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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49,801 | Taxonomy/overview of machine learning techniques [duplicate] | You can find a very good taxonomy of the most important ML methods in the table of contents of the book Machine Learning: a Probabilistic Perspective by Kevin Patrick Murphy.
Given your background in statistics, I'm pretty confident that you will find that book resourceful. It has both introductory descriptions and in-... | Taxonomy/overview of machine learning techniques [duplicate] | You can find a very good taxonomy of the most important ML methods in the table of contents of the book Machine Learning: a Probabilistic Perspective by Kevin Patrick Murphy.
Given your background in | Taxonomy/overview of machine learning techniques [duplicate]
You can find a very good taxonomy of the most important ML methods in the table of contents of the book Machine Learning: a Probabilistic Perspective by Kevin Patrick Murphy.
Given your background in statistics, I'm pretty confident that you will find that bo... | Taxonomy/overview of machine learning techniques [duplicate]
You can find a very good taxonomy of the most important ML methods in the table of contents of the book Machine Learning: a Probabilistic Perspective by Kevin Patrick Murphy.
Given your background in |
49,802 | Taxonomy/overview of machine learning techniques [duplicate] | Tree-based methods
A group of regression and classification methods built around decision trees. In a decision tree, data is recursively partitioned based on its predictors, and new predictions are generated by averaging data points at the relevant tips ('leaves') of each tree. Weaknesses of standard decision trees (su... | Taxonomy/overview of machine learning techniques [duplicate] | Tree-based methods
A group of regression and classification methods built around decision trees. In a decision tree, data is recursively partitioned based on its predictors, and new predictions are ge | Taxonomy/overview of machine learning techniques [duplicate]
Tree-based methods
A group of regression and classification methods built around decision trees. In a decision tree, data is recursively partitioned based on its predictors, and new predictions are generated by averaging data points at the relevant tips ('lea... | Taxonomy/overview of machine learning techniques [duplicate]
Tree-based methods
A group of regression and classification methods built around decision trees. In a decision tree, data is recursively partitioned based on its predictors, and new predictions are ge |
49,803 | What is pseudomedian in R function `wilcox.test`? | A good clue is to look at the actual code of wilcox.test:
https://github.com/SurajGupta/r-source/blob/master/src/library/stats/R/wilcox.test.R
Specifically the bit concerning the estimate of the pseudo median for a 1 sample test is line 91-122:
x <- x + mu # we want a conf.int for the median
alpha <- 1 - co... | What is pseudomedian in R function `wilcox.test`? | A good clue is to look at the actual code of wilcox.test:
https://github.com/SurajGupta/r-source/blob/master/src/library/stats/R/wilcox.test.R
Specifically the bit concerning the estimate of the pseud | What is pseudomedian in R function `wilcox.test`?
A good clue is to look at the actual code of wilcox.test:
https://github.com/SurajGupta/r-source/blob/master/src/library/stats/R/wilcox.test.R
Specifically the bit concerning the estimate of the pseudo median for a 1 sample test is line 91-122:
x <- x + mu #... | What is pseudomedian in R function `wilcox.test`?
A good clue is to look at the actual code of wilcox.test:
https://github.com/SurajGupta/r-source/blob/master/src/library/stats/R/wilcox.test.R
Specifically the bit concerning the estimate of the pseud |
49,804 | How can I calculate the number of degrees of freedom in the Elastic Net regularization, specifically in R? | The answer to your question is here:
This is from a talk by Hui Zou. You can find the full talk here.
This should be relatively easy to implement in R. If you need some guidance, you can check the lassovar package by A. Kock and L. Callot; see the command .ridge.df in lassovar-ada.R.
Related reference:
Zou, H., Hast... | How can I calculate the number of degrees of freedom in the Elastic Net regularization, specifically | The answer to your question is here:
This is from a talk by Hui Zou. You can find the full talk here.
This should be relatively easy to implement in R. If you need some guidance, you can check the | How can I calculate the number of degrees of freedom in the Elastic Net regularization, specifically in R?
The answer to your question is here:
This is from a talk by Hui Zou. You can find the full talk here.
This should be relatively easy to implement in R. If you need some guidance, you can check the lassovar pack... | How can I calculate the number of degrees of freedom in the Elastic Net regularization, specifically
The answer to your question is here:
This is from a talk by Hui Zou. You can find the full talk here.
This should be relatively easy to implement in R. If you need some guidance, you can check the |
49,805 | Bias caused by optional stopping | Some relevant posts here and here.
According to an answer from the second post, it seems that as the number of flips goes to infinity, at some point the significance test will be positive (almost surely), which is to say, there exists some finite number of samples after which it will almost surely happen.
According to... | Bias caused by optional stopping | Some relevant posts here and here.
According to an answer from the second post, it seems that as the number of flips goes to infinity, at some point the significance test will be positive (almost sur | Bias caused by optional stopping
Some relevant posts here and here.
According to an answer from the second post, it seems that as the number of flips goes to infinity, at some point the significance test will be positive (almost surely), which is to say, there exists some finite number of samples after which it will a... | Bias caused by optional stopping
Some relevant posts here and here.
According to an answer from the second post, it seems that as the number of flips goes to infinity, at some point the significance test will be positive (almost sur |
49,806 | Bias caused by optional stopping | I did some simulations (under $H_0$: a fair coin $p=0.5$). I limited the number of flips to $n_\max$ because the raw stopping time $T$ has such a huge tail that sometimes the computer wouldn't stop in a reasonable time. Anyway it's more realistic with a limit.
The experiment is:
do some first $100$ flips to initialize... | Bias caused by optional stopping | I did some simulations (under $H_0$: a fair coin $p=0.5$). I limited the number of flips to $n_\max$ because the raw stopping time $T$ has such a huge tail that sometimes the computer wouldn't stop in | Bias caused by optional stopping
I did some simulations (under $H_0$: a fair coin $p=0.5$). I limited the number of flips to $n_\max$ because the raw stopping time $T$ has such a huge tail that sometimes the computer wouldn't stop in a reasonable time. Anyway it's more realistic with a limit.
The experiment is:
do som... | Bias caused by optional stopping
I did some simulations (under $H_0$: a fair coin $p=0.5$). I limited the number of flips to $n_\max$ because the raw stopping time $T$ has such a huge tail that sometimes the computer wouldn't stop in |
49,807 | How to calculate CV performance? | As you said, the second method is preferred for small hold out sets (or large values of $k$ compared to the $n$ of your data-set if you will). At the extreme end, you will almost always use the second for leave one out. (Think twice before scoring on $R^2$ though.)
The first has the advantage that you can use the multi... | How to calculate CV performance? | As you said, the second method is preferred for small hold out sets (or large values of $k$ compared to the $n$ of your data-set if you will). At the extreme end, you will almost always use the second | How to calculate CV performance?
As you said, the second method is preferred for small hold out sets (or large values of $k$ compared to the $n$ of your data-set if you will). At the extreme end, you will almost always use the second for leave one out. (Think twice before scoring on $R^2$ though.)
The first has the adv... | How to calculate CV performance?
As you said, the second method is preferred for small hold out sets (or large values of $k$ compared to the $n$ of your data-set if you will). At the extreme end, you will almost always use the second |
49,808 | In GLMs, why do we solve score(beta)=0 instead of just minimizing the negative log-likelihood? | The solutions to the score equation are critical points of the objective function in your optimisation, so generally the fitted coefficient estimator should solve the score equation. This is not really a "step further" than using numerical techniques; it is just a way of characterising the fitted value, which is the p... | In GLMs, why do we solve score(beta)=0 instead of just minimizing the negative log-likelihood? | The solutions to the score equation are critical points of the objective function in your optimisation, so generally the fitted coefficient estimator should solve the score equation. This is not real | In GLMs, why do we solve score(beta)=0 instead of just minimizing the negative log-likelihood?
The solutions to the score equation are critical points of the objective function in your optimisation, so generally the fitted coefficient estimator should solve the score equation. This is not really a "step further" than ... | In GLMs, why do we solve score(beta)=0 instead of just minimizing the negative log-likelihood?
The solutions to the score equation are critical points of the objective function in your optimisation, so generally the fitted coefficient estimator should solve the score equation. This is not real |
49,809 | The relation between least-square estimation in two seemingly related problems | In the case of b, the question being asked is "What scalar is closest to my data points (in the least squares sense)?" In the case of c, the question being asked is "How can I scale my data points to make each as close as possible to 1 (in the least squares sese)?" These objective functions are different. Imagine the c... | The relation between least-square estimation in two seemingly related problems | In the case of b, the question being asked is "What scalar is closest to my data points (in the least squares sense)?" In the case of c, the question being asked is "How can I scale my data points to | The relation between least-square estimation in two seemingly related problems
In the case of b, the question being asked is "What scalar is closest to my data points (in the least squares sense)?" In the case of c, the question being asked is "How can I scale my data points to make each as close as possible to 1 (in t... | The relation between least-square estimation in two seemingly related problems
In the case of b, the question being asked is "What scalar is closest to my data points (in the least squares sense)?" In the case of c, the question being asked is "How can I scale my data points to |
49,810 | How to perform CCA with block design in R | I believe the issue is that the permutation test you are using is too liberal; it assumes a Null hypothesis in which all observations are exchangeable. From what you say, observations within a cage are exchangeable, but are not exchangeable between cages.
To use the more restrictive null in the permutation test we can ... | How to perform CCA with block design in R | I believe the issue is that the permutation test you are using is too liberal; it assumes a Null hypothesis in which all observations are exchangeable. From what you say, observations within a cage ar | How to perform CCA with block design in R
I believe the issue is that the permutation test you are using is too liberal; it assumes a Null hypothesis in which all observations are exchangeable. From what you say, observations within a cage are exchangeable, but are not exchangeable between cages.
To use the more restri... | How to perform CCA with block design in R
I believe the issue is that the permutation test you are using is too liberal; it assumes a Null hypothesis in which all observations are exchangeable. From what you say, observations within a cage ar |
49,811 | How to set the priors for Bayesian estimation of Multivariate Normal Distribution when the correlation matrix has small values? | Looking at the sampling of the $\Sigma$, I think you might have forgotten to replace the mean $\mu$ with the sampled $\mu(t)$ from your posterior distribution of the mean.
So $\eta$ should be determined as
$\eta=\Phi+\sum_n^N(x_n-\mu(t))(x_n-\mu(t))^T$
Gibbs sampling is an iterative procedure--when you sample from the ... | How to set the priors for Bayesian estimation of Multivariate Normal Distribution when the correlati | Looking at the sampling of the $\Sigma$, I think you might have forgotten to replace the mean $\mu$ with the sampled $\mu(t)$ from your posterior distribution of the mean.
So $\eta$ should be determin | How to set the priors for Bayesian estimation of Multivariate Normal Distribution when the correlation matrix has small values?
Looking at the sampling of the $\Sigma$, I think you might have forgotten to replace the mean $\mu$ with the sampled $\mu(t)$ from your posterior distribution of the mean.
So $\eta$ should be ... | How to set the priors for Bayesian estimation of Multivariate Normal Distribution when the correlati
Looking at the sampling of the $\Sigma$, I think you might have forgotten to replace the mean $\mu$ with the sampled $\mu(t)$ from your posterior distribution of the mean.
So $\eta$ should be determin |
49,812 | Given a bounded number of die rolls following unif{1,6}, produce unif{1,7} | The argument is fine. I think you can distill it to something simpler, though.
A sequence of rolls determines a branching probability tree with six branches at each node. Because the rolls are independent and each outcome has probability $6^{-1}$, the chance of reaching a given node at level $n$ (that is, a particul... | Given a bounded number of die rolls following unif{1,6}, produce unif{1,7} | The argument is fine. I think you can distill it to something simpler, though.
A sequence of rolls determines a branching probability tree with six branches at each node. Because the rolls are inde | Given a bounded number of die rolls following unif{1,6}, produce unif{1,7}
The argument is fine. I think you can distill it to something simpler, though.
A sequence of rolls determines a branching probability tree with six branches at each node. Because the rolls are independent and each outcome has probability $6^{... | Given a bounded number of die rolls following unif{1,6}, produce unif{1,7}
The argument is fine. I think you can distill it to something simpler, though.
A sequence of rolls determines a branching probability tree with six branches at each node. Because the rolls are inde |
49,813 | Given a bounded number of die rolls following unif{1,6}, produce unif{1,7} | If I follow your line, we can note that $\frac{log_2{7}}{log_2{6}}=log_6{7}$ which is bound to be irrational, so we'll always lose some information (which is true, as 5 different results are represented by one number and the 36th result is discarded).
I do think, however, that by defining the event of a re-roll and its... | Given a bounded number of die rolls following unif{1,6}, produce unif{1,7} | If I follow your line, we can note that $\frac{log_2{7}}{log_2{6}}=log_6{7}$ which is bound to be irrational, so we'll always lose some information (which is true, as 5 different results are represent | Given a bounded number of die rolls following unif{1,6}, produce unif{1,7}
If I follow your line, we can note that $\frac{log_2{7}}{log_2{6}}=log_6{7}$ which is bound to be irrational, so we'll always lose some information (which is true, as 5 different results are represented by one number and the 36th result is disca... | Given a bounded number of die rolls following unif{1,6}, produce unif{1,7}
If I follow your line, we can note that $\frac{log_2{7}}{log_2{6}}=log_6{7}$ which is bound to be irrational, so we'll always lose some information (which is true, as 5 different results are represent |
49,814 | Are predictive distributions supposed to be distributions of future data? | You almost wholly and correctly answered your blog question. I created a few simulations to show you where the differences are.
Also, I have a personal issue with the term of art, “overdispersed.” Predictive distributions are not overdispersed, they are correctly dispersed, but the true distribution in nature doesn’t... | Are predictive distributions supposed to be distributions of future data? | You almost wholly and correctly answered your blog question. I created a few simulations to show you where the differences are.
Also, I have a personal issue with the term of art, “overdispersed.” P | Are predictive distributions supposed to be distributions of future data?
You almost wholly and correctly answered your blog question. I created a few simulations to show you where the differences are.
Also, I have a personal issue with the term of art, “overdispersed.” Predictive distributions are not overdispersed,... | Are predictive distributions supposed to be distributions of future data?
You almost wholly and correctly answered your blog question. I created a few simulations to show you where the differences are.
Also, I have a personal issue with the term of art, “overdispersed.” P |
49,815 | How do I know whether future samples will remain below a threshold? | You want to assess whether the probability $\Pr(X>1)$ is significantly higher than $99\%$.
To do so, you can derive a confidence interval about $\Pr(X>1)$. For example you can get such a confidence interval using the Bayesian approach with the Jeffreys prior.
Another way is to use a lower tolerance limit. If the lower... | How do I know whether future samples will remain below a threshold? | You want to assess whether the probability $\Pr(X>1)$ is significantly higher than $99\%$.
To do so, you can derive a confidence interval about $\Pr(X>1)$. For example you can get such a confidence in | How do I know whether future samples will remain below a threshold?
You want to assess whether the probability $\Pr(X>1)$ is significantly higher than $99\%$.
To do so, you can derive a confidence interval about $\Pr(X>1)$. For example you can get such a confidence interval using the Bayesian approach with the Jeffreys... | How do I know whether future samples will remain below a threshold?
You want to assess whether the probability $\Pr(X>1)$ is significantly higher than $99\%$.
To do so, you can derive a confidence interval about $\Pr(X>1)$. For example you can get such a confidence in |
49,816 | What's the difference between a TSLM forecast and STL forecast? | I think I got my answer.
A TSLM is literally just that. Essentially a data frame is created with 3+ columns. Column 1 is your y value. Column 2 is the numbers 1 to however_many_observations_you_have. Column 3 is a factor variable that corresponds to your seasonal. In my case, 1 to 12. Then it just compiles a regressio... | What's the difference between a TSLM forecast and STL forecast? | I think I got my answer.
A TSLM is literally just that. Essentially a data frame is created with 3+ columns. Column 1 is your y value. Column 2 is the numbers 1 to however_many_observations_you_have. | What's the difference between a TSLM forecast and STL forecast?
I think I got my answer.
A TSLM is literally just that. Essentially a data frame is created with 3+ columns. Column 1 is your y value. Column 2 is the numbers 1 to however_many_observations_you_have. Column 3 is a factor variable that corresponds to your ... | What's the difference between a TSLM forecast and STL forecast?
I think I got my answer.
A TSLM is literally just that. Essentially a data frame is created with 3+ columns. Column 1 is your y value. Column 2 is the numbers 1 to however_many_observations_you_have. |
49,817 | Can we absorb the partition function into the natural parameter vector? | The definition of the log partition function,
$$A(\theta) = \log \int h(x) \exp\{\phi(\theta)^T T(x) \}dx $$
makes it clear that given fixed functions $h(x)$ and $T(x)$, then $A(\theta)$ is completely determined by $\phi(\theta)$. In your second parameterization where you've absorbed the log-partition function to the n... | Can we absorb the partition function into the natural parameter vector? | The definition of the log partition function,
$$A(\theta) = \log \int h(x) \exp\{\phi(\theta)^T T(x) \}dx $$
makes it clear that given fixed functions $h(x)$ and $T(x)$, then $A(\theta)$ is completely | Can we absorb the partition function into the natural parameter vector?
The definition of the log partition function,
$$A(\theta) = \log \int h(x) \exp\{\phi(\theta)^T T(x) \}dx $$
makes it clear that given fixed functions $h(x)$ and $T(x)$, then $A(\theta)$ is completely determined by $\phi(\theta)$. In your second pa... | Can we absorb the partition function into the natural parameter vector?
The definition of the log partition function,
$$A(\theta) = \log \int h(x) \exp\{\phi(\theta)^T T(x) \}dx $$
makes it clear that given fixed functions $h(x)$ and $T(x)$, then $A(\theta)$ is completely |
49,818 | What's the relationship between Laplace approximation and Variational Bayes methods? | As already stated in the comment section, both the Laplace Method and a certain class of Variational Inference Methods (convex-type representations) are based on locally approximating a (non-Gaussian) density.
Chris Bishop's book 'Pattern recognition and machine learning' has a chapter on this (Chapter 10.5. Local Var... | What's the relationship between Laplace approximation and Variational Bayes methods? | As already stated in the comment section, both the Laplace Method and a certain class of Variational Inference Methods (convex-type representations) are based on locally approximating a (non-Gaussian) | What's the relationship between Laplace approximation and Variational Bayes methods?
As already stated in the comment section, both the Laplace Method and a certain class of Variational Inference Methods (convex-type representations) are based on locally approximating a (non-Gaussian) density.
Chris Bishop's book 'Pat... | What's the relationship between Laplace approximation and Variational Bayes methods?
As already stated in the comment section, both the Laplace Method and a certain class of Variational Inference Methods (convex-type representations) are based on locally approximating a (non-Gaussian) |
49,819 | Are the Boltzmann distributions an exponential family? | Could you elaborate on those three issues in your question? It looks like something completely different what you are asking there. Regarding the Boltzman distribution or Maxwell Boltzman statistics: The distribution $p(a) = \frac{g_a}{Z(T)} e^{\tfrac{-E(a)}{kT}}$, with $Z(T) = \int_a g_a e^{\tfrac{-E(a)}{kT}}$ (or a s... | Are the Boltzmann distributions an exponential family? | Could you elaborate on those three issues in your question? It looks like something completely different what you are asking there. Regarding the Boltzman distribution or Maxwell Boltzman statistics: | Are the Boltzmann distributions an exponential family?
Could you elaborate on those three issues in your question? It looks like something completely different what you are asking there. Regarding the Boltzman distribution or Maxwell Boltzman statistics: The distribution $p(a) = \frac{g_a}{Z(T)} e^{\tfrac{-E(a)}{kT}}$,... | Are the Boltzmann distributions an exponential family?
Could you elaborate on those three issues in your question? It looks like something completely different what you are asking there. Regarding the Boltzman distribution or Maxwell Boltzman statistics: |
49,820 | Why are larger samples required to estimate higher moments than when estimating the mean? | To answer your second question first - "quality" means "accuracy", and accuracy can be defined in many ways, hence the lack of mathematical precision in the definition.
Higher moments are harder to estimate in many situations, easier in others. If the probability distribution of the data is such that the mean equals 0... | Why are larger samples required to estimate higher moments than when estimating the mean? | To answer your second question first - "quality" means "accuracy", and accuracy can be defined in many ways, hence the lack of mathematical precision in the definition.
Higher moments are harder to es | Why are larger samples required to estimate higher moments than when estimating the mean?
To answer your second question first - "quality" means "accuracy", and accuracy can be defined in many ways, hence the lack of mathematical precision in the definition.
Higher moments are harder to estimate in many situations, eas... | Why are larger samples required to estimate higher moments than when estimating the mean?
To answer your second question first - "quality" means "accuracy", and accuracy can be defined in many ways, hence the lack of mathematical precision in the definition.
Higher moments are harder to es |
49,821 | Combining image and scalar inputs into a neural network | There are many ways to combine scalar and image inputs. In this particular paper, a diagram on the top of page 5 should explain everything. At some point in the convolutional network there are 64 feature maps, which matches the 64 scalar values to be input. The 64 scalar values are essentially treated as bias terms so ... | Combining image and scalar inputs into a neural network | There are many ways to combine scalar and image inputs. In this particular paper, a diagram on the top of page 5 should explain everything. At some point in the convolutional network there are 64 feat | Combining image and scalar inputs into a neural network
There are many ways to combine scalar and image inputs. In this particular paper, a diagram on the top of page 5 should explain everything. At some point in the convolutional network there are 64 feature maps, which matches the 64 scalar values to be input. The 64... | Combining image and scalar inputs into a neural network
There are many ways to combine scalar and image inputs. In this particular paper, a diagram on the top of page 5 should explain everything. At some point in the convolutional network there are 64 feat |
49,822 | Combining image and scalar inputs into a neural network | The features vector can be combined to an image by -
Adjusting the features shape by using tf.reshape and tf.tile
Combining the features and image by performing concatenation, add (as described in Research document) or other merge operators
Here is a code example for creating a Custom Keras Layer that merge features ... | Combining image and scalar inputs into a neural network | The features vector can be combined to an image by -
Adjusting the features shape by using tf.reshape and tf.tile
Combining the features and image by performing concatenation, add (as described in Re | Combining image and scalar inputs into a neural network
The features vector can be combined to an image by -
Adjusting the features shape by using tf.reshape and tf.tile
Combining the features and image by performing concatenation, add (as described in Research document) or other merge operators
Here is a code exampl... | Combining image and scalar inputs into a neural network
The features vector can be combined to an image by -
Adjusting the features shape by using tf.reshape and tf.tile
Combining the features and image by performing concatenation, add (as described in Re |
49,823 | combining text and non-text features in a classification model | I am not aware of a standard way as such but here's a one thing I'll try. This will contain two models in the pipeline.
Train on the textual data to predict a class (like Fiance, Hardware) and get the model's prediction as a one categorical variable.
Append that categorical variable to the existing metadata featues, a... | combining text and non-text features in a classification model | I am not aware of a standard way as such but here's a one thing I'll try. This will contain two models in the pipeline.
Train on the textual data to predict a class (like Fiance, Hardware) and get th | combining text and non-text features in a classification model
I am not aware of a standard way as such but here's a one thing I'll try. This will contain two models in the pipeline.
Train on the textual data to predict a class (like Fiance, Hardware) and get the model's prediction as a one categorical variable.
Appen... | combining text and non-text features in a classification model
I am not aware of a standard way as such but here's a one thing I'll try. This will contain two models in the pipeline.
Train on the textual data to predict a class (like Fiance, Hardware) and get th |
49,824 | A point of view on Central Limit Theorem | Formally speaking, the CLT is in principle, indeed concerned with the limiting behavior of standardized sums of random variables, say $S_n=(1/n)\sum X_i$,
$$\frac{S_n - \mathbb{E}\left[S_n\right]}{\sqrt{\text{Var}(S_n)}}$$
So indeed the $\sqrt n$ term comes from the standard deviation of the sum.
Still, thinking of it ... | A point of view on Central Limit Theorem | Formally speaking, the CLT is in principle, indeed concerned with the limiting behavior of standardized sums of random variables, say $S_n=(1/n)\sum X_i$,
$$\frac{S_n - \mathbb{E}\left[S_n\right]}{\sq | A point of view on Central Limit Theorem
Formally speaking, the CLT is in principle, indeed concerned with the limiting behavior of standardized sums of random variables, say $S_n=(1/n)\sum X_i$,
$$\frac{S_n - \mathbb{E}\left[S_n\right]}{\sqrt{\text{Var}(S_n)}}$$
So indeed the $\sqrt n$ term comes from the standard dev... | A point of view on Central Limit Theorem
Formally speaking, the CLT is in principle, indeed concerned with the limiting behavior of standardized sums of random variables, say $S_n=(1/n)\sum X_i$,
$$\frac{S_n - \mathbb{E}\left[S_n\right]}{\sq |
49,825 | ARIMA model has trouble forecasting next month | Whenever possible, it is best to develop one equation that effectively characterizes the data see “Joint estimation of all parameters is preferred.” from lecture 3 http://faculty.chicagobooth.edu/ruey.tsay/teaching/bs41202/sp2011/.
As you suggested, there are fairly strong deterministic factors in your data. We have se... | ARIMA model has trouble forecasting next month | Whenever possible, it is best to develop one equation that effectively characterizes the data see “Joint estimation of all parameters is preferred.” from lecture 3 http://faculty.chicagobooth.edu/ruey | ARIMA model has trouble forecasting next month
Whenever possible, it is best to develop one equation that effectively characterizes the data see “Joint estimation of all parameters is preferred.” from lecture 3 http://faculty.chicagobooth.edu/ruey.tsay/teaching/bs41202/sp2011/.
As you suggested, there are fairly strong... | ARIMA model has trouble forecasting next month
Whenever possible, it is best to develop one equation that effectively characterizes the data see “Joint estimation of all parameters is preferred.” from lecture 3 http://faculty.chicagobooth.edu/ruey |
49,826 | ARIMA model has trouble forecasting next month | For this you will want to split the date into 3 parts (day, month, year) and then do a seasonal time series potentially.
Chicaco booth have some good uni lecture notes available here (Try week 3): http://faculty.chicagobooth.edu/ruey.tsay/teaching/bs41202/sp2011/
R bloggers also have a brief section on this:
https://... | ARIMA model has trouble forecasting next month | For this you will want to split the date into 3 parts (day, month, year) and then do a seasonal time series potentially.
Chicaco booth have some good uni lecture notes available here (Try week 3): ht | ARIMA model has trouble forecasting next month
For this you will want to split the date into 3 parts (day, month, year) and then do a seasonal time series potentially.
Chicaco booth have some good uni lecture notes available here (Try week 3): http://faculty.chicagobooth.edu/ruey.tsay/teaching/bs41202/sp2011/
R blogge... | ARIMA model has trouble forecasting next month
For this you will want to split the date into 3 parts (day, month, year) and then do a seasonal time series potentially.
Chicaco booth have some good uni lecture notes available here (Try week 3): ht |
49,827 | How to get approximative confidence interval for Gini and AUC? | Assumptions addressed
The paper that proposed your formula (Hanely and MacNeil 1982) explicitly states that a key assumption is that the ratings are derived from a continuous scale that does not produce ‘ties’.
A typical explanation of "AUC is the probability that a sample randomly taken from the positive cases will r... | How to get approximative confidence interval for Gini and AUC? | Assumptions addressed
The paper that proposed your formula (Hanely and MacNeil 1982) explicitly states that a key assumption is that the ratings are derived from a continuous scale that does not produ | How to get approximative confidence interval for Gini and AUC?
Assumptions addressed
The paper that proposed your formula (Hanely and MacNeil 1982) explicitly states that a key assumption is that the ratings are derived from a continuous scale that does not produce ‘ties’.
A typical explanation of "AUC is the probabil... | How to get approximative confidence interval for Gini and AUC?
Assumptions addressed
The paper that proposed your formula (Hanely and MacNeil 1982) explicitly states that a key assumption is that the ratings are derived from a continuous scale that does not produ |
49,828 | Weighting for stratified random sample with non-proportionally allocated sample | A stratified design effectively means that separate surveys are designed within each stratum - units selected within one stratum are independent of all selections within other strata. Estimates of total are made within each stratum, and then combined to come up with the estimate of total across the population:
$$
\hat{... | Weighting for stratified random sample with non-proportionally allocated sample | A stratified design effectively means that separate surveys are designed within each stratum - units selected within one stratum are independent of all selections within other strata. Estimates of tot | Weighting for stratified random sample with non-proportionally allocated sample
A stratified design effectively means that separate surveys are designed within each stratum - units selected within one stratum are independent of all selections within other strata. Estimates of total are made within each stratum, and the... | Weighting for stratified random sample with non-proportionally allocated sample
A stratified design effectively means that separate surveys are designed within each stratum - units selected within one stratum are independent of all selections within other strata. Estimates of tot |
49,829 | What is cross-validation for? | Cross-validation is, in my opinion, a method to estimate performance of your model AND its parameters. It is also a good measure of how robust your model with its parameters is.
Let's say you decided two methods are appropriate for your data: ordinary least squares(OLS) and ridge regression.
For ridge regression case,... | What is cross-validation for? | Cross-validation is, in my opinion, a method to estimate performance of your model AND its parameters. It is also a good measure of how robust your model with its parameters is.
Let's say you decided | What is cross-validation for?
Cross-validation is, in my opinion, a method to estimate performance of your model AND its parameters. It is also a good measure of how robust your model with its parameters is.
Let's say you decided two methods are appropriate for your data: ordinary least squares(OLS) and ridge regressio... | What is cross-validation for?
Cross-validation is, in my opinion, a method to estimate performance of your model AND its parameters. It is also a good measure of how robust your model with its parameters is.
Let's say you decided |
49,830 | What is cross-validation for? | Cross-validation is, obviously, for validation.
It results with some measure of how good your model is (by the way, I'd use MeanSquaredError instead of MinimumSquaredError, whatever it is). So it enables you to assess model's future performance and to compare models.
Of, course, you can assess MSE without cross-validat... | What is cross-validation for? | Cross-validation is, obviously, for validation.
It results with some measure of how good your model is (by the way, I'd use MeanSquaredError instead of MinimumSquaredError, whatever it is). So it enab | What is cross-validation for?
Cross-validation is, obviously, for validation.
It results with some measure of how good your model is (by the way, I'd use MeanSquaredError instead of MinimumSquaredError, whatever it is). So it enables you to assess model's future performance and to compare models.
Of, course, you can as... | What is cross-validation for?
Cross-validation is, obviously, for validation.
It results with some measure of how good your model is (by the way, I'd use MeanSquaredError instead of MinimumSquaredError, whatever it is). So it enab |
49,831 | What is cross-validation for? | Cross-validation is a method to validate a model, which is used mostly in cases when you have a very limited amount of data available.
You never want to train on data on which you are validating. On the other hand, sometimes it is costly to totally remove part of the training set (for validation). Cross-validation is ... | What is cross-validation for? | Cross-validation is a method to validate a model, which is used mostly in cases when you have a very limited amount of data available.
You never want to train on data on which you are validating. On | What is cross-validation for?
Cross-validation is a method to validate a model, which is used mostly in cases when you have a very limited amount of data available.
You never want to train on data on which you are validating. On the other hand, sometimes it is costly to totally remove part of the training set (for val... | What is cross-validation for?
Cross-validation is a method to validate a model, which is used mostly in cases when you have a very limited amount of data available.
You never want to train on data on which you are validating. On |
49,832 | Interpretation of p-value histogram for differential methylation analysis: what can explain prevalence of large p-values? | Edit: As Amoeba pointed out there was an error in my code, and the first plot is from an unpaired t-test. I re-ran with paired t-tests and different alpha and beta, and the results are at the bottom.
I simulated it in Matlab with the code below. I generated 1000 random alphas (1x3 vectors); corresponding betas are made... | Interpretation of p-value histogram for differential methylation analysis: what can explain prevalen | Edit: As Amoeba pointed out there was an error in my code, and the first plot is from an unpaired t-test. I re-ran with paired t-tests and different alpha and beta, and the results are at the bottom.
| Interpretation of p-value histogram for differential methylation analysis: what can explain prevalence of large p-values?
Edit: As Amoeba pointed out there was an error in my code, and the first plot is from an unpaired t-test. I re-ran with paired t-tests and different alpha and beta, and the results are at the bottom... | Interpretation of p-value histogram for differential methylation analysis: what can explain prevalen
Edit: As Amoeba pointed out there was an error in my code, and the first plot is from an unpaired t-test. I re-ran with paired t-tests and different alpha and beta, and the results are at the bottom.
|
49,833 | lm.ridge returns different results that are from manual calculation | To deal with scaling problem, I suggest you replace lambda with lambda*(n/(n-1)). This will resolve the discrepancies.
In your example, it would be lam*(100/99).
set.seed(1)
x <- rnorm(1000,1,2)
x <- matrix(x,ncol=10,nrow=100)
y <- rnorm(100,2,5)
xs <- scale(x,TRUE,TRUE)
ys <- scale(y,TRUE,TRUE)
p <- dim(x)[2]
lam <... | lm.ridge returns different results that are from manual calculation | To deal with scaling problem, I suggest you replace lambda with lambda*(n/(n-1)). This will resolve the discrepancies.
In your example, it would be lam*(100/99).
set.seed(1)
x <- rnorm(1000,1,2)
x <- | lm.ridge returns different results that are from manual calculation
To deal with scaling problem, I suggest you replace lambda with lambda*(n/(n-1)). This will resolve the discrepancies.
In your example, it would be lam*(100/99).
set.seed(1)
x <- rnorm(1000,1,2)
x <- matrix(x,ncol=10,nrow=100)
y <- rnorm(100,2,5)
xs <... | lm.ridge returns different results that are from manual calculation
To deal with scaling problem, I suggest you replace lambda with lambda*(n/(n-1)). This will resolve the discrepancies.
In your example, it would be lam*(100/99).
set.seed(1)
x <- rnorm(1000,1,2)
x <- |
49,834 | Bayesian A/B testing with uniform prior | You seem to have answered the new formulation of your question yourself, in the comments. A primary appeal of Bayesian analysis of an experiment (which is what marketers call an A/B test) is that it lets you answer probabilistic questions about population values, such as "What is the probability that treatment A is bet... | Bayesian A/B testing with uniform prior | You seem to have answered the new formulation of your question yourself, in the comments. A primary appeal of Bayesian analysis of an experiment (which is what marketers call an A/B test) is that it l | Bayesian A/B testing with uniform prior
You seem to have answered the new formulation of your question yourself, in the comments. A primary appeal of Bayesian analysis of an experiment (which is what marketers call an A/B test) is that it lets you answer probabilistic questions about population values, such as "What is... | Bayesian A/B testing with uniform prior
You seem to have answered the new formulation of your question yourself, in the comments. A primary appeal of Bayesian analysis of an experiment (which is what marketers call an A/B test) is that it l |
49,835 | Bayesian A/B testing with uniform prior | I can think of two reasons that you might want to do this:
The posterior distribution $\mathbb{P}(\theta|D)$ gives us a detailed view of our knowledge about the conversation rate, $\theta$. It allows us to visualize our knowledge about the parameter's value, compare the similarity of two test variants, and use decisio... | Bayesian A/B testing with uniform prior | I can think of two reasons that you might want to do this:
The posterior distribution $\mathbb{P}(\theta|D)$ gives us a detailed view of our knowledge about the conversation rate, $\theta$. It allows | Bayesian A/B testing with uniform prior
I can think of two reasons that you might want to do this:
The posterior distribution $\mathbb{P}(\theta|D)$ gives us a detailed view of our knowledge about the conversation rate, $\theta$. It allows us to visualize our knowledge about the parameter's value, compare the similari... | Bayesian A/B testing with uniform prior
I can think of two reasons that you might want to do this:
The posterior distribution $\mathbb{P}(\theta|D)$ gives us a detailed view of our knowledge about the conversation rate, $\theta$. It allows |
49,836 | choosing lambda for multi-reponse lasso in glmnet | Short answer for the simplest case (no intercept, no standardization)
library(glmnet)
set.seed(125)
n <- 50
p <- 5
k <- 2
X <- matrix(rnorm(n * p), ncol=p)
y <- matrix(rnorm(n * k), ncol=k)
max(glmnet(X, y, family="mgaussian",
standardize = FALSE,
standardize.response = FALSE,
int... | choosing lambda for multi-reponse lasso in glmnet | Short answer for the simplest case (no intercept, no standardization)
library(glmnet)
set.seed(125)
n <- 50
p <- 5
k <- 2
X <- matrix(rnorm(n * p), ncol=p)
y <- matrix(rnorm(n * k), ncol=k)
max(glm | choosing lambda for multi-reponse lasso in glmnet
Short answer for the simplest case (no intercept, no standardization)
library(glmnet)
set.seed(125)
n <- 50
p <- 5
k <- 2
X <- matrix(rnorm(n * p), ncol=p)
y <- matrix(rnorm(n * k), ncol=k)
max(glmnet(X, y, family="mgaussian",
standardize = FALSE,
... | choosing lambda for multi-reponse lasso in glmnet
Short answer for the simplest case (no intercept, no standardization)
library(glmnet)
set.seed(125)
n <- 50
p <- 5
k <- 2
X <- matrix(rnorm(n * p), ncol=p)
y <- matrix(rnorm(n * k), ncol=k)
max(glm |
49,837 | choosing lambda for multi-reponse lasso in glmnet | sorry I'm new to the community, still trying to get the hang of it! Thank for editing my question @F. Tusell. The link to the original article came from: https://web.stanford.edu/~hastie/Papers/glmnet.pdf.
But the paper did not mention much about what was done regarding multi-variate response. The vignette for the R pa... | choosing lambda for multi-reponse lasso in glmnet | sorry I'm new to the community, still trying to get the hang of it! Thank for editing my question @F. Tusell. The link to the original article came from: https://web.stanford.edu/~hastie/Papers/glmnet | choosing lambda for multi-reponse lasso in glmnet
sorry I'm new to the community, still trying to get the hang of it! Thank for editing my question @F. Tusell. The link to the original article came from: https://web.stanford.edu/~hastie/Papers/glmnet.pdf.
But the paper did not mention much about what was done regarding... | choosing lambda for multi-reponse lasso in glmnet
sorry I'm new to the community, still trying to get the hang of it! Thank for editing my question @F. Tusell. The link to the original article came from: https://web.stanford.edu/~hastie/Papers/glmnet |
49,838 | Causal model assumptions - regression adjustment to experiments | There are some things that need clarification here.
Is $Y = \beta_1X + \beta_2R + \epsilon$ a structural equation? That is, do you believe the structural relationship between the variables you listed and the outcome is truly linear?
If this is the case, that is, if you truly believe the regression represents the stru... | Causal model assumptions - regression adjustment to experiments | There are some things that need clarification here.
Is $Y = \beta_1X + \beta_2R + \epsilon$ a structural equation? That is, do you believe the structural relationship between the variables you liste | Causal model assumptions - regression adjustment to experiments
There are some things that need clarification here.
Is $Y = \beta_1X + \beta_2R + \epsilon$ a structural equation? That is, do you believe the structural relationship between the variables you listed and the outcome is truly linear?
If this is the case, ... | Causal model assumptions - regression adjustment to experiments
There are some things that need clarification here.
Is $Y = \beta_1X + \beta_2R + \epsilon$ a structural equation? That is, do you believe the structural relationship between the variables you liste |
49,839 | Is bias a frequentist concept or a Bayesian concept? | Suppose there is a model for the data $Y$ that depends on a parameter $\theta$ and, for a particular experiment, there is a true value of the parameter, $\theta_0$.
You develop an estimator $\hat\theta = \hat\theta(Y)$, i.e. the estimator is a function of the data $Y$. Then the bias is
$$ bias(\hat\theta) = E_{Y|\the... | Is bias a frequentist concept or a Bayesian concept? | Suppose there is a model for the data $Y$ that depends on a parameter $\theta$ and, for a particular experiment, there is a true value of the parameter, $\theta_0$.
You develop an estimator $\hat\the | Is bias a frequentist concept or a Bayesian concept?
Suppose there is a model for the data $Y$ that depends on a parameter $\theta$ and, for a particular experiment, there is a true value of the parameter, $\theta_0$.
You develop an estimator $\hat\theta = \hat\theta(Y)$, i.e. the estimator is a function of the data $... | Is bias a frequentist concept or a Bayesian concept?
Suppose there is a model for the data $Y$ that depends on a parameter $\theta$ and, for a particular experiment, there is a true value of the parameter, $\theta_0$.
You develop an estimator $\hat\the |
49,840 | Word2vec that can distinguish words with different meanings | You're right that word2vec can't distinguish between 'palm' the tree and 'palm' the part of a hand, and related problems. More broadly, it struggles to handle polysemy and homonymy.
The typical way to address this is to learn word sense embeddings instead of word embeddings. In general, this requires assigning word tok... | Word2vec that can distinguish words with different meanings | You're right that word2vec can't distinguish between 'palm' the tree and 'palm' the part of a hand, and related problems. More broadly, it struggles to handle polysemy and homonymy.
The typical way to | Word2vec that can distinguish words with different meanings
You're right that word2vec can't distinguish between 'palm' the tree and 'palm' the part of a hand, and related problems. More broadly, it struggles to handle polysemy and homonymy.
The typical way to address this is to learn word sense embeddings instead of w... | Word2vec that can distinguish words with different meanings
You're right that word2vec can't distinguish between 'palm' the tree and 'palm' the part of a hand, and related problems. More broadly, it struggles to handle polysemy and homonymy.
The typical way to |
49,841 | Word2vec that can distinguish words with different meanings | If you wanted to naively encode a word as a vector, the easiest way would be one-hot encoding, where each seperate word becomes a bit entry in a vector. The only thing that word2vec does is that it compresses this one-hot vector into a lower dimension. So the word 'book' will have a vector representation with fewer dim... | Word2vec that can distinguish words with different meanings | If you wanted to naively encode a word as a vector, the easiest way would be one-hot encoding, where each seperate word becomes a bit entry in a vector. The only thing that word2vec does is that it co | Word2vec that can distinguish words with different meanings
If you wanted to naively encode a word as a vector, the easiest way would be one-hot encoding, where each seperate word becomes a bit entry in a vector. The only thing that word2vec does is that it compresses this one-hot vector into a lower dimension. So the ... | Word2vec that can distinguish words with different meanings
If you wanted to naively encode a word as a vector, the easiest way would be one-hot encoding, where each seperate word becomes a bit entry in a vector. The only thing that word2vec does is that it co |
49,842 | EM algorithm is always used for mixture copula | There are many varieties of EM algorithms. In some of the problems I have worked on, fancy EM algorithms are absolutely state of the art.
That being said, in regards to mixture models, the "vanilla EM" algorithm, which I am pretty sure you are referring to, has two major advantages; extremely easy to implement and ext... | EM algorithm is always used for mixture copula | There are many varieties of EM algorithms. In some of the problems I have worked on, fancy EM algorithms are absolutely state of the art.
That being said, in regards to mixture models, the "vanilla E | EM algorithm is always used for mixture copula
There are many varieties of EM algorithms. In some of the problems I have worked on, fancy EM algorithms are absolutely state of the art.
That being said, in regards to mixture models, the "vanilla EM" algorithm, which I am pretty sure you are referring to, has two major ... | EM algorithm is always used for mixture copula
There are many varieties of EM algorithms. In some of the problems I have worked on, fancy EM algorithms are absolutely state of the art.
That being said, in regards to mixture models, the "vanilla E |
49,843 | Feed Forward Neural Network - How to Visualize the Weight Matrix? | You're right, and there should be 50 images. You could easily verfiy this by:
[coef.shape for coef in mlp.coefs_[0]]
where mlp is the trained MLP classifer in the example.
So here are the two things caused confusion:
Clearly, the author of the example did not mention anything about why only 16 images
In Python when y... | Feed Forward Neural Network - How to Visualize the Weight Matrix? | You're right, and there should be 50 images. You could easily verfiy this by:
[coef.shape for coef in mlp.coefs_[0]]
where mlp is the trained MLP classifer in the example.
So here are the two things | Feed Forward Neural Network - How to Visualize the Weight Matrix?
You're right, and there should be 50 images. You could easily verfiy this by:
[coef.shape for coef in mlp.coefs_[0]]
where mlp is the trained MLP classifer in the example.
So here are the two things caused confusion:
Clearly, the author of the example ... | Feed Forward Neural Network - How to Visualize the Weight Matrix?
You're right, and there should be 50 images. You could easily verfiy this by:
[coef.shape for coef in mlp.coefs_[0]]
where mlp is the trained MLP classifer in the example.
So here are the two things |
49,844 | Using Rule of Three to obtain confidence interval for a binomial population | The procedure described in the question is intuitive, clear, and accurate.
Problem Formulation
Formally, this is a hypergeometric sampling problem: in a population of $N=1000$ subjects, of which $K$ are in Class 1 and $N-K$ are in Class 2, a sample of size $n=50$ is taken without replacement and it is observed that all... | Using Rule of Three to obtain confidence interval for a binomial population | The procedure described in the question is intuitive, clear, and accurate.
Problem Formulation
Formally, this is a hypergeometric sampling problem: in a population of $N=1000$ subjects, of which $K$ a | Using Rule of Three to obtain confidence interval for a binomial population
The procedure described in the question is intuitive, clear, and accurate.
Problem Formulation
Formally, this is a hypergeometric sampling problem: in a population of $N=1000$ subjects, of which $K$ are in Class 1 and $N-K$ are in Class 2, a sa... | Using Rule of Three to obtain confidence interval for a binomial population
The procedure described in the question is intuitive, clear, and accurate.
Problem Formulation
Formally, this is a hypergeometric sampling problem: in a population of $N=1000$ subjects, of which $K$ a |
49,845 | What's the difference between Leave-One-Out and K-Fold Cross validation? | Leave-one-out fits the model with k-1 observations and classifies the remaining observation left out. It differs from your description because this process is repeated another k-1 times with a different observation left out. You can learn about this from the original paper by Lachenbruch and Mickey in 1968. In my ans... | What's the difference between Leave-One-Out and K-Fold Cross validation? | Leave-one-out fits the model with k-1 observations and classifies the remaining observation left out. It differs from your description because this process is repeated another k-1 times with a differ | What's the difference between Leave-One-Out and K-Fold Cross validation?
Leave-one-out fits the model with k-1 observations and classifies the remaining observation left out. It differs from your description because this process is repeated another k-1 times with a different observation left out. You can learn about ... | What's the difference between Leave-One-Out and K-Fold Cross validation?
Leave-one-out fits the model with k-1 observations and classifies the remaining observation left out. It differs from your description because this process is repeated another k-1 times with a differ |
49,846 | What's the difference between Leave-One-Out and K-Fold Cross validation? | In loocv method we divide the dataset as one data point for test data while all the remaining data points as our train data. We then validate our model by using this n-1 train data against 1 test data. We perform n iterations like this with 1 test data being forwarded and remaining n-1 data being our new train data. Th... | What's the difference between Leave-One-Out and K-Fold Cross validation? | In loocv method we divide the dataset as one data point for test data while all the remaining data points as our train data. We then validate our model by using this n-1 train data against 1 test data | What's the difference between Leave-One-Out and K-Fold Cross validation?
In loocv method we divide the dataset as one data point for test data while all the remaining data points as our train data. We then validate our model by using this n-1 train data against 1 test data. We perform n iterations like this with 1 test... | What's the difference between Leave-One-Out and K-Fold Cross validation?
In loocv method we divide the dataset as one data point for test data while all the remaining data points as our train data. We then validate our model by using this n-1 train data against 1 test data |
49,847 | Relation between Wiener and Kalman filtering | Dan Simon, in his book Optimal State Estimation, discusses this quite comprehensively.
Until 1960, Wiener filtering was the state of the art in signal estimation. The paradigm of signal estimation was shattered with the publication of Rudolph Kalman’s work and related papers in the early 1960s, but it is still worthwh... | Relation between Wiener and Kalman filtering | Dan Simon, in his book Optimal State Estimation, discusses this quite comprehensively.
Until 1960, Wiener filtering was the state of the art in signal estimation. The paradigm of signal estimation wa | Relation between Wiener and Kalman filtering
Dan Simon, in his book Optimal State Estimation, discusses this quite comprehensively.
Until 1960, Wiener filtering was the state of the art in signal estimation. The paradigm of signal estimation was shattered with the publication of Rudolph Kalman’s work and related paper... | Relation between Wiener and Kalman filtering
Dan Simon, in his book Optimal State Estimation, discusses this quite comprehensively.
Until 1960, Wiener filtering was the state of the art in signal estimation. The paradigm of signal estimation wa |
49,848 | Can someone explain the Fisher transformation and why it is used in layman's terms? | The Fisher transformation https://en.wikipedia.org/wiki/Fisher_transformation of an estimated correlation coefficient $r$ is
$$
z= \frac12 \ln\left(\frac{1+r}{1-r}\right).
$$
It is an approximate variance-stabilizing transform, so that its variance which is about $\frac{1}{N-3}$, where $N$ is the sample size, does... | Can someone explain the Fisher transformation and why it is used in layman's terms? | The Fisher transformation https://en.wikipedia.org/wiki/Fisher_transformation of an estimated correlation coefficient $r$ is
$$
z= \frac12 \ln\left(\frac{1+r}{1-r}\right).
$$
It is an approximate | Can someone explain the Fisher transformation and why it is used in layman's terms?
The Fisher transformation https://en.wikipedia.org/wiki/Fisher_transformation of an estimated correlation coefficient $r$ is
$$
z= \frac12 \ln\left(\frac{1+r}{1-r}\right).
$$
It is an approximate variance-stabilizing transform, so t... | Can someone explain the Fisher transformation and why it is used in layman's terms?
The Fisher transformation https://en.wikipedia.org/wiki/Fisher_transformation of an estimated correlation coefficient $r$ is
$$
z= \frac12 \ln\left(\frac{1+r}{1-r}\right).
$$
It is an approximate |
49,849 | Why Adam and batch normalization are considered approximating second-order behavior? | It's kind of an imprecise statement, so It's hard to give a firm answer. Momentum and normalisation methods such as Adam, (diagonal-)AdaGrad and batch-normalization are (effectively) using diagonal approximations to the Hessian. Obviously, that's a very crude approximation, but it is approximating second-order (hessian... | Why Adam and batch normalization are considered approximating second-order behavior? | It's kind of an imprecise statement, so It's hard to give a firm answer. Momentum and normalisation methods such as Adam, (diagonal-)AdaGrad and batch-normalization are (effectively) using diagonal ap | Why Adam and batch normalization are considered approximating second-order behavior?
It's kind of an imprecise statement, so It's hard to give a firm answer. Momentum and normalisation methods such as Adam, (diagonal-)AdaGrad and batch-normalization are (effectively) using diagonal approximations to the Hessian. Obviou... | Why Adam and batch normalization are considered approximating second-order behavior?
It's kind of an imprecise statement, so It's hard to give a firm answer. Momentum and normalisation methods such as Adam, (diagonal-)AdaGrad and batch-normalization are (effectively) using diagonal ap |
49,850 | MCMC: invalid covariance matrix due to numerical error | You can add a tiny epsilon to the diagonal, say $1e-8$ or similar, to the covariance matrix.
So, let's say your covariance matrix is $\mathbf{\Sigma}$. And when you do stuff that involves $\text{inv}(\mathbf{\Sigma})$, or similar, it doesn't work very well, because your $\Sigma$ is not positive definite. So, therefore ... | MCMC: invalid covariance matrix due to numerical error | You can add a tiny epsilon to the diagonal, say $1e-8$ or similar, to the covariance matrix.
So, let's say your covariance matrix is $\mathbf{\Sigma}$. And when you do stuff that involves $\text{inv}( | MCMC: invalid covariance matrix due to numerical error
You can add a tiny epsilon to the diagonal, say $1e-8$ or similar, to the covariance matrix.
So, let's say your covariance matrix is $\mathbf{\Sigma}$. And when you do stuff that involves $\text{inv}(\mathbf{\Sigma})$, or similar, it doesn't work very well, because... | MCMC: invalid covariance matrix due to numerical error
You can add a tiny epsilon to the diagonal, say $1e-8$ or similar, to the covariance matrix.
So, let's say your covariance matrix is $\mathbf{\Sigma}$. And when you do stuff that involves $\text{inv}( |
49,851 | Negative autocorrelation in linear regressions : examples and consequences | So I have wandered online and found some examples of negative autocorrelation :
If you've ever seen a row of cabbages growing in a garden, you'll frequently notice an alternating pattern--big cabbage, little cabbage, big cabbage, little cabbage, etc. This happens because one cabbage might have a slight edge in growth... | Negative autocorrelation in linear regressions : examples and consequences | So I have wandered online and found some examples of negative autocorrelation :
If you've ever seen a row of cabbages growing in a garden, you'll frequently notice an alternating pattern--big cabbag | Negative autocorrelation in linear regressions : examples and consequences
So I have wandered online and found some examples of negative autocorrelation :
If you've ever seen a row of cabbages growing in a garden, you'll frequently notice an alternating pattern--big cabbage, little cabbage, big cabbage, little cabbag... | Negative autocorrelation in linear regressions : examples and consequences
So I have wandered online and found some examples of negative autocorrelation :
If you've ever seen a row of cabbages growing in a garden, you'll frequently notice an alternating pattern--big cabbag |
49,852 | Difference between mean square residual and mean square error | The answer to this question depends on how you define mean squared error (MSE).
In the context of regression, some define it to be
$MSE = \sum (y-\hat{y})^2/(n-p)$
where p is the number of parameters in the regression (including the intercept). Note that since residuals are $y-\hat{y}$, this is equivalent to mean sq... | Difference between mean square residual and mean square error | The answer to this question depends on how you define mean squared error (MSE).
In the context of regression, some define it to be
$MSE = \sum (y-\hat{y})^2/(n-p)$
where p is the number of parameter | Difference between mean square residual and mean square error
The answer to this question depends on how you define mean squared error (MSE).
In the context of regression, some define it to be
$MSE = \sum (y-\hat{y})^2/(n-p)$
where p is the number of parameters in the regression (including the intercept). Note that ... | Difference between mean square residual and mean square error
The answer to this question depends on how you define mean squared error (MSE).
In the context of regression, some define it to be
$MSE = \sum (y-\hat{y})^2/(n-p)$
where p is the number of parameter |
49,853 | Difference between mean square residual and mean square error | I'll try to explain how I see it from statistical point of view.
I don't think MSE and MSR are the same thing (however most people don't differentiate between those two I guess).
Let's say that you do a simulation of data that can be described using regression model. Let's say that you generate the data "randomly" arou... | Difference between mean square residual and mean square error | I'll try to explain how I see it from statistical point of view.
I don't think MSE and MSR are the same thing (however most people don't differentiate between those two I guess).
Let's say that you do | Difference between mean square residual and mean square error
I'll try to explain how I see it from statistical point of view.
I don't think MSE and MSR are the same thing (however most people don't differentiate between those two I guess).
Let's say that you do a simulation of data that can be described using regressi... | Difference between mean square residual and mean square error
I'll try to explain how I see it from statistical point of view.
I don't think MSE and MSR are the same thing (however most people don't differentiate between those two I guess).
Let's say that you do |
49,854 | Difference between mean square residual and mean square error | In short, Mean squared error (MSE) is the square of RMSE. For linear regression standard equation: Y=a+bX, considering MSE equals to the sum of squared differences between actual sample values of X´ and Y´ that are used to fit the linear model, and divided by number of paird samples (n).
For Mean Squared Residues (MSR)... | Difference between mean square residual and mean square error | In short, Mean squared error (MSE) is the square of RMSE. For linear regression standard equation: Y=a+bX, considering MSE equals to the sum of squared differences between actual sample values of X´ a | Difference between mean square residual and mean square error
In short, Mean squared error (MSE) is the square of RMSE. For linear regression standard equation: Y=a+bX, considering MSE equals to the sum of squared differences between actual sample values of X´ and Y´ that are used to fit the linear model, and divided b... | Difference between mean square residual and mean square error
In short, Mean squared error (MSE) is the square of RMSE. For linear regression standard equation: Y=a+bX, considering MSE equals to the sum of squared differences between actual sample values of X´ a |
49,855 | Difference between mean square residual and mean square error | There is no difference between the mean square residual and mean square error. | Difference between mean square residual and mean square error | There is no difference between the mean square residual and mean square error. | Difference between mean square residual and mean square error
There is no difference between the mean square residual and mean square error. | Difference between mean square residual and mean square error
There is no difference between the mean square residual and mean square error. |
49,856 | Python package that allows to train a CRF on two datasets | You can use Wapiti (mirror):
Wapiti is a very fast toolkit for segmenting and labeling sequences with discriminative models. It is based on maxent models, maximum entropy Markov models and linear-chain CRF and proposes various optimization and regularization methods to improve both the computational complexity and th... | Python package that allows to train a CRF on two datasets | You can use Wapiti (mirror):
Wapiti is a very fast toolkit for segmenting and labeling sequences with discriminative models. It is based on maxent models, maximum entropy Markov models and linear-ch | Python package that allows to train a CRF on two datasets
You can use Wapiti (mirror):
Wapiti is a very fast toolkit for segmenting and labeling sequences with discriminative models. It is based on maxent models, maximum entropy Markov models and linear-chain CRF and proposes various optimization and regularization m... | Python package that allows to train a CRF on two datasets
You can use Wapiti (mirror):
Wapiti is a very fast toolkit for segmenting and labeling sequences with discriminative models. It is based on maxent models, maximum entropy Markov models and linear-ch |
49,857 | Python package that allows to train a CRF on two datasets | You can use NeuroNER:
It implements of a bi-directional LSTM + CRF network in TensorFlow
works on Linux/Mac/Windows
written in Python
open source
allows to train a CRF on two datasets with the options use_pretrained_model = True + train_model = True | Python package that allows to train a CRF on two datasets | You can use NeuroNER:
It implements of a bi-directional LSTM + CRF network in TensorFlow
works on Linux/Mac/Windows
written in Python
open source
allows to train a CRF on two datasets with the optio | Python package that allows to train a CRF on two datasets
You can use NeuroNER:
It implements of a bi-directional LSTM + CRF network in TensorFlow
works on Linux/Mac/Windows
written in Python
open source
allows to train a CRF on two datasets with the options use_pretrained_model = True + train_model = True | Python package that allows to train a CRF on two datasets
You can use NeuroNER:
It implements of a bi-directional LSTM + CRF network in TensorFlow
works on Linux/Mac/Windows
written in Python
open source
allows to train a CRF on two datasets with the optio |
49,858 | Proving equation 3.3.12 in Angrist Pischke Mostly Harmless Econometrics (inverse probability weighting formula for ATT effect) | Since $\rho(X_i)=E(D_i|X_i)=P(D_i=1|X_i)$:
$$
E(Y_i D_i|X_i)=\rho(X_i) E(Y_{1i}|X_i) \\
\Rightarrow E(Y_{1i}|X_i)=\frac{1}{\rho(X_i)}E(Y_i D_i|X_i)
$$
similarly,
$$
E(Y_i (1-D_i)|X_i)=(1-\rho(X_i)) E(Y_{0i}|X_i) \\
\Rightarrow E(Y_{0i}|X_i)=\frac{1}{1-\rho(X_i)}E(Y_i (1-D_i)|X_i)
$$
We have
$$
E(Y_{1i} - Y_{0i}\vert X_... | Proving equation 3.3.12 in Angrist Pischke Mostly Harmless Econometrics (inverse probability weighti | Since $\rho(X_i)=E(D_i|X_i)=P(D_i=1|X_i)$:
$$
E(Y_i D_i|X_i)=\rho(X_i) E(Y_{1i}|X_i) \\
\Rightarrow E(Y_{1i}|X_i)=\frac{1}{\rho(X_i)}E(Y_i D_i|X_i)
$$
similarly,
$$
E(Y_i (1-D_i)|X_i)=(1-\rho(X_i)) E( | Proving equation 3.3.12 in Angrist Pischke Mostly Harmless Econometrics (inverse probability weighting formula for ATT effect)
Since $\rho(X_i)=E(D_i|X_i)=P(D_i=1|X_i)$:
$$
E(Y_i D_i|X_i)=\rho(X_i) E(Y_{1i}|X_i) \\
\Rightarrow E(Y_{1i}|X_i)=\frac{1}{\rho(X_i)}E(Y_i D_i|X_i)
$$
similarly,
$$
E(Y_i (1-D_i)|X_i)=(1-\rho(X... | Proving equation 3.3.12 in Angrist Pischke Mostly Harmless Econometrics (inverse probability weighti
Since $\rho(X_i)=E(D_i|X_i)=P(D_i=1|X_i)$:
$$
E(Y_i D_i|X_i)=\rho(X_i) E(Y_{1i}|X_i) \\
\Rightarrow E(Y_{1i}|X_i)=\frac{1}{\rho(X_i)}E(Y_i D_i|X_i)
$$
similarly,
$$
E(Y_i (1-D_i)|X_i)=(1-\rho(X_i)) E( |
49,859 | Proving equation 3.3.12 in Angrist Pischke Mostly Harmless Econometrics (inverse probability weighting formula for ATT effect) | I also get confused when facing eq. 3.3.12 yesterday, it seemed not "so" obvious as mentioned in the text. When I searched for answers, the only method was the above by @Steve and @user106860, thanks a lot. But soon I realized that using $D_i(Y_{1i}-Y_{0i}) = Y_{1i}-Y_{0i}$ in the condition $D_i=1$ seems to be a little... | Proving equation 3.3.12 in Angrist Pischke Mostly Harmless Econometrics (inverse probability weighti | I also get confused when facing eq. 3.3.12 yesterday, it seemed not "so" obvious as mentioned in the text. When I searched for answers, the only method was the above by @Steve and @user106860, thanks | Proving equation 3.3.12 in Angrist Pischke Mostly Harmless Econometrics (inverse probability weighting formula for ATT effect)
I also get confused when facing eq. 3.3.12 yesterday, it seemed not "so" obvious as mentioned in the text. When I searched for answers, the only method was the above by @Steve and @user106860, ... | Proving equation 3.3.12 in Angrist Pischke Mostly Harmless Econometrics (inverse probability weighti
I also get confused when facing eq. 3.3.12 yesterday, it seemed not "so" obvious as mentioned in the text. When I searched for answers, the only method was the above by @Steve and @user106860, thanks |
49,860 | How to derive the time computational complexity of k-medoids (PAM) clustering algorithm? | I hope this question is still relevant. Big O notation denotes the upper bound of an algorithm. Let's assume that the first sets of medoids are the worst medoids. The cost function calculated through these medoids is the maximum of all the possible sets of medoids. Every time we choose a random medoid for comparing the... | How to derive the time computational complexity of k-medoids (PAM) clustering algorithm? | I hope this question is still relevant. Big O notation denotes the upper bound of an algorithm. Let's assume that the first sets of medoids are the worst medoids. The cost function calculated through | How to derive the time computational complexity of k-medoids (PAM) clustering algorithm?
I hope this question is still relevant. Big O notation denotes the upper bound of an algorithm. Let's assume that the first sets of medoids are the worst medoids. The cost function calculated through these medoids is the maximum of... | How to derive the time computational complexity of k-medoids (PAM) clustering algorithm?
I hope this question is still relevant. Big O notation denotes the upper bound of an algorithm. Let's assume that the first sets of medoids are the worst medoids. The cost function calculated through |
49,861 | How to handle skewed data and response variable when predicting | For 1) if the response is also skewed, you better log-transform the response variable as well.
For 2) Once you log-transform, your multiple linear regression(if more than 1 predictor) coefficients explains differently than non-transformed coefficients.
Ex: $\log Y = a_1 \log(X_1) + a_2 \log(X_2)+\cdots$.
Interpretati... | How to handle skewed data and response variable when predicting | For 1) if the response is also skewed, you better log-transform the response variable as well.
For 2) Once you log-transform, your multiple linear regression(if more than 1 predictor) coefficients ex | How to handle skewed data and response variable when predicting
For 1) if the response is also skewed, you better log-transform the response variable as well.
For 2) Once you log-transform, your multiple linear regression(if more than 1 predictor) coefficients explains differently than non-transformed coefficients.
E... | How to handle skewed data and response variable when predicting
For 1) if the response is also skewed, you better log-transform the response variable as well.
For 2) Once you log-transform, your multiple linear regression(if more than 1 predictor) coefficients ex |
49,862 | Reference to support using binomial GLM for proportion response | Recommended in comments:
McCullagh, P., & Nelder, J. A. (1989). Generalized linear models (Monographs on Statistics and Applied Probability 37). CRC press.
Hardin, J. W. & Hilbe, J. M. (2007). Generalized linear models and extensions. Stata press.
Zhao, L., Chen, Y., & Schaffner, D. W. (2001). Comparison of logistic r... | Reference to support using binomial GLM for proportion response | Recommended in comments:
McCullagh, P., & Nelder, J. A. (1989). Generalized linear models (Monographs on Statistics and Applied Probability 37). CRC press.
Hardin, J. W. & Hilbe, J. M. (2007). Genera | Reference to support using binomial GLM for proportion response
Recommended in comments:
McCullagh, P., & Nelder, J. A. (1989). Generalized linear models (Monographs on Statistics and Applied Probability 37). CRC press.
Hardin, J. W. & Hilbe, J. M. (2007). Generalized linear models and extensions. Stata press.
Zhao, L... | Reference to support using binomial GLM for proportion response
Recommended in comments:
McCullagh, P., & Nelder, J. A. (1989). Generalized linear models (Monographs on Statistics and Applied Probability 37). CRC press.
Hardin, J. W. & Hilbe, J. M. (2007). Genera |
49,863 | What does the base distribution of the Dirichlet Process mean? | Let
$$
G \sim \textsf{DP}(\alpha, H)
$$
which says that the random distribution $G$ is itself distributed according to the Dirichlet Process with concentration parameter $\alpha$ and base distribution $H$. There is an explicit representation for $G$ and it's useful for understanding the role of the base distribution ... | What does the base distribution of the Dirichlet Process mean? | Let
$$
G \sim \textsf{DP}(\alpha, H)
$$
which says that the random distribution $G$ is itself distributed according to the Dirichlet Process with concentration parameter $\alpha$ and base distributi | What does the base distribution of the Dirichlet Process mean?
Let
$$
G \sim \textsf{DP}(\alpha, H)
$$
which says that the random distribution $G$ is itself distributed according to the Dirichlet Process with concentration parameter $\alpha$ and base distribution $H$. There is an explicit representation for $G$ and i... | What does the base distribution of the Dirichlet Process mean?
Let
$$
G \sim \textsf{DP}(\alpha, H)
$$
which says that the random distribution $G$ is itself distributed according to the Dirichlet Process with concentration parameter $\alpha$ and base distributi |
49,864 | ABRACADABRA Problem | The solution is reached thinking about the process as a martingale betting game with some conditions. At every keystroke, a different gambler jumps in the game with a $\small \$1$ bet. If any given bettor loses at the following round (next keystroke of the monkey), he leaves the game with a $-\small \$1$ balance; if he... | ABRACADABRA Problem | The solution is reached thinking about the process as a martingale betting game with some conditions. At every keystroke, a different gambler jumps in the game with a $\small \$1$ bet. If any given be | ABRACADABRA Problem
The solution is reached thinking about the process as a martingale betting game with some conditions. At every keystroke, a different gambler jumps in the game with a $\small \$1$ bet. If any given bettor loses at the following round (next keystroke of the monkey), he leaves the game with a $-\small... | ABRACADABRA Problem
The solution is reached thinking about the process as a martingale betting game with some conditions. At every keystroke, a different gambler jumps in the game with a $\small \$1$ bet. If any given be |
49,865 | McNemar test with multiple scores for the same subject | You want Cochran's Q test. Just as the one way repeated measures ANOVA generalizes the paired t test to two or more measurements in the same individual (or more than two individuals matched per block), Cochran's Q test generalizes McNemars' test to two or more measurements in the same individual (or more than two indiv... | McNemar test with multiple scores for the same subject | You want Cochran's Q test. Just as the one way repeated measures ANOVA generalizes the paired t test to two or more measurements in the same individual (or more than two individuals matched per block) | McNemar test with multiple scores for the same subject
You want Cochran's Q test. Just as the one way repeated measures ANOVA generalizes the paired t test to two or more measurements in the same individual (or more than two individuals matched per block), Cochran's Q test generalizes McNemars' test to two or more meas... | McNemar test with multiple scores for the same subject
You want Cochran's Q test. Just as the one way repeated measures ANOVA generalizes the paired t test to two or more measurements in the same individual (or more than two individuals matched per block) |
49,866 | Why does the jackknife-after-bootstrap estimation of variance give an overestimate? | The over-estimation is due to the error in the ensemble mean due to the finite size of the ensemble. This is discussed, along with a correction term, in this paper by Wager et al. There are implementations in C++/R and scala (disclosure: I am the primary author of the scala package). | Why does the jackknife-after-bootstrap estimation of variance give an overestimate? | The over-estimation is due to the error in the ensemble mean due to the finite size of the ensemble. This is discussed, along with a correction term, in this paper by Wager et al. There are implemen | Why does the jackknife-after-bootstrap estimation of variance give an overestimate?
The over-estimation is due to the error in the ensemble mean due to the finite size of the ensemble. This is discussed, along with a correction term, in this paper by Wager et al. There are implementations in C++/R and scala (disclosu... | Why does the jackknife-after-bootstrap estimation of variance give an overestimate?
The over-estimation is due to the error in the ensemble mean due to the finite size of the ensemble. This is discussed, along with a correction term, in this paper by Wager et al. There are implemen |
49,867 | Find correlation between two time series. Theory and practice (R) | Your very straightforward simple question has unfortunately both a simple and a complex answer. I will avoid the simple . In summary the whole idea is that one needs to account for / condition for intra-correlation while identifying the inter-correlation . Following are some references that you might consider before at... | Find correlation between two time series. Theory and practice (R) | Your very straightforward simple question has unfortunately both a simple and a complex answer. I will avoid the simple . In summary the whole idea is that one needs to account for / condition for int | Find correlation between two time series. Theory and practice (R)
Your very straightforward simple question has unfortunately both a simple and a complex answer. I will avoid the simple . In summary the whole idea is that one needs to account for / condition for intra-correlation while identifying the inter-correlation... | Find correlation between two time series. Theory and practice (R)
Your very straightforward simple question has unfortunately both a simple and a complex answer. I will avoid the simple . In summary the whole idea is that one needs to account for / condition for int |
49,868 | Why use perplexity rather than nearest neighbor match in t-SNE? | "The perplexity can be interpreted as a smooth measure of the effective number of neighbors" could be interpreted as $\frac{\delta \sigma_i}{\delta P}$ being smooth. That is, varying Perplexity has an effect on $\sigma_i$ for a fixed i that is continuous in all derivatives.
This is not true of the k-NN approach. One c... | Why use perplexity rather than nearest neighbor match in t-SNE? | "The perplexity can be interpreted as a smooth measure of the effective number of neighbors" could be interpreted as $\frac{\delta \sigma_i}{\delta P}$ being smooth. That is, varying Perplexity has an | Why use perplexity rather than nearest neighbor match in t-SNE?
"The perplexity can be interpreted as a smooth measure of the effective number of neighbors" could be interpreted as $\frac{\delta \sigma_i}{\delta P}$ being smooth. That is, varying Perplexity has an effect on $\sigma_i$ for a fixed i that is continuous i... | Why use perplexity rather than nearest neighbor match in t-SNE?
"The perplexity can be interpreted as a smooth measure of the effective number of neighbors" could be interpreted as $\frac{\delta \sigma_i}{\delta P}$ being smooth. That is, varying Perplexity has an |
49,869 | "Uncertainty range" versus "confidence interval" - what is the difference, and which is preferred? | If you look at some other papers from the project "Global burden of diseases", you will see that data imputation for missing cases have been carried out using proxy. As in case of modelling the global burden of diarrhoea, due to unavailability of data from systematic surveillance in countries like Liberia, Libya, Afgha... | "Uncertainty range" versus "confidence interval" - what is the difference, and which is preferred? | If you look at some other papers from the project "Global burden of diseases", you will see that data imputation for missing cases have been carried out using proxy. As in case of modelling the global | "Uncertainty range" versus "confidence interval" - what is the difference, and which is preferred?
If you look at some other papers from the project "Global burden of diseases", you will see that data imputation for missing cases have been carried out using proxy. As in case of modelling the global burden of diarrhoea,... | "Uncertainty range" versus "confidence interval" - what is the difference, and which is preferred?
If you look at some other papers from the project "Global burden of diseases", you will see that data imputation for missing cases have been carried out using proxy. As in case of modelling the global |
49,870 | correlation of decision trees | This is an important measure for decision trees in a random forest and is a component of the generalization error of the random forest.
Please read Breiman's original paper(page 6) where he defines correlation as $\bar{\rho}=\mathbf{E}_{\Theta, \Theta^\prime}[\rho(h(\cdot,\Theta), h(\cdot,\Theta^\prime)]$. So that $\b... | correlation of decision trees | This is an important measure for decision trees in a random forest and is a component of the generalization error of the random forest.
Please read Breiman's original paper(page 6) where he defines c | correlation of decision trees
This is an important measure for decision trees in a random forest and is a component of the generalization error of the random forest.
Please read Breiman's original paper(page 6) where he defines correlation as $\bar{\rho}=\mathbf{E}_{\Theta, \Theta^\prime}[\rho(h(\cdot,\Theta), h(\cdot... | correlation of decision trees
This is an important measure for decision trees in a random forest and is a component of the generalization error of the random forest.
Please read Breiman's original paper(page 6) where he defines c |
49,871 | CDF of a transformation of variables with a flat region | You can visualize the CDF of $Y$, $F_Y$, in terms of (a) a graph of the transformation $\phi:X\to Y$ and (b) a graph of the CDF of $X$, $F_X$.
In this figure the top plot shows the graph of $\phi$ while the second plot shows the CDF.
To see the value of $F_Y$ at some trial value $y$, draw a horizontal line at height $... | CDF of a transformation of variables with a flat region | You can visualize the CDF of $Y$, $F_Y$, in terms of (a) a graph of the transformation $\phi:X\to Y$ and (b) a graph of the CDF of $X$, $F_X$.
In this figure the top plot shows the graph of $\phi$ whi | CDF of a transformation of variables with a flat region
You can visualize the CDF of $Y$, $F_Y$, in terms of (a) a graph of the transformation $\phi:X\to Y$ and (b) a graph of the CDF of $X$, $F_X$.
In this figure the top plot shows the graph of $\phi$ while the second plot shows the CDF.
To see the value of $F_Y$ at ... | CDF of a transformation of variables with a flat region
You can visualize the CDF of $Y$, $F_Y$, in terms of (a) a graph of the transformation $\phi:X\to Y$ and (b) a graph of the CDF of $X$, $F_X$.
In this figure the top plot shows the graph of $\phi$ whi |
49,872 | Cox Snell residuals in R | Based on the book's formulas, I wrote this code :
#rC : Cox-Snell residuals
#rM : Martingale residuals
#rD : Deviance residuals
rC<-exp(((fit$y[,1])-log(predict(fit,lung,na.action = "na.omit")))/fit$scale)
rM<-fit$y[,2]-rC
rD<-sign(rM)*sqrt(-2*(rM+fit$y[,2]*log(rC))) # -residuals(fit,type='deviance')
mean(rC)
var(r... | Cox Snell residuals in R | Based on the book's formulas, I wrote this code :
#rC : Cox-Snell residuals
#rM : Martingale residuals
#rD : Deviance residuals
rC<-exp(((fit$y[,1])-log(predict(fit,lung,na.action = "na.omit")))/fit | Cox Snell residuals in R
Based on the book's formulas, I wrote this code :
#rC : Cox-Snell residuals
#rM : Martingale residuals
#rD : Deviance residuals
rC<-exp(((fit$y[,1])-log(predict(fit,lung,na.action = "na.omit")))/fit$scale)
rM<-fit$y[,2]-rC
rD<-sign(rM)*sqrt(-2*(rM+fit$y[,2]*log(rC))) # -residuals(fit,type='d... | Cox Snell residuals in R
Based on the book's formulas, I wrote this code :
#rC : Cox-Snell residuals
#rM : Martingale residuals
#rD : Deviance residuals
rC<-exp(((fit$y[,1])-log(predict(fit,lung,na.action = "na.omit")))/fit |
49,873 | Cox Snell residuals in R | The Cox-Snell residual for case $j$ in a survival model is $r_j=\hat H(T_j|X_j)$, where $\hat H(T|X)$ is the estimated cumulative hazard function, $T_j$ is the event/censoring time for the case and $X_j$ its vector of covariate values. That's a convenient form for proportional hazard models, for which $\hat H(T_j|X_j)=... | Cox Snell residuals in R | The Cox-Snell residual for case $j$ in a survival model is $r_j=\hat H(T_j|X_j)$, where $\hat H(T|X)$ is the estimated cumulative hazard function, $T_j$ is the event/censoring time for the case and $X | Cox Snell residuals in R
The Cox-Snell residual for case $j$ in a survival model is $r_j=\hat H(T_j|X_j)$, where $\hat H(T|X)$ is the estimated cumulative hazard function, $T_j$ is the event/censoring time for the case and $X_j$ its vector of covariate values. That's a convenient form for proportional hazard models, fo... | Cox Snell residuals in R
The Cox-Snell residual for case $j$ in a survival model is $r_j=\hat H(T_j|X_j)$, where $\hat H(T|X)$ is the estimated cumulative hazard function, $T_j$ is the event/censoring time for the case and $X |
49,874 | Linear model of 2 samples t-test | This is just the standard idea of the data generating process that lies behind a run of the mill t-test.
$\alpha$ is just the difference between the two groups' means in raw units (i.e., not standardized). That is, $\alpha$ isn't "obtained" from somewhere else, it just is. It is a primitive with respect to this se... | Linear model of 2 samples t-test | This is just the standard idea of the data generating process that lies behind a run of the mill t-test.
$\alpha$ is just the difference between the two groups' means in raw units (i.e., not standa | Linear model of 2 samples t-test
This is just the standard idea of the data generating process that lies behind a run of the mill t-test.
$\alpha$ is just the difference between the two groups' means in raw units (i.e., not standardized). That is, $\alpha$ isn't "obtained" from somewhere else, it just is. It is a ... | Linear model of 2 samples t-test
This is just the standard idea of the data generating process that lies behind a run of the mill t-test.
$\alpha$ is just the difference between the two groups' means in raw units (i.e., not standa |
49,875 | Comparing two classifiers from a binary response | Why use accuracy?
Accuracy metric (what you call misclassification) is horrible, don't use it. However, there are reason why it is used.
Sometimes, that's what you care about. It doesn't matter if the spam filter, missclassify 5 spam emails by one percent or by 40 percent, you will still get 5 spam emails. In this ca... | Comparing two classifiers from a binary response | Why use accuracy?
Accuracy metric (what you call misclassification) is horrible, don't use it. However, there are reason why it is used.
Sometimes, that's what you care about. It doesn't matter if t | Comparing two classifiers from a binary response
Why use accuracy?
Accuracy metric (what you call misclassification) is horrible, don't use it. However, there are reason why it is used.
Sometimes, that's what you care about. It doesn't matter if the spam filter, missclassify 5 spam emails by one percent or by 40 perc... | Comparing two classifiers from a binary response
Why use accuracy?
Accuracy metric (what you call misclassification) is horrible, don't use it. However, there are reason why it is used.
Sometimes, that's what you care about. It doesn't matter if t |
49,876 | Comparing two classifiers from a binary response | I'd encourage you to think about loss. Each algorithm is outputting a distribution which represents its "bet" for a value of 0 or 1. What should its loss be for such a bet, given the actual value? What would your ideal algorithm minimize? Generally it would be expected loss, but it could be something else (e.g., loss a... | Comparing two classifiers from a binary response | I'd encourage you to think about loss. Each algorithm is outputting a distribution which represents its "bet" for a value of 0 or 1. What should its loss be for such a bet, given the actual value? Wha | Comparing two classifiers from a binary response
I'd encourage you to think about loss. Each algorithm is outputting a distribution which represents its "bet" for a value of 0 or 1. What should its loss be for such a bet, given the actual value? What would your ideal algorithm minimize? Generally it would be expected l... | Comparing two classifiers from a binary response
I'd encourage you to think about loss. Each algorithm is outputting a distribution which represents its "bet" for a value of 0 or 1. What should its loss be for such a bet, given the actual value? Wha |
49,877 | Combining two linear regression model into a single linear model using covariates | It sounds like you want a fully interacted model.
In which case, you interact all the terms with the dummy variable:
$Y_i = \beta_0 + \beta_1 X_{1,i} + \beta_2 X_{2,i} + \beta_3 X_{3,i} + \beta_4 (X_{1,i}*X_{3,i}) + \beta_5 (X_{2,i}*X_{3,i}) + \epsilon_i$
$\beta_1$ and $\beta_2$ are the effects of $X_1$ and $X_2$ whe... | Combining two linear regression model into a single linear model using covariates | It sounds like you want a fully interacted model.
In which case, you interact all the terms with the dummy variable:
$Y_i = \beta_0 + \beta_1 X_{1,i} + \beta_2 X_{2,i} + \beta_3 X_{3,i} + \beta_4 (X_{ | Combining two linear regression model into a single linear model using covariates
It sounds like you want a fully interacted model.
In which case, you interact all the terms with the dummy variable:
$Y_i = \beta_0 + \beta_1 X_{1,i} + \beta_2 X_{2,i} + \beta_3 X_{3,i} + \beta_4 (X_{1,i}*X_{3,i}) + \beta_5 (X_{2,i}*X_{3,... | Combining two linear regression model into a single linear model using covariates
It sounds like you want a fully interacted model.
In which case, you interact all the terms with the dummy variable:
$Y_i = \beta_0 + \beta_1 X_{1,i} + \beta_2 X_{2,i} + \beta_3 X_{3,i} + \beta_4 (X_{ |
49,878 | Robustness of the Student t-test to non-Gaussian data | Here is an attempt at answering the question using numerical experiments: using Monte Carlo estimation it is easy to determine the rate of type I errors for the test with a given distribution of input data. Here I try data from the following distributions:
Normally distributed data: here the t-test is guaranteed to w... | Robustness of the Student t-test to non-Gaussian data | Here is an attempt at answering the question using numerical experiments: using Monte Carlo estimation it is easy to determine the rate of type I errors for the test with a given distribution of input | Robustness of the Student t-test to non-Gaussian data
Here is an attempt at answering the question using numerical experiments: using Monte Carlo estimation it is easy to determine the rate of type I errors for the test with a given distribution of input data. Here I try data from the following distributions:
Normall... | Robustness of the Student t-test to non-Gaussian data
Here is an attempt at answering the question using numerical experiments: using Monte Carlo estimation it is easy to determine the rate of type I errors for the test with a given distribution of input |
49,879 | Meta-analysis of proportions | This is a meta-analysis of proportions. Just as you mentioned, the m-a of proportions is a little different than other types of meta-analysis- it includes studies that do not use controls. You can use R to do a meta-analysis of proportions. I recently made a tutorial on that on YouTube and shared my code on Github. Thi... | Meta-analysis of proportions | This is a meta-analysis of proportions. Just as you mentioned, the m-a of proportions is a little different than other types of meta-analysis- it includes studies that do not use controls. You can use | Meta-analysis of proportions
This is a meta-analysis of proportions. Just as you mentioned, the m-a of proportions is a little different than other types of meta-analysis- it includes studies that do not use controls. You can use R to do a meta-analysis of proportions. I recently made a tutorial on that on YouTube and ... | Meta-analysis of proportions
This is a meta-analysis of proportions. Just as you mentioned, the m-a of proportions is a little different than other types of meta-analysis- it includes studies that do not use controls. You can use |
49,880 | Meta-analysis of proportions | Yes it is perfectly possible to do this either in Stata or in R. Since I use R I offer a few hints to get you going.
A list of software for meta-analysis in R is available in the CRAN Task View (Disclaimer, I maintain it). There are several packages there which will do what you are proposing. I personally use metafor b... | Meta-analysis of proportions | Yes it is perfectly possible to do this either in Stata or in R. Since I use R I offer a few hints to get you going.
A list of software for meta-analysis in R is available in the CRAN Task View (Discl | Meta-analysis of proportions
Yes it is perfectly possible to do this either in Stata or in R. Since I use R I offer a few hints to get you going.
A list of software for meta-analysis in R is available in the CRAN Task View (Disclaimer, I maintain it). There are several packages there which will do what you are proposin... | Meta-analysis of proportions
Yes it is perfectly possible to do this either in Stata or in R. Since I use R I offer a few hints to get you going.
A list of software for meta-analysis in R is available in the CRAN Task View (Discl |
49,881 | What is the difference between "inverse reinforcement learning" and supervised learning? | Disclaimer: I am MSc student of Control theory (with engineering background) who is starting his thesis on Reinforcement Learning. I am just beginning to get a feel for the field. Kinda like I just am taking my first walk around the lake of machine learning. So my information may not be spot on. I am answering because ... | What is the difference between "inverse reinforcement learning" and supervised learning? | Disclaimer: I am MSc student of Control theory (with engineering background) who is starting his thesis on Reinforcement Learning. I am just beginning to get a feel for the field. Kinda like I just am | What is the difference between "inverse reinforcement learning" and supervised learning?
Disclaimer: I am MSc student of Control theory (with engineering background) who is starting his thesis on Reinforcement Learning. I am just beginning to get a feel for the field. Kinda like I just am taking my first walk around th... | What is the difference between "inverse reinforcement learning" and supervised learning?
Disclaimer: I am MSc student of Control theory (with engineering background) who is starting his thesis on Reinforcement Learning. I am just beginning to get a feel for the field. Kinda like I just am |
49,882 | What is the difference between "inverse reinforcement learning" and supervised learning? | Inverse reinforcement learning (IRL) can be seen an instance of supervised learning. The data is the demonstrations and the target is the reward function. So the 'learning' task is just to look for the mapping from the space of demonstrations to reward functions, under the constraints of the specification of the MDP.
... | What is the difference between "inverse reinforcement learning" and supervised learning? | Inverse reinforcement learning (IRL) can be seen an instance of supervised learning. The data is the demonstrations and the target is the reward function. So the 'learning' task is just to look for th | What is the difference between "inverse reinforcement learning" and supervised learning?
Inverse reinforcement learning (IRL) can be seen an instance of supervised learning. The data is the demonstrations and the target is the reward function. So the 'learning' task is just to look for the mapping from the space of dem... | What is the difference between "inverse reinforcement learning" and supervised learning?
Inverse reinforcement learning (IRL) can be seen an instance of supervised learning. The data is the demonstrations and the target is the reward function. So the 'learning' task is just to look for th |
49,883 | Why does the direction with highest eigenvalue have the largest semi-axis? | I think there are two ellipses that we could consider. First, consider the image of the unit circle with respect to the map $x \mapsto x^T A x$ for PD $A \in \mathbb R^{n \times n}$. It is a standard result that $f(x) = x^T A x$ is maximized over unit vectors $x$ by the unit eigenvector $v_1$ with largest eigenvalue $\... | Why does the direction with highest eigenvalue have the largest semi-axis? | I think there are two ellipses that we could consider. First, consider the image of the unit circle with respect to the map $x \mapsto x^T A x$ for PD $A \in \mathbb R^{n \times n}$. It is a standard | Why does the direction with highest eigenvalue have the largest semi-axis?
I think there are two ellipses that we could consider. First, consider the image of the unit circle with respect to the map $x \mapsto x^T A x$ for PD $A \in \mathbb R^{n \times n}$. It is a standard result that $f(x) = x^T A x$ is maximized ove... | Why does the direction with highest eigenvalue have the largest semi-axis?
I think there are two ellipses that we could consider. First, consider the image of the unit circle with respect to the map $x \mapsto x^T A x$ for PD $A \in \mathbb R^{n \times n}$. It is a standard |
49,884 | Forecasting models for time series with lots of zero values | The problem you are referring to is called sparse data analysis/intermittent demand analysis.The ACF/PACF is meaningless due to the false correlation induced by consecutive 0's. One earlier method to deal with this is called Croston's Method but lacks generality to deal with unusual values and level/trend changes in th... | Forecasting models for time series with lots of zero values | The problem you are referring to is called sparse data analysis/intermittent demand analysis.The ACF/PACF is meaningless due to the false correlation induced by consecutive 0's. One earlier method to | Forecasting models for time series with lots of zero values
The problem you are referring to is called sparse data analysis/intermittent demand analysis.The ACF/PACF is meaningless due to the false correlation induced by consecutive 0's. One earlier method to deal with this is called Croston's Method but lacks generali... | Forecasting models for time series with lots of zero values
The problem you are referring to is called sparse data analysis/intermittent demand analysis.The ACF/PACF is meaningless due to the false correlation induced by consecutive 0's. One earlier method to |
49,885 | Does it make sense to multiply two embedding vectors? | Yes it does. Here you can find example of network that uses multiplication, among other methods, for combining embeddings. As described in my answer
element-wise product $u*v$, is basically an interaction term, this can
catch similarities between values (big * big = bigger; small * small =
smaller), or the discrep... | Does it make sense to multiply two embedding vectors? | Yes it does. Here you can find example of network that uses multiplication, among other methods, for combining embeddings. As described in my answer
element-wise product $u*v$, is basically an intera | Does it make sense to multiply two embedding vectors?
Yes it does. Here you can find example of network that uses multiplication, among other methods, for combining embeddings. As described in my answer
element-wise product $u*v$, is basically an interaction term, this can
catch similarities between values (big * bi... | Does it make sense to multiply two embedding vectors?
Yes it does. Here you can find example of network that uses multiplication, among other methods, for combining embeddings. As described in my answer
element-wise product $u*v$, is basically an intera |
49,886 | Does it make sense to multiply two embedding vectors? | I started working with words vectors for several weeks.
I suspect that in order to obtain a valid answer to something like: "what is blood color?"
the network will handle better Vec(blood)*Vec(color) insted of Vec(blood)+Vec(color) before calculating the sinus with all database words.
Alas, I didn't test it yet.
Some s... | Does it make sense to multiply two embedding vectors? | I started working with words vectors for several weeks.
I suspect that in order to obtain a valid answer to something like: "what is blood color?"
the network will handle better Vec(blood)*Vec(color) | Does it make sense to multiply two embedding vectors?
I started working with words vectors for several weeks.
I suspect that in order to obtain a valid answer to something like: "what is blood color?"
the network will handle better Vec(blood)*Vec(color) insted of Vec(blood)+Vec(color) before calculating the sinus with ... | Does it make sense to multiply two embedding vectors?
I started working with words vectors for several weeks.
I suspect that in order to obtain a valid answer to something like: "what is blood color?"
the network will handle better Vec(blood)*Vec(color) |
49,887 | Does it make sense to multiply two embedding vectors? | Not only does it make sense, it is one of the key operations in one of the biggest breakthroughs in network design of recent years, the idea of "attention" as used by, e.g. Google Translate, ChatGPT and all other GPT-based applications, Stable Diffusion, and many other recent machine learning systems.
Attention is esse... | Does it make sense to multiply two embedding vectors? | Not only does it make sense, it is one of the key operations in one of the biggest breakthroughs in network design of recent years, the idea of "attention" as used by, e.g. Google Translate, ChatGPT a | Does it make sense to multiply two embedding vectors?
Not only does it make sense, it is one of the key operations in one of the biggest breakthroughs in network design of recent years, the idea of "attention" as used by, e.g. Google Translate, ChatGPT and all other GPT-based applications, Stable Diffusion, and many ot... | Does it make sense to multiply two embedding vectors?
Not only does it make sense, it is one of the key operations in one of the biggest breakthroughs in network design of recent years, the idea of "attention" as used by, e.g. Google Translate, ChatGPT a |
49,888 | How is the tail of a distribution defined (about heavy-tailed distributions)? | We distinguish what distributions are heavy tailed by first limiting our discussion to those tails that are long, that is, there is always an $\epsilon>0$, no matter how small, for which $f(x)>\epsilon>0$ for any $x<M$ no matter how large $M$ (for right tails), or $x>M$ for $M$ large magnitude negative (for left tails)... | How is the tail of a distribution defined (about heavy-tailed distributions)? | We distinguish what distributions are heavy tailed by first limiting our discussion to those tails that are long, that is, there is always an $\epsilon>0$, no matter how small, for which $f(x)>\epsilo | How is the tail of a distribution defined (about heavy-tailed distributions)?
We distinguish what distributions are heavy tailed by first limiting our discussion to those tails that are long, that is, there is always an $\epsilon>0$, no matter how small, for which $f(x)>\epsilon>0$ for any $x<M$ no matter how large $M$... | How is the tail of a distribution defined (about heavy-tailed distributions)?
We distinguish what distributions are heavy tailed by first limiting our discussion to those tails that are long, that is, there is always an $\epsilon>0$, no matter how small, for which $f(x)>\epsilo |
49,889 | With two restrictions on the parameters, how does an AR(p) process change as we increase p | Here is a partial answer for the case AR(1) vs. AR(2).
In the AR(1) case, the variance is (setting $\sigma^2=1$)
$$
\gamma_0=\frac{1}{1-\phi^2}
$$
In the AR(2) case, one may show that
$$
\gamma_0=\frac {(1-\phi_2)} {1-\phi_2-\phi_1^2 -\phi_1^2\phi_2 - \phi_2^2(1-\phi_2)}
$$
This expression maybe helps motivate why I ... | With two restrictions on the parameters, how does an AR(p) process change as we increase p | Here is a partial answer for the case AR(1) vs. AR(2).
In the AR(1) case, the variance is (setting $\sigma^2=1$)
$$
\gamma_0=\frac{1}{1-\phi^2}
$$
In the AR(2) case, one may show that
$$
\gamma_0=\fr | With two restrictions on the parameters, how does an AR(p) process change as we increase p
Here is a partial answer for the case AR(1) vs. AR(2).
In the AR(1) case, the variance is (setting $\sigma^2=1$)
$$
\gamma_0=\frac{1}{1-\phi^2}
$$
In the AR(2) case, one may show that
$$
\gamma_0=\frac {(1-\phi_2)} {1-\phi_2-\ph... | With two restrictions on the parameters, how does an AR(p) process change as we increase p
Here is a partial answer for the case AR(1) vs. AR(2).
In the AR(1) case, the variance is (setting $\sigma^2=1$)
$$
\gamma_0=\frac{1}{1-\phi^2}
$$
In the AR(2) case, one may show that
$$
\gamma_0=\fr |
49,890 | How to prove that Bernoulli random variable's sum is binomial distribution? | If you start from $$X_1,\ldots,X_n\stackrel{\text{i.i.d.}}{\sim}\mathcal{B}(p)$$ and define $$Y=X_1+\cdots+X_n$$ you can compute directly$$\mathbb{P}(Y=y)={n \choose y} p^y (1-p)^{n-y}\qquad y=0,1,\ldots,n$$ by a combinatoric argument. | How to prove that Bernoulli random variable's sum is binomial distribution? | If you start from $$X_1,\ldots,X_n\stackrel{\text{i.i.d.}}{\sim}\mathcal{B}(p)$$ and define $$Y=X_1+\cdots+X_n$$ you can compute directly$$\mathbb{P}(Y=y)={n \choose y} p^y (1-p)^{n-y}\qquad y=0,1,\ld | How to prove that Bernoulli random variable's sum is binomial distribution?
If you start from $$X_1,\ldots,X_n\stackrel{\text{i.i.d.}}{\sim}\mathcal{B}(p)$$ and define $$Y=X_1+\cdots+X_n$$ you can compute directly$$\mathbb{P}(Y=y)={n \choose y} p^y (1-p)^{n-y}\qquad y=0,1,\ldots,n$$ by a combinatoric argument. | How to prove that Bernoulli random variable's sum is binomial distribution?
If you start from $$X_1,\ldots,X_n\stackrel{\text{i.i.d.}}{\sim}\mathcal{B}(p)$$ and define $$Y=X_1+\cdots+X_n$$ you can compute directly$$\mathbb{P}(Y=y)={n \choose y} p^y (1-p)^{n-y}\qquad y=0,1,\ld |
49,891 | How to interpret GLM coefficients? | The original author of the analysis was kind enough to respond and clear this up for me. The calculation converts odds ratio (which are highly unintuitive) to relative risk (which is easier to understand). More details are provided here.
The GLM coefficients only show the multiplicative change in odds ratio. so if p1 i... | How to interpret GLM coefficients? | The original author of the analysis was kind enough to respond and clear this up for me. The calculation converts odds ratio (which are highly unintuitive) to relative risk (which is easier to underst | How to interpret GLM coefficients?
The original author of the analysis was kind enough to respond and clear this up for me. The calculation converts odds ratio (which are highly unintuitive) to relative risk (which is easier to understand). More details are provided here.
The GLM coefficients only show the multiplicati... | How to interpret GLM coefficients?
The original author of the analysis was kind enough to respond and clear this up for me. The calculation converts odds ratio (which are highly unintuitive) to relative risk (which is easier to underst |
49,892 | Are the No Free Lunch Theorem and Halting Problem connected? | No they are not related. In NFL, a function can be considered as a look-up-table (that is, a list of input-output pairs.) We are not concerned with how a function is implemented with NFL. With computability theory, we are concerned with how a function is actually computed.
try Woodward J. Computable and Incomputable S... | Are the No Free Lunch Theorem and Halting Problem connected? | No they are not related. In NFL, a function can be considered as a look-up-table (that is, a list of input-output pairs.) We are not concerned with how a function is implemented with NFL. With computa | Are the No Free Lunch Theorem and Halting Problem connected?
No they are not related. In NFL, a function can be considered as a look-up-table (that is, a list of input-output pairs.) We are not concerned with how a function is implemented with NFL. With computability theory, we are concerned with how a function is actu... | Are the No Free Lunch Theorem and Halting Problem connected?
No they are not related. In NFL, a function can be considered as a look-up-table (that is, a list of input-output pairs.) We are not concerned with how a function is implemented with NFL. With computa |
49,893 | What does "orthogonalize" mean? | I believe the quote refers to this algorithm, where the relevant line reads:
$x_j^m=x_j^{m-1}-\frac{\langle z_m,x_j^{m-1}\rangle}{\langle z_m,z_m\rangle}z_m$
Here the authors are using the angle-brackets to denote an inner product, which is essentially the standard vector dot product from Physics 101.
The second term i... | What does "orthogonalize" mean? | I believe the quote refers to this algorithm, where the relevant line reads:
$x_j^m=x_j^{m-1}-\frac{\langle z_m,x_j^{m-1}\rangle}{\langle z_m,z_m\rangle}z_m$
Here the authors are using the angle-brack | What does "orthogonalize" mean?
I believe the quote refers to this algorithm, where the relevant line reads:
$x_j^m=x_j^{m-1}-\frac{\langle z_m,x_j^{m-1}\rangle}{\langle z_m,z_m\rangle}z_m$
Here the authors are using the angle-brackets to denote an inner product, which is essentially the standard vector dot product fro... | What does "orthogonalize" mean?
I believe the quote refers to this algorithm, where the relevant line reads:
$x_j^m=x_j^{m-1}-\frac{\langle z_m,x_j^{m-1}\rangle}{\langle z_m,z_m\rangle}z_m$
Here the authors are using the angle-brack |
49,894 | Different definitions of cross entropy loss function not equivalent? | Your extension of the two-class definition requires a bit of care. If there are more than two classes, we have to stipulate that in this case, $\sum a_i=1$ and that $a_i\ge 0\forall i,$ i.e. the predicted class memberships are all positive and sum to 1. Then the one-hot encoding provides that precisely one of the $y_i=... | Different definitions of cross entropy loss function not equivalent? | Your extension of the two-class definition requires a bit of care. If there are more than two classes, we have to stipulate that in this case, $\sum a_i=1$ and that $a_i\ge 0\forall i,$ i.e. the predi | Different definitions of cross entropy loss function not equivalent?
Your extension of the two-class definition requires a bit of care. If there are more than two classes, we have to stipulate that in this case, $\sum a_i=1$ and that $a_i\ge 0\forall i,$ i.e. the predicted class memberships are all positive and sum to ... | Different definitions of cross entropy loss function not equivalent?
Your extension of the two-class definition requires a bit of care. If there are more than two classes, we have to stipulate that in this case, $\sum a_i=1$ and that $a_i\ge 0\forall i,$ i.e. the predi |
49,895 | How does one Initialize Neural Networks as suggested by Saxe et al using Orthogonal matrices and a gain factor? | Here is what Lasagne does, it should answer your two questions:
class Orthogonal(Initializer):
"""Intialize weights as Orthogonal matrix.
Orthogonal matrix initialization [1]_. For n-dimensional shapes where
n > 2, the n-1 trailing axes are flattened. For convolutional layers, this
corresponds to the fa... | How does one Initialize Neural Networks as suggested by Saxe et al using Orthogonal matrices and a g | Here is what Lasagne does, it should answer your two questions:
class Orthogonal(Initializer):
"""Intialize weights as Orthogonal matrix.
Orthogonal matrix initialization [1]_. For n-dimension | How does one Initialize Neural Networks as suggested by Saxe et al using Orthogonal matrices and a gain factor?
Here is what Lasagne does, it should answer your two questions:
class Orthogonal(Initializer):
"""Intialize weights as Orthogonal matrix.
Orthogonal matrix initialization [1]_. For n-dimensional shape... | How does one Initialize Neural Networks as suggested by Saxe et al using Orthogonal matrices and a g
Here is what Lasagne does, it should answer your two questions:
class Orthogonal(Initializer):
"""Intialize weights as Orthogonal matrix.
Orthogonal matrix initialization [1]_. For n-dimension |
49,896 | Sampling variance for meta-analysis one-sample data | This is an interesting question because (so far as I know) there is no widely used formula for computing the variance in this situation. Some time ago, I did some simulations to examine the performance of different formulas to estimate the sampling variance of Cohen's d in case of a one-sample t-test.
I was aware of th... | Sampling variance for meta-analysis one-sample data | This is an interesting question because (so far as I know) there is no widely used formula for computing the variance in this situation. Some time ago, I did some simulations to examine the performanc | Sampling variance for meta-analysis one-sample data
This is an interesting question because (so far as I know) there is no widely used formula for computing the variance in this situation. Some time ago, I did some simulations to examine the performance of different formulas to estimate the sampling variance of Cohen's... | Sampling variance for meta-analysis one-sample data
This is an interesting question because (so far as I know) there is no widely used formula for computing the variance in this situation. Some time ago, I did some simulations to examine the performanc |
49,897 | Choosing regressors for inclusion in regression with ARMA errors | The gold standard in time series model selection is to use a holdout sample. Hold out the last few months of data, fit the different models (with different combinations of regressors) to the data before that, forecast into your holdout sample and pick the model with the lowest forecast error - MAE or MSE.
That said, I ... | Choosing regressors for inclusion in regression with ARMA errors | The gold standard in time series model selection is to use a holdout sample. Hold out the last few months of data, fit the different models (with different combinations of regressors) to the data befo | Choosing regressors for inclusion in regression with ARMA errors
The gold standard in time series model selection is to use a holdout sample. Hold out the last few months of data, fit the different models (with different combinations of regressors) to the data before that, forecast into your holdout sample and pick the... | Choosing regressors for inclusion in regression with ARMA errors
The gold standard in time series model selection is to use a holdout sample. Hold out the last few months of data, fit the different models (with different combinations of regressors) to the data befo |
49,898 | Linear mixed effects model and - multiplicity issue and adjusting for p-values | Since the reviewer only seems to be concerned about the two outcomes measured on the same subjects (and did not question the modeling procedure itself), I would simply use a sequential Bonferroni adjustment (a.k.a. Holm-Bonferroni method) to correct for it.
Sort your $p$-values in ascending order
Refer to them as $p_... | Linear mixed effects model and - multiplicity issue and adjusting for p-values | Since the reviewer only seems to be concerned about the two outcomes measured on the same subjects (and did not question the modeling procedure itself), I would simply use a sequential Bonferroni adju | Linear mixed effects model and - multiplicity issue and adjusting for p-values
Since the reviewer only seems to be concerned about the two outcomes measured on the same subjects (and did not question the modeling procedure itself), I would simply use a sequential Bonferroni adjustment (a.k.a. Holm-Bonferroni method) to... | Linear mixed effects model and - multiplicity issue and adjusting for p-values
Since the reviewer only seems to be concerned about the two outcomes measured on the same subjects (and did not question the modeling procedure itself), I would simply use a sequential Bonferroni adju |
49,899 | How are performance measures affected in PU learning? | Introduction
Many practical applications have only positive and unlabeled data (aka PU learning), which poses problems in building and evaluating classifiers. Evaluating classifiers using only positive and unlabeled data is a tricky task, and can only be done by making some assumptions, which may or may not be reasonab... | How are performance measures affected in PU learning? | Introduction
Many practical applications have only positive and unlabeled data (aka PU learning), which poses problems in building and evaluating classifiers. Evaluating classifiers using only positiv | How are performance measures affected in PU learning?
Introduction
Many practical applications have only positive and unlabeled data (aka PU learning), which poses problems in building and evaluating classifiers. Evaluating classifiers using only positive and unlabeled data is a tricky task, and can only be done by mak... | How are performance measures affected in PU learning?
Introduction
Many practical applications have only positive and unlabeled data (aka PU learning), which poses problems in building and evaluating classifiers. Evaluating classifiers using only positiv |
49,900 | R: anova() vs. Anova() for test of categorical predictor from glmer or glm.nb object | anova{stats} is for Type I only, and has no way of doing Type III ANOVA. Anova{car} uses Type II or III tests.
You might find other helpful bits of information in these two threads:
Choice between Type-I, Type-II, or Type-III ANOVA
Difference between anova and Anova function | R: anova() vs. Anova() for test of categorical predictor from glmer or glm.nb object | anova{stats} is for Type I only, and has no way of doing Type III ANOVA. Anova{car} uses Type II or III tests.
You might find other helpful bits of information in these two threads:
Choice between Typ | R: anova() vs. Anova() for test of categorical predictor from glmer or glm.nb object
anova{stats} is for Type I only, and has no way of doing Type III ANOVA. Anova{car} uses Type II or III tests.
You might find other helpful bits of information in these two threads:
Choice between Type-I, Type-II, or Type-III ANOVA
Dif... | R: anova() vs. Anova() for test of categorical predictor from glmer or glm.nb object
anova{stats} is for Type I only, and has no way of doing Type III ANOVA. Anova{car} uses Type II or III tests.
You might find other helpful bits of information in these two threads:
Choice between Typ |
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