary to do $k$-fold cross validation for decision trees in random forests? | For decision trees, is it better to use the full train data set to construct the tree?
It is always better to have more data to train your model. But if you use all data that you have in hand, then yo | Is it necessary to do $k$-fold cross validation for decision trees in random forests?
For decision trees, is it better to use the full train data set to construct the tree?
It is always better to have more data to train your model. But if you use all data that you have in hand, then you have no idea about your test err... | Is it necessary to do $k$-fold cross validation for decision trees in random forests?
For decision trees, is it better to use the full train data set to construct the tree?
It is always better to have more data to train your model. But if you use all data that you have in hand, then yo |
43,154 | Is it necessary to do $k$-fold cross validation for decision trees in random forests? | The answer is No. Random forests don't need k-fold CV. As an example, when I compare RF classification results with other classifiers for which k-fold CV was used, I only perform a single run with the entire input dataset for the RF model. RF will take care of the training and testing data by itself -- so it is unlik... | Is it necessary to do $k$-fold cross validation for decision trees in random forests? | The answer is No. Random forests don't need k-fold CV. As an example, when I compare RF classification results with other classifiers for which k-fold CV was used, I only perform a single run with th | Is it necessary to do $k$-fold cross validation for decision trees in random forests?
The answer is No. Random forests don't need k-fold CV. As an example, when I compare RF classification results with other classifiers for which k-fold CV was used, I only perform a single run with the entire input dataset for the RF ... | Is it necessary to do $k$-fold cross validation for decision trees in random forests?
The answer is No. Random forests don't need k-fold CV. As an example, when I compare RF classification results with other classifiers for which k-fold CV was used, I only perform a single run with th |
43,155 | Multiple and long seasonality for a SARIMA model in R [closed] | Structure your data as an msts (multiple seasonality time series), where you can specify
msts(your_data, start=2010, seasonal.periods=c(144,1008,52560)).
Then, when fitting fourier terms for seasonality you must specify the three seasonal periods on fourier function:
reg <- fourier(your_data, K=c(i,n,j)), this will ... | Multiple and long seasonality for a SARIMA model in R [closed] | Structure your data as an msts (multiple seasonality time series), where you can specify
msts(your_data, start=2010, seasonal.periods=c(144,1008,52560)).
Then, when fitting fourier terms for seasona | Multiple and long seasonality for a SARIMA model in R [closed]
Structure your data as an msts (multiple seasonality time series), where you can specify
msts(your_data, start=2010, seasonal.periods=c(144,1008,52560)).
Then, when fitting fourier terms for seasonality you must specify the three seasonal periods on fouri... | Multiple and long seasonality for a SARIMA model in R [closed]
Structure your data as an msts (multiple seasonality time series), where you can specify
msts(your_data, start=2010, seasonal.periods=c(144,1008,52560)).
Then, when fitting fourier terms for seasona |
43,156 | Given loads of data, can we always model it with polynomials? | Imagine replacing an arbitrary model with polynomial parameters with a series of dummies for all values of the explanatory variables and all their interactions. If you have enough experimental data that's going to be as general as possible. The highest order polynomial function of all the interactions is going to fit t... | Given loads of data, can we always model it with polynomials? | Imagine replacing an arbitrary model with polynomial parameters with a series of dummies for all values of the explanatory variables and all their interactions. If you have enough experimental data th | Given loads of data, can we always model it with polynomials?
Imagine replacing an arbitrary model with polynomial parameters with a series of dummies for all values of the explanatory variables and all their interactions. If you have enough experimental data that's going to be as general as possible. The highest order... | Given loads of data, can we always model it with polynomials?
Imagine replacing an arbitrary model with polynomial parameters with a series of dummies for all values of the explanatory variables and all their interactions. If you have enough experimental data th |
43,157 | ACF and PACF plot analysis | The threshold statistical significance of the autocorrelations has been noted in the comments and in another answer. What looks interesting is that the autocorrelations in Lag 4 and Lag 8 persist also in the Partial ACF.
Reality should come into play at this point: what are these data? By whatever knowledge you have ... | ACF and PACF plot analysis | The threshold statistical significance of the autocorrelations has been noted in the comments and in another answer. What looks interesting is that the autocorrelations in Lag 4 and Lag 8 persist also | ACF and PACF plot analysis
The threshold statistical significance of the autocorrelations has been noted in the comments and in another answer. What looks interesting is that the autocorrelations in Lag 4 and Lag 8 persist also in the Partial ACF.
Reality should come into play at this point: what are these data? By w... | ACF and PACF plot analysis
The threshold statistical significance of the autocorrelations has been noted in the comments and in another answer. What looks interesting is that the autocorrelations in Lag 4 and Lag 8 persist also |
43,158 | Backshift operator property not clear | That step comes from the Taylor expansion of $\frac{1}{1-x}$, which is $1 + x + x^2 + ...$. Just substitute $x$ for the backward shift operator $B$ in the author's derivation and you'll arrive at the same result.
Have you taken a class on integral calculus? Usually you'll go through that derivation when you cover ser... | Backshift operator property not clear | That step comes from the Taylor expansion of $\frac{1}{1-x}$, which is $1 + x + x^2 + ...$. Just substitute $x$ for the backward shift operator $B$ in the author's derivation and you'll arrive at the | Backshift operator property not clear
That step comes from the Taylor expansion of $\frac{1}{1-x}$, which is $1 + x + x^2 + ...$. Just substitute $x$ for the backward shift operator $B$ in the author's derivation and you'll arrive at the same result.
Have you taken a class on integral calculus? Usually you'll go thro... | Backshift operator property not clear
That step comes from the Taylor expansion of $\frac{1}{1-x}$, which is $1 + x + x^2 + ...$. Just substitute $x$ for the backward shift operator $B$ in the author's derivation and you'll arrive at the |
43,159 | How to do a power analysis for an unbalanced mixed effects ANOVA? | This is only a way to solution not a definitive answer: The paper below could give some direction to this kind of design:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4394709/
The supplementary material show power calculations examples for t tests and regressions in R. Since regressions and Anovas are the same thing in... | How to do a power analysis for an unbalanced mixed effects ANOVA? | This is only a way to solution not a definitive answer: The paper below could give some direction to this kind of design:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4394709/
The supplementary materi | How to do a power analysis for an unbalanced mixed effects ANOVA?
This is only a way to solution not a definitive answer: The paper below could give some direction to this kind of design:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4394709/
The supplementary material show power calculations examples for t tests and re... | How to do a power analysis for an unbalanced mixed effects ANOVA?
This is only a way to solution not a definitive answer: The paper below could give some direction to this kind of design:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4394709/
The supplementary materi |
43,160 | How to do a power analysis for an unbalanced mixed effects ANOVA? | A pragmatic choice is to take the smaller of the two treatment groups as the $n$ of both groups. This gives you a conservative measure of power. In G*Power you would just use the default proportion test sample size calculation. | How to do a power analysis for an unbalanced mixed effects ANOVA? | A pragmatic choice is to take the smaller of the two treatment groups as the $n$ of both groups. This gives you a conservative measure of power. In G*Power you would just use the default proportion te | How to do a power analysis for an unbalanced mixed effects ANOVA?
A pragmatic choice is to take the smaller of the two treatment groups as the $n$ of both groups. This gives you a conservative measure of power. In G*Power you would just use the default proportion test sample size calculation. | How to do a power analysis for an unbalanced mixed effects ANOVA?
A pragmatic choice is to take the smaller of the two treatment groups as the $n$ of both groups. This gives you a conservative measure of power. In G*Power you would just use the default proportion te |
43,161 | Most significantly frequent category | Not directly, because the categories you chose to compare are based on their observed values.
It's still possible to test such a thing using a chi-squared test statistic, but the distribution of the test statistic under the null hypothesis may not be (and I expect is not) well approximated by the distribution that appl... | Most significantly frequent category | Not directly, because the categories you chose to compare are based on their observed values.
It's still possible to test such a thing using a chi-squared test statistic, but the distribution of the t | Most significantly frequent category
Not directly, because the categories you chose to compare are based on their observed values.
It's still possible to test such a thing using a chi-squared test statistic, but the distribution of the test statistic under the null hypothesis may not be (and I expect is not) well appro... | Most significantly frequent category
Not directly, because the categories you chose to compare are based on their observed values.
It's still possible to test such a thing using a chi-squared test statistic, but the distribution of the t |
43,162 | How to visualize a range (min/med/max)? | Example number 1 seems to be nice if you have different minimum thresholds among the categories.
As pointed by Glen_b and whuber, it seems that examples number 2 and number 3 do not show the ranges of your categories, but just one unique statistic (it could be the median, or the maximum values) at the top of the horiz... | How to visualize a range (min/med/max)? | Example number 1 seems to be nice if you have different minimum thresholds among the categories.
As pointed by Glen_b and whuber, it seems that examples number 2 and number 3 do not show the ranges o | How to visualize a range (min/med/max)?
Example number 1 seems to be nice if you have different minimum thresholds among the categories.
As pointed by Glen_b and whuber, it seems that examples number 2 and number 3 do not show the ranges of your categories, but just one unique statistic (it could be the median, or the... | How to visualize a range (min/med/max)?
Example number 1 seems to be nice if you have different minimum thresholds among the categories.
As pointed by Glen_b and whuber, it seems that examples number 2 and number 3 do not show the ranges o |
43,163 | Linear regression without intercept - sampling variance of coefficient | In your problem, assuming joint-normality of the variables, you can write the joint distribution of a single data point $(X_i, Y_i)$ as:
$$\begin{bmatrix} X_i \\ Y_i \end{bmatrix} \text{ ~ N} \left( \begin{bmatrix} 0 \\ 0 \end{bmatrix}, \begin{bmatrix} \sigma_X^2 & \rho \sigma_X \sigma_y \\ \rho \sigma_X \sigma_y & \si... | Linear regression without intercept - sampling variance of coefficient | In your problem, assuming joint-normality of the variables, you can write the joint distribution of a single data point $(X_i, Y_i)$ as:
$$\begin{bmatrix} X_i \\ Y_i \end{bmatrix} \text{ ~ N} \left( \ | Linear regression without intercept - sampling variance of coefficient
In your problem, assuming joint-normality of the variables, you can write the joint distribution of a single data point $(X_i, Y_i)$ as:
$$\begin{bmatrix} X_i \\ Y_i \end{bmatrix} \text{ ~ N} \left( \begin{bmatrix} 0 \\ 0 \end{bmatrix}, \begin{bmatr... | Linear regression without intercept - sampling variance of coefficient
In your problem, assuming joint-normality of the variables, you can write the joint distribution of a single data point $(X_i, Y_i)$ as:
$$\begin{bmatrix} X_i \\ Y_i \end{bmatrix} \text{ ~ N} \left( \ |
43,164 | Linear regression without intercept - sampling variance of coefficient | I don't know how you found that $\sigma_{\hat{\alpha_1}}^2 \neq \sigma_{\hat{\beta_1}}^2$. Using this R code
alpha <- c()
beta <- c()
for(i in 1:1000){
dat<-matrix(rnorm(200000,0,1),nrow=100000,byrow=T)
cov <- chol(matrix(c(5,2,2,5),byrow=T,nrow=2))
dat <- dat%*%cov
X1 <- matrix(0,nrow=100000,ncol=2)
... | Linear regression without intercept - sampling variance of coefficient | I don't know how you found that $\sigma_{\hat{\alpha_1}}^2 \neq \sigma_{\hat{\beta_1}}^2$. Using this R code
alpha <- c()
beta <- c()
for(i in 1:1000){
dat<-matrix(rnorm(200000,0,1),nrow=100000,by | Linear regression without intercept - sampling variance of coefficient
I don't know how you found that $\sigma_{\hat{\alpha_1}}^2 \neq \sigma_{\hat{\beta_1}}^2$. Using this R code
alpha <- c()
beta <- c()
for(i in 1:1000){
dat<-matrix(rnorm(200000,0,1),nrow=100000,byrow=T)
cov <- chol(matrix(c(5,2,2,5),byrow=T,... | Linear regression without intercept - sampling variance of coefficient
I don't know how you found that $\sigma_{\hat{\alpha_1}}^2 \neq \sigma_{\hat{\beta_1}}^2$. Using this R code
alpha <- c()
beta <- c()
for(i in 1:1000){
dat<-matrix(rnorm(200000,0,1),nrow=100000,by |
43,165 | Test whether time of maximum differs across two groups | Well, I'm not entirely sure whether I found an answer... but my idea won't fit into a comment. So I'll post and see what the smarter people here point out.
As I commented above, I'd bootstrap the max time within each group, but stratified by individual - by resampling rows of X1 and X2:
library(boot)
b1 <- boot(X1,stat... | Test whether time of maximum differs across two groups | Well, I'm not entirely sure whether I found an answer... but my idea won't fit into a comment. So I'll post and see what the smarter people here point out.
As I commented above, I'd bootstrap the max | Test whether time of maximum differs across two groups
Well, I'm not entirely sure whether I found an answer... but my idea won't fit into a comment. So I'll post and see what the smarter people here point out.
As I commented above, I'd bootstrap the max time within each group, but stratified by individual - by resampl... | Test whether time of maximum differs across two groups
Well, I'm not entirely sure whether I found an answer... but my idea won't fit into a comment. So I'll post and see what the smarter people here point out.
As I commented above, I'd bootstrap the max |
43,166 | Handling missing data in a time series | You may want to see Honaker, J. and King, G. (2010). What to do about missing values in time-series cross-section data. American Journal of Political Science, 54(2):561–581, and the related R package Amelia II for multiple imputation with respect to time series. I am not quite sure about your application as to location... | Handling missing data in a time series | You may want to see Honaker, J. and King, G. (2010). What to do about missing values in time-series cross-section data. American Journal of Political Science, 54(2):561–581, and the related R package | Handling missing data in a time series
You may want to see Honaker, J. and King, G. (2010). What to do about missing values in time-series cross-section data. American Journal of Political Science, 54(2):561–581, and the related R package Amelia II for multiple imputation with respect to time series. I am not quite sur... | Handling missing data in a time series
You may want to see Honaker, J. and King, G. (2010). What to do about missing values in time-series cross-section data. American Journal of Political Science, 54(2):561–581, and the related R package |
43,167 | Handling missing data in a time series | No, this no task for imputation algorithms.
Since there are no missing values in the time series.
What is described are measurement errors.
So instead of searching for "imputation" the term "measurment error correction" should provide better results. | Handling missing data in a time series | No, this no task for imputation algorithms.
Since there are no missing values in the time series.
What is described are measurement errors.
So instead of searching for "imputation" the term "measurme | Handling missing data in a time series
No, this no task for imputation algorithms.
Since there are no missing values in the time series.
What is described are measurement errors.
So instead of searching for "imputation" the term "measurment error correction" should provide better results. | Handling missing data in a time series
No, this no task for imputation algorithms.
Since there are no missing values in the time series.
What is described are measurement errors.
So instead of searching for "imputation" the term "measurme |
43,168 | How to forecast multivariate time-series 'accurately' with a large number of unknown factors using R? | In my experience you only get so far with traditional time series models. Given the complexity you describe I'd try a non-linear machine learning algorithm like random forests. Have a play with the R package 'rf'. There's a nice blog post with example code from a Kaggle competition here:
http://blog.kaggle.com/2012/05... | How to forecast multivariate time-series 'accurately' with a large number of unknown factors using R | In my experience you only get so far with traditional time series models. Given the complexity you describe I'd try a non-linear machine learning algorithm like random forests. Have a play with the R | How to forecast multivariate time-series 'accurately' with a large number of unknown factors using R?
In my experience you only get so far with traditional time series models. Given the complexity you describe I'd try a non-linear machine learning algorithm like random forests. Have a play with the R package 'rf'. The... | How to forecast multivariate time-series 'accurately' with a large number of unknown factors using R
In my experience you only get so far with traditional time series models. Given the complexity you describe I'd try a non-linear machine learning algorithm like random forests. Have a play with the R |
43,169 | Weibull distribution with the negative shape parameter | There is no good reason not to do such a generalization, which would unite the Weibull and inverse Weibull distributions. So reasons must be historical or accidental.
Also see the comments thread. | Weibull distribution with the negative shape parameter | There is no good reason not to do such a generalization, which would unite the Weibull and inverse Weibull distributions. So reasons must be historical or accidental.
Also see the comments thread. | Weibull distribution with the negative shape parameter
There is no good reason not to do such a generalization, which would unite the Weibull and inverse Weibull distributions. So reasons must be historical or accidental.
Also see the comments thread. | Weibull distribution with the negative shape parameter
There is no good reason not to do such a generalization, which would unite the Weibull and inverse Weibull distributions. So reasons must be historical or accidental.
Also see the comments thread. |
43,170 | How should I interpret these strange density and mixing plots when fitting a generalised pareto distribution using MCMC with JAGS? | The generalised pareto distribution has the limitation that $mu < x$. Thus, the posterior density is capped at x, as COOLSerdash noted. This is intended behaviour, not a bug.
The lesser, left-most peak in the data is due to the prior distribution being incorrectly specified with a floor of zero. | How should I interpret these strange density and mixing plots when fitting a generalised pareto dist | The generalised pareto distribution has the limitation that $mu < x$. Thus, the posterior density is capped at x, as COOLSerdash noted. This is intended behaviour, not a bug.
The lesser, left-most pe | How should I interpret these strange density and mixing plots when fitting a generalised pareto distribution using MCMC with JAGS?
The generalised pareto distribution has the limitation that $mu < x$. Thus, the posterior density is capped at x, as COOLSerdash noted. This is intended behaviour, not a bug.
The lesser, l... | How should I interpret these strange density and mixing plots when fitting a generalised pareto dist
The generalised pareto distribution has the limitation that $mu < x$. Thus, the posterior density is capped at x, as COOLSerdash noted. This is intended behaviour, not a bug.
The lesser, left-most pe |
43,171 | Repeated measures with single measurements | It's tough without truly understanding what your outcome y is, but I'll give it my best shot.
(1) This sounds like it might be approximated by a λ=1 Poisson distribution. Unless you're seeing it messing up the variance components of the model, I wouldn't worry about it. If it is, I would try transforming it by sqrt(con... | Repeated measures with single measurements | It's tough without truly understanding what your outcome y is, but I'll give it my best shot.
(1) This sounds like it might be approximated by a λ=1 Poisson distribution. Unless you're seeing it messi | Repeated measures with single measurements
It's tough without truly understanding what your outcome y is, but I'll give it my best shot.
(1) This sounds like it might be approximated by a λ=1 Poisson distribution. Unless you're seeing it messing up the variance components of the model, I wouldn't worry about it. If it ... | Repeated measures with single measurements
It's tough without truly understanding what your outcome y is, but I'll give it my best shot.
(1) This sounds like it might be approximated by a λ=1 Poisson distribution. Unless you're seeing it messi |
43,172 | Repeated measures with single measurements | I can deliver an answer to my question only empirically using a simulation. Using this two cross validation contributions mixed and logistic I could create some fake datasets and using the mixed logistic regression. With R and glmer from library(lme4) I used this formula:
fit1 <- glmer(y ~ x1 + (1|j), data = d, family... | Repeated measures with single measurements | I can deliver an answer to my question only empirically using a simulation. Using this two cross validation contributions mixed and logistic I could create some fake datasets and using the mixed logis | Repeated measures with single measurements
I can deliver an answer to my question only empirically using a simulation. Using this two cross validation contributions mixed and logistic I could create some fake datasets and using the mixed logistic regression. With R and glmer from library(lme4) I used this formula:
fit... | Repeated measures with single measurements
I can deliver an answer to my question only empirically using a simulation. Using this two cross validation contributions mixed and logistic I could create some fake datasets and using the mixed logis |
43,173 | Repeated measures with single measurements | I'm certainly no expert and would love others to comment on this, but:
I'm not sure what your outcome is but you said it was measured 1/0. for the sake of the example i'll pretend that your outcome is "happy with consultation" yes=1 and No=0.
I think that for the people with multiple consultations you have a easier ... | Repeated measures with single measurements | I'm certainly no expert and would love others to comment on this, but:
I'm not sure what your outcome is but you said it was measured 1/0. for the sake of the example i'll pretend that your outcome | Repeated measures with single measurements
I'm certainly no expert and would love others to comment on this, but:
I'm not sure what your outcome is but you said it was measured 1/0. for the sake of the example i'll pretend that your outcome is "happy with consultation" yes=1 and No=0.
I think that for the people wit... | Repeated measures with single measurements
I'm certainly no expert and would love others to comment on this, but:
I'm not sure what your outcome is but you said it was measured 1/0. for the sake of the example i'll pretend that your outcome |
43,174 | Would there be a model selection problem if we had access to an oracle that gave us the exact generalization error? | Basically I feel the question assumes that we have an oracle for determining when generalization is minimum too.
Of course, having this would be superb. Having an oracle that gives us the best model would be even better. However, you seem to misinterpret the function of the oracle.
The task of model selection is to p... | Would there be a model selection problem if we had access to an oracle that gave us the exact genera | Basically I feel the question assumes that we have an oracle for determining when generalization is minimum too.
Of course, having this would be superb. Having an oracle that gives us the best model | Would there be a model selection problem if we had access to an oracle that gave us the exact generalization error?
Basically I feel the question assumes that we have an oracle for determining when generalization is minimum too.
Of course, having this would be superb. Having an oracle that gives us the best model woul... | Would there be a model selection problem if we had access to an oracle that gave us the exact genera
Basically I feel the question assumes that we have an oracle for determining when generalization is minimum too.
Of course, having this would be superb. Having an oracle that gives us the best model |
43,175 | Calculating significance and uplift on Revenue A/B Tests | As I understand you have a 2X2 experimental design ( Factor1 - website(levels: a,b), factor2 - visitors group (levels: a,b)) and the dependent variable 'Revenue'.
I would consider ANOVA being careful to all assumptions behind. The way you measure/code dependent variable 'Revenue' has different implications.
This movie ... | Calculating significance and uplift on Revenue A/B Tests | As I understand you have a 2X2 experimental design ( Factor1 - website(levels: a,b), factor2 - visitors group (levels: a,b)) and the dependent variable 'Revenue'.
I would consider ANOVA being careful | Calculating significance and uplift on Revenue A/B Tests
As I understand you have a 2X2 experimental design ( Factor1 - website(levels: a,b), factor2 - visitors group (levels: a,b)) and the dependent variable 'Revenue'.
I would consider ANOVA being careful to all assumptions behind. The way you measure/code dependent v... | Calculating significance and uplift on Revenue A/B Tests
As I understand you have a 2X2 experimental design ( Factor1 - website(levels: a,b), factor2 - visitors group (levels: a,b)) and the dependent variable 'Revenue'.
I would consider ANOVA being careful |
43,176 | Calculating significance and uplift on Revenue A/B Tests | Probably the revenue per cookie has a normal distribution (you can check this with bootstrapping). The revenue per si do not have a normal distribution, just the revenue per cookie. That said, you can applied an hypothesis test as usually an check is the difference in revenues per user in two groups are significant.
Ot... | Calculating significance and uplift on Revenue A/B Tests | Probably the revenue per cookie has a normal distribution (you can check this with bootstrapping). The revenue per si do not have a normal distribution, just the revenue per cookie. That said, you can | Calculating significance and uplift on Revenue A/B Tests
Probably the revenue per cookie has a normal distribution (you can check this with bootstrapping). The revenue per si do not have a normal distribution, just the revenue per cookie. That said, you can applied an hypothesis test as usually an check is the differen... | Calculating significance and uplift on Revenue A/B Tests
Probably the revenue per cookie has a normal distribution (you can check this with bootstrapping). The revenue per si do not have a normal distribution, just the revenue per cookie. That said, you can |
43,177 | Variance of EM mean estimates in a simple mixture of two normals | I cannot answer with a simple formula to calculate the variances of $\mu_1$ and $\mu_2$ or their covariance. I can only depict the mathematical steps needed to obtain them which leads to the conclusion that there is not an exact analytical solution.
Let's recapitulate for a moment how the variance of an ML estimate $\m... | Variance of EM mean estimates in a simple mixture of two normals | I cannot answer with a simple formula to calculate the variances of $\mu_1$ and $\mu_2$ or their covariance. I can only depict the mathematical steps needed to obtain them which leads to the conclusio | Variance of EM mean estimates in a simple mixture of two normals
I cannot answer with a simple formula to calculate the variances of $\mu_1$ and $\mu_2$ or their covariance. I can only depict the mathematical steps needed to obtain them which leads to the conclusion that there is not an exact analytical solution.
Let's... | Variance of EM mean estimates in a simple mixture of two normals
I cannot answer with a simple formula to calculate the variances of $\mu_1$ and $\mu_2$ or their covariance. I can only depict the mathematical steps needed to obtain them which leads to the conclusio |
43,178 | Variance of EM mean estimates in a simple mixture of two normals | The trick is to write down your likelihood exactly. There are many approaches to EM normal mixture estimation. Is the number in each group known? (hypergeometric likelihood) or will you potentially have everyone in one group (binomial likelihood)? Do the 2 normal mixture variates have common variance $\sigma^2$ or are ... | Variance of EM mean estimates in a simple mixture of two normals | The trick is to write down your likelihood exactly. There are many approaches to EM normal mixture estimation. Is the number in each group known? (hypergeometric likelihood) or will you potentially ha | Variance of EM mean estimates in a simple mixture of two normals
The trick is to write down your likelihood exactly. There are many approaches to EM normal mixture estimation. Is the number in each group known? (hypergeometric likelihood) or will you potentially have everyone in one group (binomial likelihood)? Do the ... | Variance of EM mean estimates in a simple mixture of two normals
The trick is to write down your likelihood exactly. There are many approaches to EM normal mixture estimation. Is the number in each group known? (hypergeometric likelihood) or will you potentially ha |
43,179 | Variance of EM mean estimates in a simple mixture of two normals | First note that EM is an optimization algorithm.
The statistical properties of your estimator are driven by the fact that it is an MLE, and not by the optimization algorithm used to find it.
In this particular case, the MLE has no closed form solution so that you cannot really analyze its properties.
Asymptotic theor... | Variance of EM mean estimates in a simple mixture of two normals | First note that EM is an optimization algorithm.
The statistical properties of your estimator are driven by the fact that it is an MLE, and not by the optimization algorithm used to find it.
In this | Variance of EM mean estimates in a simple mixture of two normals
First note that EM is an optimization algorithm.
The statistical properties of your estimator are driven by the fact that it is an MLE, and not by the optimization algorithm used to find it.
In this particular case, the MLE has no closed form solution so... | Variance of EM mean estimates in a simple mixture of two normals
First note that EM is an optimization algorithm.
The statistical properties of your estimator are driven by the fact that it is an MLE, and not by the optimization algorithm used to find it.
In this |
43,180 | R: power calculation for beta coefficient | The answer is "no" but not for the reason in vafisher's answer.
The correct formula for the power of a two-sided hypothesis test for a single regression coefficient is
$$\begin{align}
\mathrm{power}=&\operatorname{Pr}\left(t_{\mathrm{df}} \le -\frac{D}{\operatorname{se}\left[D\right]} - {t}_{\mathrm{df},\frac{\alpha}{... | R: power calculation for beta coefficient | The answer is "no" but not for the reason in vafisher's answer.
The correct formula for the power of a two-sided hypothesis test for a single regression coefficient is
$$\begin{align}
\mathrm{power}= | R: power calculation for beta coefficient
The answer is "no" but not for the reason in vafisher's answer.
The correct formula for the power of a two-sided hypothesis test for a single regression coefficient is
$$\begin{align}
\mathrm{power}=&\operatorname{Pr}\left(t_{\mathrm{df}} \le -\frac{D}{\operatorname{se}\left[D... | R: power calculation for beta coefficient
The answer is "no" but not for the reason in vafisher's answer.
The correct formula for the power of a two-sided hypothesis test for a single regression coefficient is
$$\begin{align}
\mathrm{power}= |
43,181 | R: power calculation for beta coefficient | Short answer, no. The t-statistic you're looking at is the square root of the F discussed in this post: What is the power of the regression F test? for the removal of a single independent variable. | R: power calculation for beta coefficient | Short answer, no. The t-statistic you're looking at is the square root of the F discussed in this post: What is the power of the regression F test? for the removal of a single independent variable. | R: power calculation for beta coefficient
Short answer, no. The t-statistic you're looking at is the square root of the F discussed in this post: What is the power of the regression F test? for the removal of a single independent variable. | R: power calculation for beta coefficient
Short answer, no. The t-statistic you're looking at is the square root of the F discussed in this post: What is the power of the regression F test? for the removal of a single independent variable. |
43,182 | Ranking undergrad students by their future income - Mixture distribution | Mixture models of only two distributions, $D_1$ and $D_2$, can be considered to have the density $p D_1+(1-p) D_2$, where $0<p<1$. Now $p\neq0,1$ because it would no longer be a mixture. In general for any mixture distribution, software is available to find the best mixture model, e.g., FindDistribution in Mathematica,... | Ranking undergrad students by their future income - Mixture distribution | Mixture models of only two distributions, $D_1$ and $D_2$, can be considered to have the density $p D_1+(1-p) D_2$, where $0<p<1$. Now $p\neq0,1$ because it would no longer be a mixture. In general fo | Ranking undergrad students by their future income - Mixture distribution
Mixture models of only two distributions, $D_1$ and $D_2$, can be considered to have the density $p D_1+(1-p) D_2$, where $0<p<1$. Now $p\neq0,1$ because it would no longer be a mixture. In general for any mixture distribution, software is availab... | Ranking undergrad students by their future income - Mixture distribution
Mixture models of only two distributions, $D_1$ and $D_2$, can be considered to have the density $p D_1+(1-p) D_2$, where $0<p<1$. Now $p\neq0,1$ because it would no longer be a mixture. In general fo |
43,183 | ARIMAX model's exogenous components? | Look at the simplest form of ARIMAX(0,1,0) or IX(1):
$$\Delta y_t=c+x_t+\varepsilon_t$$
where $x_t$ - exogenous variables. Take an expectation:
$$E[\Delta y_t]=c+E[x_t]$$
If you think that your $\Delta y_t$ is stationary, then $x_t$ must be statrionary too. The same with ARX(1):
$$y_t=\phi_1 y_{t-1}+c+x_t+\varepsilon_t... | ARIMAX model's exogenous components? | Look at the simplest form of ARIMAX(0,1,0) or IX(1):
$$\Delta y_t=c+x_t+\varepsilon_t$$
where $x_t$ - exogenous variables. Take an expectation:
$$E[\Delta y_t]=c+E[x_t]$$
If you think that your $\Delt | ARIMAX model's exogenous components?
Look at the simplest form of ARIMAX(0,1,0) or IX(1):
$$\Delta y_t=c+x_t+\varepsilon_t$$
where $x_t$ - exogenous variables. Take an expectation:
$$E[\Delta y_t]=c+E[x_t]$$
If you think that your $\Delta y_t$ is stationary, then $x_t$ must be statrionary too. The same with ARX(1):
$$y... | ARIMAX model's exogenous components?
Look at the simplest form of ARIMAX(0,1,0) or IX(1):
$$\Delta y_t=c+x_t+\varepsilon_t$$
where $x_t$ - exogenous variables. Take an expectation:
$$E[\Delta y_t]=c+E[x_t]$$
If you think that your $\Delt |
43,184 | ARIMAX model's exogenous components? | This is known as transfer function model:
A(L)y(t)=B(L)e(t)+C(L)x(t)
y(t)=inv(A(L))B(L)e(t)+inv(A(L))C(L)x(t)
For stabity and invertibility you have to have some restrictions on the characteristic polynomial of this representation. Which means processes jointly has to satisfy these conditions.
You can have seasona... | ARIMAX model's exogenous components? | This is known as transfer function model:
A(L)y(t)=B(L)e(t)+C(L)x(t)
y(t)=inv(A(L))B(L)e(t)+inv(A(L))C(L)x(t)
For stabity and invertibility you have to have some restrictions on the characteristic | ARIMAX model's exogenous components?
This is known as transfer function model:
A(L)y(t)=B(L)e(t)+C(L)x(t)
y(t)=inv(A(L))B(L)e(t)+inv(A(L))C(L)x(t)
For stabity and invertibility you have to have some restrictions on the characteristic polynomial of this representation. Which means processes jointly has to satisfy the... | ARIMAX model's exogenous components?
This is known as transfer function model:
A(L)y(t)=B(L)e(t)+C(L)x(t)
y(t)=inv(A(L))B(L)e(t)+inv(A(L))C(L)x(t)
For stabity and invertibility you have to have some restrictions on the characteristic |
43,185 | Selecting problems of the appropriate difficulty based for adaptive learning [closed] | You could Item Response Theory or it's more complex version Hierarchical Item Response Theory. It will estimate students abilities and items difficulty to produce probability of success using models based on logistic regressions. | Selecting problems of the appropriate difficulty based for adaptive learning [closed] | You could Item Response Theory or it's more complex version Hierarchical Item Response Theory. It will estimate students abilities and items difficulty to produce probability of success using models b | Selecting problems of the appropriate difficulty based for adaptive learning [closed]
You could Item Response Theory or it's more complex version Hierarchical Item Response Theory. It will estimate students abilities and items difficulty to produce probability of success using models based on logistic regressions. | Selecting problems of the appropriate difficulty based for adaptive learning [closed]
You could Item Response Theory or it's more complex version Hierarchical Item Response Theory. It will estimate students abilities and items difficulty to produce probability of success using models b |
43,186 | Difference of Prediction between Graph Representation and Data Matrix Representation | I'm trying to answer the question in one aspect.
Generally a graph can be described by a matrix, with the columns and rows indexed by vertex, and elements corresponding to the edge weights. And adjacent matrix can also describe an undirect/direct graph. So graph analysis is usually equivalent to perform analysis on ma... | Difference of Prediction between Graph Representation and Data Matrix Representation | I'm trying to answer the question in one aspect.
Generally a graph can be described by a matrix, with the columns and rows indexed by vertex, and elements corresponding to the edge weights. And adjac | Difference of Prediction between Graph Representation and Data Matrix Representation
I'm trying to answer the question in one aspect.
Generally a graph can be described by a matrix, with the columns and rows indexed by vertex, and elements corresponding to the edge weights. And adjacent matrix can also describe an und... | Difference of Prediction between Graph Representation and Data Matrix Representation
I'm trying to answer the question in one aspect.
Generally a graph can be described by a matrix, with the columns and rows indexed by vertex, and elements corresponding to the edge weights. And adjac |
43,187 | What is Polychoric Correlation Coefficient intuitively? | I found Kolenikov and Angeles "The Use of Discrete Data in Principal Component Analysis" working paper to be helpful (published version here if you have access). Slides here as well.
To quote the authors (from the help-file for their polychoric Stata command):
The polychoric correlation of two ordinal variables is der... | What is Polychoric Correlation Coefficient intuitively? | I found Kolenikov and Angeles "The Use of Discrete Data in Principal Component Analysis" working paper to be helpful (published version here if you have access). Slides here as well.
To quote the auth | What is Polychoric Correlation Coefficient intuitively?
I found Kolenikov and Angeles "The Use of Discrete Data in Principal Component Analysis" working paper to be helpful (published version here if you have access). Slides here as well.
To quote the authors (from the help-file for their polychoric Stata command):
Th... | What is Polychoric Correlation Coefficient intuitively?
I found Kolenikov and Angeles "The Use of Discrete Data in Principal Component Analysis" working paper to be helpful (published version here if you have access). Slides here as well.
To quote the auth |
43,188 | "Estimated effects may be unbalanced" message when running aov in R. What does it mean? | aov is designed for balanced data (link). Balanced design is: An experimental design where all cells (i.e. treatment combinations) have the same number of observations (link). | "Estimated effects may be unbalanced" message when running aov in R. What does it mean? | aov is designed for balanced data (link). Balanced design is: An experimental design where all cells (i.e. treatment combinations) have the same number of observations (link). | "Estimated effects may be unbalanced" message when running aov in R. What does it mean?
aov is designed for balanced data (link). Balanced design is: An experimental design where all cells (i.e. treatment combinations) have the same number of observations (link). | "Estimated effects may be unbalanced" message when running aov in R. What does it mean?
aov is designed for balanced data (link). Balanced design is: An experimental design where all cells (i.e. treatment combinations) have the same number of observations (link). |
43,189 | "Estimated effects may be unbalanced" message when running aov in R. What does it mean? | Install package called car & activate it first and then calculate sum of squares using Anova(lm(y~x1*x2),type=2)
Doing this way will calculate type II SS which can be used for analysis when the interaction is not significant
and if the interaction is significant for the unbalanced data, you should calculate type III SS | "Estimated effects may be unbalanced" message when running aov in R. What does it mean? | Install package called car & activate it first and then calculate sum of squares using Anova(lm(y~x1*x2),type=2)
Doing this way will calculate type II SS which can be used for analysis when the intera | "Estimated effects may be unbalanced" message when running aov in R. What does it mean?
Install package called car & activate it first and then calculate sum of squares using Anova(lm(y~x1*x2),type=2)
Doing this way will calculate type II SS which can be used for analysis when the interaction is not significant
and if ... | "Estimated effects may be unbalanced" message when running aov in R. What does it mean?
Install package called car & activate it first and then calculate sum of squares using Anova(lm(y~x1*x2),type=2)
Doing this way will calculate type II SS which can be used for analysis when the intera |
43,190 | 2D binary classification | This is a really deep question. I am going to try to answer it for your specific case and make broader points at the same time.
Has anyone an idea on how to proceed here?
How to proceed from here is really a question of which method to use. The answer for your particular case seems to be CART (Classification and Re... | 2D binary classification | This is a really deep question. I am going to try to answer it for your specific case and make broader points at the same time.
Has anyone an idea on how to proceed here?
How to proceed from here i | 2D binary classification
This is a really deep question. I am going to try to answer it for your specific case and make broader points at the same time.
Has anyone an idea on how to proceed here?
How to proceed from here is really a question of which method to use. The answer for your particular case seems to be CA... | 2D binary classification
This is a really deep question. I am going to try to answer it for your specific case and make broader points at the same time.
Has anyone an idea on how to proceed here?
How to proceed from here i |
43,191 | Comparing power law fits with large uncertainties | Because there are errors in both variables, we do not know the true values of the $(x,y)$ data associated with each observation. Let us suppose that each of $n=6$ independent observations results from measurement errors independently made in the two coordinates $(\xi, \eta) = (\xi, f(\xi;\alpha,\beta))$ with $f(\xi;... | Comparing power law fits with large uncertainties | Because there are errors in both variables, we do not know the true values of the $(x,y)$ data associated with each observation. Let us suppose that each of $n=6$ independent observations results fr | Comparing power law fits with large uncertainties
Because there are errors in both variables, we do not know the true values of the $(x,y)$ data associated with each observation. Let us suppose that each of $n=6$ independent observations results from measurement errors independently made in the two coordinates $(\xi,... | Comparing power law fits with large uncertainties
Because there are errors in both variables, we do not know the true values of the $(x,y)$ data associated with each observation. Let us suppose that each of $n=6$ independent observations results fr |
43,192 | Analyzing repeated rank data. | I think that using a rating system, like Elo or Glicko, is a good choice.
Do the experiment with subject A, then repeat with subject B, subject C, and more.
Randomize matches' (i.e. comparisons) order and insert results in a rating system engine.
If you're interested in use more than in development, rankade, our free... | Analyzing repeated rank data. | I think that using a rating system, like Elo or Glicko, is a good choice.
Do the experiment with subject A, then repeat with subject B, subject C, and more.
Randomize matches' (i.e. comparisons) orde | Analyzing repeated rank data.
I think that using a rating system, like Elo or Glicko, is a good choice.
Do the experiment with subject A, then repeat with subject B, subject C, and more.
Randomize matches' (i.e. comparisons) order and insert results in a rating system engine.
If you're interested in use more than in ... | Analyzing repeated rank data.
I think that using a rating system, like Elo or Glicko, is a good choice.
Do the experiment with subject A, then repeat with subject B, subject C, and more.
Randomize matches' (i.e. comparisons) orde |
43,193 | Analyzing repeated rank data. | Here one possible answer, although I imagine a better one exists:
Take the row means (ignoring blanks). | Analyzing repeated rank data. | Here one possible answer, although I imagine a better one exists:
Take the row means (ignoring blanks). | Analyzing repeated rank data.
Here one possible answer, although I imagine a better one exists:
Take the row means (ignoring blanks). | Analyzing repeated rank data.
Here one possible answer, although I imagine a better one exists:
Take the row means (ignoring blanks). |
43,194 | Analyzing repeated rank data. | This might be an odd approach but logistic regression might be useful. For example, if person 1 compared items 1vs2 and 3vs4 and person 2 compared 2vs3 and 5vs6, and if the lower # items were always rated as "2", the data could be entered in R as:
data.frame(
T1=c(1,2,3,4,2,3,5,6),
T2=c(2,1,4,3,3,2,6,5),
Y =c(1,2,1,2,1... | Analyzing repeated rank data. | This might be an odd approach but logistic regression might be useful. For example, if person 1 compared items 1vs2 and 3vs4 and person 2 compared 2vs3 and 5vs6, and if the lower # items were always r | Analyzing repeated rank data.
This might be an odd approach but logistic regression might be useful. For example, if person 1 compared items 1vs2 and 3vs4 and person 2 compared 2vs3 and 5vs6, and if the lower # items were always rated as "2", the data could be entered in R as:
data.frame(
T1=c(1,2,3,4,2,3,5,6),
T2=c(2,... | Analyzing repeated rank data.
This might be an odd approach but logistic regression might be useful. For example, if person 1 compared items 1vs2 and 3vs4 and person 2 compared 2vs3 and 5vs6, and if the lower # items were always r |
43,195 | Relationship between inverse gamma and gamma distribution | Yes, but I think the first parameter of the Gamma should be $1-p/2$ instead of $1+p/2$.
$$
v \sim \text{Gamma}(1-p/2, s/2)
$$
I'm using the shape-rate parametrization, as in here. | Relationship between inverse gamma and gamma distribution | Yes, but I think the first parameter of the Gamma should be $1-p/2$ instead of $1+p/2$.
$$
v \sim \text{Gamma}(1-p/2, s/2)
$$
I'm using the shape-rate parametrization, as in here. | Relationship between inverse gamma and gamma distribution
Yes, but I think the first parameter of the Gamma should be $1-p/2$ instead of $1+p/2$.
$$
v \sim \text{Gamma}(1-p/2, s/2)
$$
I'm using the shape-rate parametrization, as in here. | Relationship between inverse gamma and gamma distribution
Yes, but I think the first parameter of the Gamma should be $1-p/2$ instead of $1+p/2$.
$$
v \sim \text{Gamma}(1-p/2, s/2)
$$
I'm using the shape-rate parametrization, as in here. |
43,196 | Relationship between inverse gamma and gamma distribution | Your scale parameter seems to be problematic. Here is the relationship between Gamma and Inv-Gamma distributions:
A random variable X is said to have the inverse Gamma distribution with
parameters $\alpha$ and $\theta$ if 1/X has the Gamma($\alpha$, $1/\theta$) distribution. | Relationship between inverse gamma and gamma distribution | Your scale parameter seems to be problematic. Here is the relationship between Gamma and Inv-Gamma distributions:
A random variable X is said to have the inverse Gamma distribution with
parameters | Relationship between inverse gamma and gamma distribution
Your scale parameter seems to be problematic. Here is the relationship between Gamma and Inv-Gamma distributions:
A random variable X is said to have the inverse Gamma distribution with
parameters $\alpha$ and $\theta$ if 1/X has the Gamma($\alpha$, $1/\theta... | Relationship between inverse gamma and gamma distribution
Your scale parameter seems to be problematic. Here is the relationship between Gamma and Inv-Gamma distributions:
A random variable X is said to have the inverse Gamma distribution with
parameters |
43,197 | Linear Regression Intuition behind least squares | Solution $\beta=(x^Tx)^{-1}x^Ty$
can be justified by following three arguments:
It is a method of moments estimator which solves certain population moment conditions
It minimizes L2 norm
It is a maximum likelihood estimator when residuals follow Gaussian distribution
Second argument is about mathematical optimization... | Linear Regression Intuition behind least squares | Solution $\beta=(x^Tx)^{-1}x^Ty$
can be justified by following three arguments:
It is a method of moments estimator which solves certain population moment conditions
It minimizes L2 norm
It is a maxi | Linear Regression Intuition behind least squares
Solution $\beta=(x^Tx)^{-1}x^Ty$
can be justified by following three arguments:
It is a method of moments estimator which solves certain population moment conditions
It minimizes L2 norm
It is a maximum likelihood estimator when residuals follow Gaussian distribution
S... | Linear Regression Intuition behind least squares
Solution $\beta=(x^Tx)^{-1}x^Ty$
can be justified by following three arguments:
It is a method of moments estimator which solves certain population moment conditions
It minimizes L2 norm
It is a maxi |
43,198 | Deep Learning Networks: Fundamental differences | Two qualitative answers that seem reasonable are that:
the more layers you have, the more computation you have to perform during a training step. This computation (think for example of backpropagation as the simplest example) may be linear with the number of layers, and with deep networks you easily get to 20-30 layer... | Deep Learning Networks: Fundamental differences | Two qualitative answers that seem reasonable are that:
the more layers you have, the more computation you have to perform during a training step. This computation (think for example of backpropagatio | Deep Learning Networks: Fundamental differences
Two qualitative answers that seem reasonable are that:
the more layers you have, the more computation you have to perform during a training step. This computation (think for example of backpropagation as the simplest example) may be linear with the number of layers, and ... | Deep Learning Networks: Fundamental differences
Two qualitative answers that seem reasonable are that:
the more layers you have, the more computation you have to perform during a training step. This computation (think for example of backpropagatio |
43,199 | Kendall-tau and RKHS spaces | By the Moore-Aronszajn theorem, $\tau$ is the kernel for some RKHS iff it's symmetric and positive semidefinite. (The link uses the term "positive definite" to mean the equivalent of psd for matrices, unfortunately; that terminology isn't standardized.)
Update: What I had here before was based on a mistaken understandi... | Kendall-tau and RKHS spaces | By the Moore-Aronszajn theorem, $\tau$ is the kernel for some RKHS iff it's symmetric and positive semidefinite. (The link uses the term "positive definite" to mean the equivalent of psd for matrices, | Kendall-tau and RKHS spaces
By the Moore-Aronszajn theorem, $\tau$ is the kernel for some RKHS iff it's symmetric and positive semidefinite. (The link uses the term "positive definite" to mean the equivalent of psd for matrices, unfortunately; that terminology isn't standardized.)
Update: What I had here before was bas... | Kendall-tau and RKHS spaces
By the Moore-Aronszajn theorem, $\tau$ is the kernel for some RKHS iff it's symmetric and positive semidefinite. (The link uses the term "positive definite" to mean the equivalent of psd for matrices, |
43,200 | PAC learning theory and lower bound on the amount of input samples | To answer my own question, it is easy to get a lower bound when you assume that all variables are uniformly distributed. Then the probability of this event (let's call it A) becomes:
$$
P(A) = 1 - P (X_1 = 0, X_2 = 0, \ldots, X_n = 0) \\
= 1 - \prod P(X_i = 0) \quad \quad \quad \quad \quad\\
= 1 - \left[ ... | PAC learning theory and lower bound on the amount of input samples | To answer my own question, it is easy to get a lower bound when you assume that all variables are uniformly distributed. Then the probability of this event (let's call it A) becomes:
$$
P(A) = 1 - P | PAC learning theory and lower bound on the amount of input samples
To answer my own question, it is easy to get a lower bound when you assume that all variables are uniformly distributed. Then the probability of this event (let's call it A) becomes:
$$
P(A) = 1 - P (X_1 = 0, X_2 = 0, \ldots, X_n = 0) \\
= 1 - \p... | PAC learning theory and lower bound on the amount of input samples
To answer my own question, it is easy to get a lower bound when you assume that all variables are uniformly distributed. Then the probability of this event (let's call it A) becomes:
$$
P(A) = 1 - P |
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