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 |
|---|---|---|---|---|---|---|
49,901 | Do examples in the training and test sets have to be independent? | Training on multiple records/observations from the same user/subject is ok, but you want your test data independent of your training data.
For example, you might imagine two approaches to constructing a test set (eg. for cross-validation):
Record wise: select records at random and assign to test set.
Subject wise: se... | Do examples in the training and test sets have to be independent? | Training on multiple records/observations from the same user/subject is ok, but you want your test data independent of your training data.
For example, you might imagine two approaches to constructin | Do examples in the training and test sets have to be independent?
Training on multiple records/observations from the same user/subject is ok, but you want your test data independent of your training data.
For example, you might imagine two approaches to constructing a test set (eg. for cross-validation):
Record wise:... | Do examples in the training and test sets have to be independent?
Training on multiple records/observations from the same user/subject is ok, but you want your test data independent of your training data.
For example, you might imagine two approaches to constructin |
49,902 | Are Maximum Likelihood Estimators asymptotically unbiased? | I have presented in this answer the issues surrounding the concept of "asymptotic unbiasedness". In short, the issue is whether it is defined as "convergence of the sequence of first moments to the true value", or as "asymptotic distribution having expected value equal to the true value" (of the parameter under estimat... | Are Maximum Likelihood Estimators asymptotically unbiased? | I have presented in this answer the issues surrounding the concept of "asymptotic unbiasedness". In short, the issue is whether it is defined as "convergence of the sequence of first moments to the tr | Are Maximum Likelihood Estimators asymptotically unbiased?
I have presented in this answer the issues surrounding the concept of "asymptotic unbiasedness". In short, the issue is whether it is defined as "convergence of the sequence of first moments to the true value", or as "asymptotic distribution having expected val... | Are Maximum Likelihood Estimators asymptotically unbiased?
I have presented in this answer the issues surrounding the concept of "asymptotic unbiasedness". In short, the issue is whether it is defined as "convergence of the sequence of first moments to the tr |
49,903 | Am I introducing bias by assuming birthdate is middle of month? | Is my derived age in days more accurate than calculating age in whole
months?
Obviously not. You cannot make measurement more precise then it was actually measured. Imagine that besides assuming middle of month, you assumed also that the patients were born at 12:30, 30 seconds, 30 milliseconds, etc. - would it make ... | Am I introducing bias by assuming birthdate is middle of month? | Is my derived age in days more accurate than calculating age in whole
months?
Obviously not. You cannot make measurement more precise then it was actually measured. Imagine that besides assuming mi | Am I introducing bias by assuming birthdate is middle of month?
Is my derived age in days more accurate than calculating age in whole
months?
Obviously not. You cannot make measurement more precise then it was actually measured. Imagine that besides assuming middle of month, you assumed also that the patients were b... | Am I introducing bias by assuming birthdate is middle of month?
Is my derived age in days more accurate than calculating age in whole
months?
Obviously not. You cannot make measurement more precise then it was actually measured. Imagine that besides assuming mi |
49,904 | Am I introducing bias by assuming birthdate is middle of month? | I'm just going to state the obvious and say that I agree with you and I can't evaluate your colleague's explanation without seeing it. For (1), I can't even tell what direction the bias should be expected to be in. Are people substantially more likely to be born near the beginning or end of a month? Not that I know of.... | Am I introducing bias by assuming birthdate is middle of month? | I'm just going to state the obvious and say that I agree with you and I can't evaluate your colleague's explanation without seeing it. For (1), I can't even tell what direction the bias should be expe | Am I introducing bias by assuming birthdate is middle of month?
I'm just going to state the obvious and say that I agree with you and I can't evaluate your colleague's explanation without seeing it. For (1), I can't even tell what direction the bias should be expected to be in. Are people substantially more likely to b... | Am I introducing bias by assuming birthdate is middle of month?
I'm just going to state the obvious and say that I agree with you and I can't evaluate your colleague's explanation without seeing it. For (1), I can't even tell what direction the bias should be expe |
49,905 | Identical variable importance values for different model types | Alright, looking into the code of varImp.train I see, that in case of a classification problem, the variable importance is just computed via the filterVarImp function. So the variables are just ranked by the AUC, as stated in the documentation varImp under model independent metrics.
I tested it, by calling varImp on ea... | Identical variable importance values for different model types | Alright, looking into the code of varImp.train I see, that in case of a classification problem, the variable importance is just computed via the filterVarImp function. So the variables are just ranked | Identical variable importance values for different model types
Alright, looking into the code of varImp.train I see, that in case of a classification problem, the variable importance is just computed via the filterVarImp function. So the variables are just ranked by the AUC, as stated in the documentation varImp under ... | Identical variable importance values for different model types
Alright, looking into the code of varImp.train I see, that in case of a classification problem, the variable importance is just computed via the filterVarImp function. So the variables are just ranked |
49,906 | Variance computed using Taylor series does not agree with numerical experiment | It does not matter that whether the mean squared error is decreasing with $n$. All that matters is that it can be made arbitrarily small. Here is a simple demonstration.
Fixing $\theta$, let $s=\sin(\theta)$ and $c=\cos(\theta)$. The estimator $\hat\theta$ is the slope of the ray through the origin and the point
$$(... | Variance computed using Taylor series does not agree with numerical experiment | It does not matter that whether the mean squared error is decreasing with $n$. All that matters is that it can be made arbitrarily small. Here is a simple demonstration.
Fixing $\theta$, let $s=\sin | Variance computed using Taylor series does not agree with numerical experiment
It does not matter that whether the mean squared error is decreasing with $n$. All that matters is that it can be made arbitrarily small. Here is a simple demonstration.
Fixing $\theta$, let $s=\sin(\theta)$ and $c=\cos(\theta)$. The esti... | Variance computed using Taylor series does not agree with numerical experiment
It does not matter that whether the mean squared error is decreasing with $n$. All that matters is that it can be made arbitrarily small. Here is a simple demonstration.
Fixing $\theta$, let $s=\sin |
49,907 | What is the best way to detect repetition in xyz data for purposes of splitting data? | It sounds like you have a set of known patterns and want to find places in your signal where these patterns occur. A typical way of doing this is using the cross correlation. In this approach, you'd compute the cross correlation of your pattern with the signal. You can think of this as repeatedly shifting the pattern b... | What is the best way to detect repetition in xyz data for purposes of splitting data? | It sounds like you have a set of known patterns and want to find places in your signal where these patterns occur. A typical way of doing this is using the cross correlation. In this approach, you'd c | What is the best way to detect repetition in xyz data for purposes of splitting data?
It sounds like you have a set of known patterns and want to find places in your signal where these patterns occur. A typical way of doing this is using the cross correlation. In this approach, you'd compute the cross correlation of yo... | What is the best way to detect repetition in xyz data for purposes of splitting data?
It sounds like you have a set of known patterns and want to find places in your signal where these patterns occur. A typical way of doing this is using the cross correlation. In this approach, you'd c |
49,908 | What is the best way to detect repetition in xyz data for purposes of splitting data? | If you know the patterns ahead of time, you can just make a hash table of the patterns and pattern detection is just a matter of hashing segments of the input signal and looking for collisions. Conventional hashing will only work for exact, noise-free input signals. Locality-sensitive hashing can be made insensitive to... | What is the best way to detect repetition in xyz data for purposes of splitting data? | If you know the patterns ahead of time, you can just make a hash table of the patterns and pattern detection is just a matter of hashing segments of the input signal and looking for collisions. Conven | What is the best way to detect repetition in xyz data for purposes of splitting data?
If you know the patterns ahead of time, you can just make a hash table of the patterns and pattern detection is just a matter of hashing segments of the input signal and looking for collisions. Conventional hashing will only work for ... | What is the best way to detect repetition in xyz data for purposes of splitting data?
If you know the patterns ahead of time, you can just make a hash table of the patterns and pattern detection is just a matter of hashing segments of the input signal and looking for collisions. Conven |
49,909 | What is the best way to detect repetition in xyz data for purposes of splitting data? | This is exactly the definition of time series motifs
Here is a tutorial on the topic
http://www.cs.unm.edu/~mueen/Tutorial/ICDMTutorial3.ppt
eamonn | What is the best way to detect repetition in xyz data for purposes of splitting data? | This is exactly the definition of time series motifs
Here is a tutorial on the topic
http://www.cs.unm.edu/~mueen/Tutorial/ICDMTutorial3.ppt
eamonn | What is the best way to detect repetition in xyz data for purposes of splitting data?
This is exactly the definition of time series motifs
Here is a tutorial on the topic
http://www.cs.unm.edu/~mueen/Tutorial/ICDMTutorial3.ppt
eamonn | What is the best way to detect repetition in xyz data for purposes of splitting data?
This is exactly the definition of time series motifs
Here is a tutorial on the topic
http://www.cs.unm.edu/~mueen/Tutorial/ICDMTutorial3.ppt
eamonn |
49,910 | What is the best way to detect repetition in xyz data for purposes of splitting data? | If the activity is sinusoidal within a specific frequency band you could use the frequency to classify patterns. To achieve this you perform a fast-fourier transform (FFT) on the data and search for global maxima in the resulting power spectrum. Using different band-pass filters you can target specific frequency bands.... | What is the best way to detect repetition in xyz data for purposes of splitting data? | If the activity is sinusoidal within a specific frequency band you could use the frequency to classify patterns. To achieve this you perform a fast-fourier transform (FFT) on the data and search for g | What is the best way to detect repetition in xyz data for purposes of splitting data?
If the activity is sinusoidal within a specific frequency band you could use the frequency to classify patterns. To achieve this you perform a fast-fourier transform (FFT) on the data and search for global maxima in the resulting powe... | What is the best way to detect repetition in xyz data for purposes of splitting data?
If the activity is sinusoidal within a specific frequency band you could use the frequency to classify patterns. To achieve this you perform a fast-fourier transform (FFT) on the data and search for g |
49,911 | What is the best way to detect repetition in xyz data for purposes of splitting data? | I agree with @user20160 that cross correlation (CC) will most likely be a valid and fast solution to your problem (in combination with scaling of your reference pattern + selecting the window position where correlation peaks occur).
What I want to point out is: if you run into problems because the pattern you search fo... | What is the best way to detect repetition in xyz data for purposes of splitting data? | I agree with @user20160 that cross correlation (CC) will most likely be a valid and fast solution to your problem (in combination with scaling of your reference pattern + selecting the window position | What is the best way to detect repetition in xyz data for purposes of splitting data?
I agree with @user20160 that cross correlation (CC) will most likely be a valid and fast solution to your problem (in combination with scaling of your reference pattern + selecting the window position where correlation peaks occur).
W... | What is the best way to detect repetition in xyz data for purposes of splitting data?
I agree with @user20160 that cross correlation (CC) will most likely be a valid and fast solution to your problem (in combination with scaling of your reference pattern + selecting the window position |
49,912 | Can a classifier trained with oversampled data be used to classify unbalanced data | This is actually an interesting question that comes across alot in medical data. One of the ways to understand oversampling and classification of unbalanced data is because oversampling is an active bias of sampling the data, the results will be biased. When compensating for the minority class, remember that the goal o... | Can a classifier trained with oversampled data be used to classify unbalanced data | This is actually an interesting question that comes across alot in medical data. One of the ways to understand oversampling and classification of unbalanced data is because oversampling is an active b | Can a classifier trained with oversampled data be used to classify unbalanced data
This is actually an interesting question that comes across alot in medical data. One of the ways to understand oversampling and classification of unbalanced data is because oversampling is an active bias of sampling the data, the results... | Can a classifier trained with oversampled data be used to classify unbalanced data
This is actually an interesting question that comes across alot in medical data. One of the ways to understand oversampling and classification of unbalanced data is because oversampling is an active b |
49,913 | Can a classifier trained with oversampled data be used to classify unbalanced data | If your classifier works well at production mode, it is legitimate to use it.
You can build it in whatever method you like.
Working on a balanced dataset is a good way to build a model that differ between the majority and minority classes. However, as @akash87 and you noted, it might cause a bias.
You might have been... | Can a classifier trained with oversampled data be used to classify unbalanced data | If your classifier works well at production mode, it is legitimate to use it.
You can build it in whatever method you like.
Working on a balanced dataset is a good way to build a model that differ be | Can a classifier trained with oversampled data be used to classify unbalanced data
If your classifier works well at production mode, it is legitimate to use it.
You can build it in whatever method you like.
Working on a balanced dataset is a good way to build a model that differ between the majority and minority class... | Can a classifier trained with oversampled data be used to classify unbalanced data
If your classifier works well at production mode, it is legitimate to use it.
You can build it in whatever method you like.
Working on a balanced dataset is a good way to build a model that differ be |
49,914 | Determining proper K value for Elo rating | I discussed briefly this solution with professional mathematician and he didn't discard the solution.
K depends on n the number of competitors:
$$
K = An^2 + Bn + C
$$
Then I worked on my data set through various values and assumed that best chosen K should have minimal differences between expected result and actual re... | Determining proper K value for Elo rating | I discussed briefly this solution with professional mathematician and he didn't discard the solution.
K depends on n the number of competitors:
$$
K = An^2 + Bn + C
$$
Then I worked on my data set thr | Determining proper K value for Elo rating
I discussed briefly this solution with professional mathematician and he didn't discard the solution.
K depends on n the number of competitors:
$$
K = An^2 + Bn + C
$$
Then I worked on my data set through various values and assumed that best chosen K should have minimal differe... | Determining proper K value for Elo rating
I discussed briefly this solution with professional mathematician and he didn't discard the solution.
K depends on n the number of competitors:
$$
K = An^2 + Bn + C
$$
Then I worked on my data set thr |
49,915 | Determining proper K value for Elo rating | Considering each game of multiple players be a group of 1vs1 matches between all pairs of players is not the best option, and it leads to the problems you said.
If you're interested in use (more than in development), you should give a try to rankade, our ranking system (here's a comparison between most known ranking sy... | Determining proper K value for Elo rating | Considering each game of multiple players be a group of 1vs1 matches between all pairs of players is not the best option, and it leads to the problems you said.
If you're interested in use (more than | Determining proper K value for Elo rating
Considering each game of multiple players be a group of 1vs1 matches between all pairs of players is not the best option, and it leads to the problems you said.
If you're interested in use (more than in development), you should give a try to rankade, our ranking system (here's ... | Determining proper K value for Elo rating
Considering each game of multiple players be a group of 1vs1 matches between all pairs of players is not the best option, and it leads to the problems you said.
If you're interested in use (more than |
49,916 | How can I experiment with Lagrange multiplier in PCA optimization? | I think I got the answer by myself but wish some experts can confirm.
The confusion is that, in CVX book we are converting one optimization problem with constraints to another optimization problem without constraints and solve the dual problem. But in PCA optimization we cannot.
For example, page 227, we convert
$$
\... | How can I experiment with Lagrange multiplier in PCA optimization? | I think I got the answer by myself but wish some experts can confirm.
The confusion is that, in CVX book we are converting one optimization problem with constraints to another optimization problem wit | How can I experiment with Lagrange multiplier in PCA optimization?
I think I got the answer by myself but wish some experts can confirm.
The confusion is that, in CVX book we are converting one optimization problem with constraints to another optimization problem without constraints and solve the dual problem. But in P... | How can I experiment with Lagrange multiplier in PCA optimization?
I think I got the answer by myself but wish some experts can confirm.
The confusion is that, in CVX book we are converting one optimization problem with constraints to another optimization problem wit |
49,917 | Why take the gradient of the moments (mean and variance) when using Batch Normalization in a Neural Network? | Derivatives of the moments are used for backpropagation.
Along the two derivatives of the moments on page 4, it gives the derivatives with respect to the input, which makes use of the derivative of the moments, $$\frac{\partial l}{\partial x}=\frac{\partial l}{\partial \hat{x}}\cdot\frac{1}{\sqrt{\sigma^2+\epsilon}}+\... | Why take the gradient of the moments (mean and variance) when using Batch Normalization in a Neural | Derivatives of the moments are used for backpropagation.
Along the two derivatives of the moments on page 4, it gives the derivatives with respect to the input, which makes use of the derivative of t | Why take the gradient of the moments (mean and variance) when using Batch Normalization in a Neural Network?
Derivatives of the moments are used for backpropagation.
Along the two derivatives of the moments on page 4, it gives the derivatives with respect to the input, which makes use of the derivative of the moments,... | Why take the gradient of the moments (mean and variance) when using Batch Normalization in a Neural
Derivatives of the moments are used for backpropagation.
Along the two derivatives of the moments on page 4, it gives the derivatives with respect to the input, which makes use of the derivative of t |
49,918 | Why take the gradient of the moments (mean and variance) when using Batch Normalization in a Neural Network? | There's no reason for the moments to be thought of as constants.
The quote
we make the second simplification: since we use mini-batches in stochastic gradient training, each mini-batch produces estimates of the mean and variance of each activation.
doesn't imply that they are constant, it just makes them scalars.
An... | Why take the gradient of the moments (mean and variance) when using Batch Normalization in a Neural | There's no reason for the moments to be thought of as constants.
The quote
we make the second simplification: since we use mini-batches in stochastic gradient training, each mini-batch produces esti | Why take the gradient of the moments (mean and variance) when using Batch Normalization in a Neural Network?
There's no reason for the moments to be thought of as constants.
The quote
we make the second simplification: since we use mini-batches in stochastic gradient training, each mini-batch produces estimates of th... | Why take the gradient of the moments (mean and variance) when using Batch Normalization in a Neural
There's no reason for the moments to be thought of as constants.
The quote
we make the second simplification: since we use mini-batches in stochastic gradient training, each mini-batch produces esti |
49,919 | Why take the gradient of the moments (mean and variance) when using Batch Normalization in a Neural Network? | There is a reason, why you should propagate gradient through mean and variance.
I will try to show you a simple example.
Let's just start with the mean. Imagine, that you have two samples (with one attribute) with values: $x_1$ and $x_2$.
Now mean is $m = \frac{x_1 + x_2}{2}$ and output after subtracting the mean would... | Why take the gradient of the moments (mean and variance) when using Batch Normalization in a Neural | There is a reason, why you should propagate gradient through mean and variance.
I will try to show you a simple example.
Let's just start with the mean. Imagine, that you have two samples (with one at | Why take the gradient of the moments (mean and variance) when using Batch Normalization in a Neural Network?
There is a reason, why you should propagate gradient through mean and variance.
I will try to show you a simple example.
Let's just start with the mean. Imagine, that you have two samples (with one attribute) wi... | Why take the gradient of the moments (mean and variance) when using Batch Normalization in a Neural
There is a reason, why you should propagate gradient through mean and variance.
I will try to show you a simple example.
Let's just start with the mean. Imagine, that you have two samples (with one at |
49,920 | Is data visualization a sufficient indication for the separability of the data? What are other indications of data separation? | There is an asymmetry worth noting here.
If a PCA plot shows distinct, separated clusters, then it is clear evidence for the separability of the data. But an absence of this kind of structure in the PCA plot (such as in your example) is not evidence for a lack of separability.
This is because (as pointed out in the c... | Is data visualization a sufficient indication for the separability of the data? What are other indic | There is an asymmetry worth noting here.
If a PCA plot shows distinct, separated clusters, then it is clear evidence for the separability of the data. But an absence of this kind of structure in the | Is data visualization a sufficient indication for the separability of the data? What are other indications of data separation?
There is an asymmetry worth noting here.
If a PCA plot shows distinct, separated clusters, then it is clear evidence for the separability of the data. But an absence of this kind of structure ... | Is data visualization a sufficient indication for the separability of the data? What are other indic
There is an asymmetry worth noting here.
If a PCA plot shows distinct, separated clusters, then it is clear evidence for the separability of the data. But an absence of this kind of structure in the |
49,921 | Interpretation of hidden states in HMM in the part-of-speech tagging task | Two cases:
supervised POS tagging: no need for EM, you can simply count to learn the emission and transition probabilities (2). Each hidden state is mapped to one single POS.
unsupervised POS tagging: the Baum-Welch (EM) is typically used learn the emission and transition probabilities. To map the hidden states to act... | Interpretation of hidden states in HMM in the part-of-speech tagging task | Two cases:
supervised POS tagging: no need for EM, you can simply count to learn the emission and transition probabilities (2). Each hidden state is mapped to one single POS.
unsupervised POS tagging | Interpretation of hidden states in HMM in the part-of-speech tagging task
Two cases:
supervised POS tagging: no need for EM, you can simply count to learn the emission and transition probabilities (2). Each hidden state is mapped to one single POS.
unsupervised POS tagging: the Baum-Welch (EM) is typically used learn ... | Interpretation of hidden states in HMM in the part-of-speech tagging task
Two cases:
supervised POS tagging: no need for EM, you can simply count to learn the emission and transition probabilities (2). Each hidden state is mapped to one single POS.
unsupervised POS tagging |
49,922 | Can logistic regression be used with "years" as a continuous variable? | Yes, you can use years as a continuous variable in your model. But, I would not be estimating a logit model for this problem. Some specific issues:
The way to show your data here is as a plot, where the x-axis shows the years, and the y-axis shows the proportion of jelly beans. Estimating a logit model to do this brin... | Can logistic regression be used with "years" as a continuous variable? | Yes, you can use years as a continuous variable in your model. But, I would not be estimating a logit model for this problem. Some specific issues:
The way to show your data here is as a plot, where | Can logistic regression be used with "years" as a continuous variable?
Yes, you can use years as a continuous variable in your model. But, I would not be estimating a logit model for this problem. Some specific issues:
The way to show your data here is as a plot, where the x-axis shows the years, and the y-axis shows ... | Can logistic regression be used with "years" as a continuous variable?
Yes, you can use years as a continuous variable in your model. But, I would not be estimating a logit model for this problem. Some specific issues:
The way to show your data here is as a plot, where |
49,923 | Covariance of order statistics | Let $(X_1,\dots,X_n,X_{n+1})$ denote a random sample of size $(n+1)$ drawn on $X$, and let $$Z_n = \min\{X_1,...,X_n\} \quad \text{and} \quad Z_{n+1} = \min\{X_1,...,X_n,X_{n+1}\}$$
By including the extra $X_{n+1}$ term, there are only 2 possibilities:
EITHER CASE A $\rightarrow$ with probability $\frac{n}{n+1}$
$... | Covariance of order statistics | Let $(X_1,\dots,X_n,X_{n+1})$ denote a random sample of size $(n+1)$ drawn on $X$, and let $$Z_n = \min\{X_1,...,X_n\} \quad \text{and} \quad Z_{n+1} = \min\{X_1,...,X_n,X_{n+1}\}$$
By including the | Covariance of order statistics
Let $(X_1,\dots,X_n,X_{n+1})$ denote a random sample of size $(n+1)$ drawn on $X$, and let $$Z_n = \min\{X_1,...,X_n\} \quad \text{and} \quad Z_{n+1} = \min\{X_1,...,X_n,X_{n+1}\}$$
By including the extra $X_{n+1}$ term, there are only 2 possibilities:
EITHER CASE A $\rightarrow$ with... | Covariance of order statistics
Let $(X_1,\dots,X_n,X_{n+1})$ denote a random sample of size $(n+1)$ drawn on $X$, and let $$Z_n = \min\{X_1,...,X_n\} \quad \text{and} \quad Z_{n+1} = \min\{X_1,...,X_n,X_{n+1}\}$$
By including the |
49,924 | Covariance of order statistics | This seems to imply that Var(zn)/Var(zn+1) if far from 1 as well. If zi is really the minimum of a sample of size i, then for standard computable examples, like the exponential distribution, the ratio of variances is close to 1 for n reasonably large, for example ((n+1)/n)^2 for the exponential. Perhaps you're simulati... | Covariance of order statistics | This seems to imply that Var(zn)/Var(zn+1) if far from 1 as well. If zi is really the minimum of a sample of size i, then for standard computable examples, like the exponential distribution, the ratio | Covariance of order statistics
This seems to imply that Var(zn)/Var(zn+1) if far from 1 as well. If zi is really the minimum of a sample of size i, then for standard computable examples, like the exponential distribution, the ratio of variances is close to 1 for n reasonably large, for example ((n+1)/n)^2 for the expon... | Covariance of order statistics
This seems to imply that Var(zn)/Var(zn+1) if far from 1 as well. If zi is really the minimum of a sample of size i, then for standard computable examples, like the exponential distribution, the ratio |
49,925 | Double lasso variable selection | A major advantage of the double selection method is that it is heteroskedasticity robust.
Belloni, Chernozhukov and Hansen (ReStud 2014) showed that this is true even if the selection is not perfect.
We propose robust methods for inference about the effect of a treatment variable on a scalar outcome in the presence of... | Double lasso variable selection | A major advantage of the double selection method is that it is heteroskedasticity robust.
Belloni, Chernozhukov and Hansen (ReStud 2014) showed that this is true even if the selection is not perfect.
| Double lasso variable selection
A major advantage of the double selection method is that it is heteroskedasticity robust.
Belloni, Chernozhukov and Hansen (ReStud 2014) showed that this is true even if the selection is not perfect.
We propose robust methods for inference about the effect of a treatment variable on a s... | Double lasso variable selection
A major advantage of the double selection method is that it is heteroskedasticity robust.
Belloni, Chernozhukov and Hansen (ReStud 2014) showed that this is true even if the selection is not perfect.
|
49,926 | ergodic theory for markov processes | Say your state space is $\Omega$ and your process is $X_{t}$. Consider now a new state space - $\Omega \times \Omega$. Then $Y_{y} := (X_{t-1}, X_{t})$ is a Markov process on $\Omega \times \Omega$. Now, you can use the ergodic theorem, provided you know the invariant distribution of $Y_t$. This is a distribution of p... | ergodic theory for markov processes | Say your state space is $\Omega$ and your process is $X_{t}$. Consider now a new state space - $\Omega \times \Omega$. Then $Y_{y} := (X_{t-1}, X_{t})$ is a Markov process on $\Omega \times \Omega$. | ergodic theory for markov processes
Say your state space is $\Omega$ and your process is $X_{t}$. Consider now a new state space - $\Omega \times \Omega$. Then $Y_{y} := (X_{t-1}, X_{t})$ is a Markov process on $\Omega \times \Omega$. Now, you can use the ergodic theorem, provided you know the invariant distribution o... | ergodic theory for markov processes
Say your state space is $\Omega$ and your process is $X_{t}$. Consider now a new state space - $\Omega \times \Omega$. Then $Y_{y} := (X_{t-1}, X_{t})$ is a Markov process on $\Omega \times \Omega$. |
49,927 | When is there a point for using regression with controls to analyze experimental data? | An alternative way to write the standard error (assuming homoscedasticity) of the regression coefficient estimate in your first model is
\begin{equation}
se(\hat \beta) = \sqrt{\frac{\sum_{i=1}^n e^2}{(n-k-1)\sum_{i=1}^n(T_{i}-\bar T)^2(1-R^2_T)}}
\end{equation}
where $e$ are the residuals from the regression and $R^2... | When is there a point for using regression with controls to analyze experimental data? | An alternative way to write the standard error (assuming homoscedasticity) of the regression coefficient estimate in your first model is
\begin{equation}
se(\hat \beta) = \sqrt{\frac{\sum_{i=1}^n e^2 | When is there a point for using regression with controls to analyze experimental data?
An alternative way to write the standard error (assuming homoscedasticity) of the regression coefficient estimate in your first model is
\begin{equation}
se(\hat \beta) = \sqrt{\frac{\sum_{i=1}^n e^2}{(n-k-1)\sum_{i=1}^n(T_{i}-\bar ... | When is there a point for using regression with controls to analyze experimental data?
An alternative way to write the standard error (assuming homoscedasticity) of the regression coefficient estimate in your first model is
\begin{equation}
se(\hat \beta) = \sqrt{\frac{\sum_{i=1}^n e^2 |
49,928 | How to combine likert items into a single variable | You should clarify what you mean by "combined all the likert scale questions". If you asked 5 likert scale questions that together are a conventional way to measure e.g. self-confidence, then those should be combined into one variable (provided some conditions described below are met). If you asked 5 likert scale quest... | How to combine likert items into a single variable | You should clarify what you mean by "combined all the likert scale questions". If you asked 5 likert scale questions that together are a conventional way to measure e.g. self-confidence, then those sh | How to combine likert items into a single variable
You should clarify what you mean by "combined all the likert scale questions". If you asked 5 likert scale questions that together are a conventional way to measure e.g. self-confidence, then those should be combined into one variable (provided some conditions describe... | How to combine likert items into a single variable
You should clarify what you mean by "combined all the likert scale questions". If you asked 5 likert scale questions that together are a conventional way to measure e.g. self-confidence, then those sh |
49,929 | Residual network dimension changing blocks identity function | Instead of max pooling you can use 2D average pooling with stride (2,2) and kernel size (2,2), optionally concatenating it with itself to get 512 features instead of 256.
The benefit of this is that average pooling is linear operation which does not prevent gradient propagation and does not lose any information.
The pr... | Residual network dimension changing blocks identity function | Instead of max pooling you can use 2D average pooling with stride (2,2) and kernel size (2,2), optionally concatenating it with itself to get 512 features instead of 256.
The benefit of this is that a | Residual network dimension changing blocks identity function
Instead of max pooling you can use 2D average pooling with stride (2,2) and kernel size (2,2), optionally concatenating it with itself to get 512 features instead of 256.
The benefit of this is that average pooling is linear operation which does not prevent g... | Residual network dimension changing blocks identity function
Instead of max pooling you can use 2D average pooling with stride (2,2) and kernel size (2,2), optionally concatenating it with itself to get 512 features instead of 256.
The benefit of this is that a |
49,930 | how can I calculate the mutual information between two normal densities using the parameters mu and sigma? | The parameters you have only tell you about the marginal distributions of $X_1$ and $X_2$ so no, you cannot compute a measure of dependence like mutual information. Consider for instance that given $\mu_1, \mu_2, \sigma^2_1$ and $\sigma^2_2$ the random variables $X_1$ and $X_2$ could either be perfectly correlated or ... | how can I calculate the mutual information between two normal densities using the parameters mu and | The parameters you have only tell you about the marginal distributions of $X_1$ and $X_2$ so no, you cannot compute a measure of dependence like mutual information. Consider for instance that given $ | how can I calculate the mutual information between two normal densities using the parameters mu and sigma?
The parameters you have only tell you about the marginal distributions of $X_1$ and $X_2$ so no, you cannot compute a measure of dependence like mutual information. Consider for instance that given $\mu_1, \mu_2,... | how can I calculate the mutual information between two normal densities using the parameters mu and
The parameters you have only tell you about the marginal distributions of $X_1$ and $X_2$ so no, you cannot compute a measure of dependence like mutual information. Consider for instance that given $ |
49,931 | time varying coefficients in cox proportional hazard model | Since the seasonal dummy variables are static by nature, and their coefficients clearly vary with the time variable, how much does it matter?
The value that you get is a form of average over time. Unfortunately as you naturally have more cases in time-to-event analyses early on, you can't simply say that the effect is... | time varying coefficients in cox proportional hazard model | Since the seasonal dummy variables are static by nature, and their coefficients clearly vary with the time variable, how much does it matter?
The value that you get is a form of average over time. Un | time varying coefficients in cox proportional hazard model
Since the seasonal dummy variables are static by nature, and their coefficients clearly vary with the time variable, how much does it matter?
The value that you get is a form of average over time. Unfortunately as you naturally have more cases in time-to-event... | time varying coefficients in cox proportional hazard model
Since the seasonal dummy variables are static by nature, and their coefficients clearly vary with the time variable, how much does it matter?
The value that you get is a form of average over time. Un |
49,932 | Bootstrapping in Binary Response Data with Few Clusters and Within-Cluster Correlation | There is an extension of the wild bootstrap called the "score bootstrap" developed by Kline and Santos (2012) (working paper here). Whereas the wild works for OLS, the score method works additionally for ML models such as logit/probit and 2SLS and GMM models. The user-written Stata command boottest can calculate p-valu... | Bootstrapping in Binary Response Data with Few Clusters and Within-Cluster Correlation | There is an extension of the wild bootstrap called the "score bootstrap" developed by Kline and Santos (2012) (working paper here). Whereas the wild works for OLS, the score method works additionally | Bootstrapping in Binary Response Data with Few Clusters and Within-Cluster Correlation
There is an extension of the wild bootstrap called the "score bootstrap" developed by Kline and Santos (2012) (working paper here). Whereas the wild works for OLS, the score method works additionally for ML models such as logit/probi... | Bootstrapping in Binary Response Data with Few Clusters and Within-Cluster Correlation
There is an extension of the wild bootstrap called the "score bootstrap" developed by Kline and Santos (2012) (working paper here). Whereas the wild works for OLS, the score method works additionally |
49,933 | Is it possible to use LASSO regression with multi-levlel data? | Evan! Hi! It's Sam B, former resident of one-office-over. Funny meeting you here. Did you ever find a solution to your problem? In googling, I discovered both your question and this R package, which seems to have been released since your post. | Is it possible to use LASSO regression with multi-levlel data? | Evan! Hi! It's Sam B, former resident of one-office-over. Funny meeting you here. Did you ever find a solution to your problem? In googling, I discovered both your question and this R package, which s | Is it possible to use LASSO regression with multi-levlel data?
Evan! Hi! It's Sam B, former resident of one-office-over. Funny meeting you here. Did you ever find a solution to your problem? In googling, I discovered both your question and this R package, which seems to have been released since your post. | Is it possible to use LASSO regression with multi-levlel data?
Evan! Hi! It's Sam B, former resident of one-office-over. Funny meeting you here. Did you ever find a solution to your problem? In googling, I discovered both your question and this R package, which s |
49,934 | Calculating Jeffreys prior - where's the mistake? | It is likely that derivating/integrating wrt to discrete variables may be problematic. Nevertheless, considering the continuous analogous to the discrete model for derivated the associated Jeffreys is a situation discussed by Berger in https://www2.stat.duke.edu/~berger/papers/discrete.pdf (among others). Moreover, in ... | Calculating Jeffreys prior - where's the mistake? | It is likely that derivating/integrating wrt to discrete variables may be problematic. Nevertheless, considering the continuous analogous to the discrete model for derivated the associated Jeffreys is | Calculating Jeffreys prior - where's the mistake?
It is likely that derivating/integrating wrt to discrete variables may be problematic. Nevertheless, considering the continuous analogous to the discrete model for derivated the associated Jeffreys is a situation discussed by Berger in https://www2.stat.duke.edu/~berger... | Calculating Jeffreys prior - where's the mistake?
It is likely that derivating/integrating wrt to discrete variables may be problematic. Nevertheless, considering the continuous analogous to the discrete model for derivated the associated Jeffreys is |
49,935 | Is the sample mean a better point estimate of the population median than the sample median? | It would depend on details of the distribution family. For normal distributions, what you said would be true. For some more heavy-tailed distribution, it might not. You could for instance check with some t-distribution with low degrees of freedom. | Is the sample mean a better point estimate of the population median than the sample median? | It would depend on details of the distribution family. For normal distributions, what you said would be true. For some more heavy-tailed distribution, it might not. You could for instance check with s | Is the sample mean a better point estimate of the population median than the sample median?
It would depend on details of the distribution family. For normal distributions, what you said would be true. For some more heavy-tailed distribution, it might not. You could for instance check with some t-distribution with low ... | Is the sample mean a better point estimate of the population median than the sample median?
It would depend on details of the distribution family. For normal distributions, what you said would be true. For some more heavy-tailed distribution, it might not. You could for instance check with s |
49,936 | Comparing relative risks of independent samples | In this case, you should directly quantify the size of the interaction (between the treatment group variable and the age group variable) within studies. You can do this by taking the difference between the two log RRs within studies. The variance of the difference is just the sum of the two squared standard errors, sin... | Comparing relative risks of independent samples | In this case, you should directly quantify the size of the interaction (between the treatment group variable and the age group variable) within studies. You can do this by taking the difference betwee | Comparing relative risks of independent samples
In this case, you should directly quantify the size of the interaction (between the treatment group variable and the age group variable) within studies. You can do this by taking the difference between the two log RRs within studies. The variance of the difference is just... | Comparing relative risks of independent samples
In this case, you should directly quantify the size of the interaction (between the treatment group variable and the age group variable) within studies. You can do this by taking the difference betwee |
49,937 | Comparing relative risks of independent samples | You could consider this as an example of meta-regression. You would set up your data frame to have columns for RR, CILB, CIUB, study, agegrp. Then you would enter both study and agregrp as moderators in the model. The effect for study is unimportant it is just there to take out study differences in overall treatment ef... | Comparing relative risks of independent samples | You could consider this as an example of meta-regression. You would set up your data frame to have columns for RR, CILB, CIUB, study, agegrp. Then you would enter both study and agregrp as moderators | Comparing relative risks of independent samples
You could consider this as an example of meta-regression. You would set up your data frame to have columns for RR, CILB, CIUB, study, agegrp. Then you would enter both study and agregrp as moderators in the model. The effect for study is unimportant it is just there to ta... | Comparing relative risks of independent samples
You could consider this as an example of meta-regression. You would set up your data frame to have columns for RR, CILB, CIUB, study, agegrp. Then you would enter both study and agregrp as moderators |
49,938 | Dealing with 0 in cell count for Fisher's exact test | Fisher's exact test does deal with zero cells without any problem.
Adding 0.5 to all cells is a commonly done to remove improve the small sample properties from the Chi-square test (and it asymptotically removes the first-order bias from the estimate of the log-odds ratio). This is (for a simple 2x2 table) equivalent t... | Dealing with 0 in cell count for Fisher's exact test | Fisher's exact test does deal with zero cells without any problem.
Adding 0.5 to all cells is a commonly done to remove improve the small sample properties from the Chi-square test (and it asymptotica | Dealing with 0 in cell count for Fisher's exact test
Fisher's exact test does deal with zero cells without any problem.
Adding 0.5 to all cells is a commonly done to remove improve the small sample properties from the Chi-square test (and it asymptotically removes the first-order bias from the estimate of the log-odds ... | Dealing with 0 in cell count for Fisher's exact test
Fisher's exact test does deal with zero cells without any problem.
Adding 0.5 to all cells is a commonly done to remove improve the small sample properties from the Chi-square test (and it asymptotica |
49,939 | Introductory Statistics and Basic Experimental Designs for Computer Scientists | There are two ways I can see making these things interesting to graduate students in computer science. You can share statistical problems with them and ask them to think critically about the computational problems. Or you can share computational problems with them, and ask them to think critically about how statistics ... | Introductory Statistics and Basic Experimental Designs for Computer Scientists | There are two ways I can see making these things interesting to graduate students in computer science. You can share statistical problems with them and ask them to think critically about the computati | Introductory Statistics and Basic Experimental Designs for Computer Scientists
There are two ways I can see making these things interesting to graduate students in computer science. You can share statistical problems with them and ask them to think critically about the computational problems. Or you can share computati... | Introductory Statistics and Basic Experimental Designs for Computer Scientists
There are two ways I can see making these things interesting to graduate students in computer science. You can share statistical problems with them and ask them to think critically about the computati |
49,940 | Introductory Statistics and Basic Experimental Designs for Computer Scientists | There are already quite some questions like this on this site, with good answers. Some are What should a graduate course in experimental design cover?
Recommended Text for Essential Experimental Statistics or search this site!
But you say "for computer scientists". What will you do use experimental design for? One ... | Introductory Statistics and Basic Experimental Designs for Computer Scientists | There are already quite some questions like this on this site, with good answers. Some are What should a graduate course in experimental design cover?
Recommended Text for Essential Experimental Stat | Introductory Statistics and Basic Experimental Designs for Computer Scientists
There are already quite some questions like this on this site, with good answers. Some are What should a graduate course in experimental design cover?
Recommended Text for Essential Experimental Statistics or search this site!
But you sa... | Introductory Statistics and Basic Experimental Designs for Computer Scientists
There are already quite some questions like this on this site, with good answers. Some are What should a graduate course in experimental design cover?
Recommended Text for Essential Experimental Stat |
49,941 | Including both individual and state fixed effects | If you have individual fixed effects, your estimate of the state dummy will be based upon within individual variation (i.e. it will be based upon the people that move across state lines). If no one switches state, then the state dummy will not be identified. | Including both individual and state fixed effects | If you have individual fixed effects, your estimate of the state dummy will be based upon within individual variation (i.e. it will be based upon the people that move across state lines). If no one sw | Including both individual and state fixed effects
If you have individual fixed effects, your estimate of the state dummy will be based upon within individual variation (i.e. it will be based upon the people that move across state lines). If no one switches state, then the state dummy will not be identified. | Including both individual and state fixed effects
If you have individual fixed effects, your estimate of the state dummy will be based upon within individual variation (i.e. it will be based upon the people that move across state lines). If no one sw |
49,942 | Is there a word for believing events are independent when they are not? | "Pseudo-replication" is one such name for the result of the error, if not the act of believing the premise. In a repeated measurements design, for instance, ignoring the correlation structure arising from the groups would make it look like you had more information than you actually did. (I remember an example where bio... | Is there a word for believing events are independent when they are not? | "Pseudo-replication" is one such name for the result of the error, if not the act of believing the premise. In a repeated measurements design, for instance, ignoring the correlation structure arising | Is there a word for believing events are independent when they are not?
"Pseudo-replication" is one such name for the result of the error, if not the act of believing the premise. In a repeated measurements design, for instance, ignoring the correlation structure arising from the groups would make it look like you had ... | Is there a word for believing events are independent when they are not?
"Pseudo-replication" is one such name for the result of the error, if not the act of believing the premise. In a repeated measurements design, for instance, ignoring the correlation structure arising |
49,943 | Ways to make a straight in poker | I am not a keen poker player but I believe this refers to the possibility of selecting a card from each of the four suits. For each of the five cards in the straight, this can be done in $\binom{4}{1} = 4$ ways . For instance, for a straight of 1,2,3,4,5 there are four fives among which you can choose. And likewise for... | Ways to make a straight in poker | I am not a keen poker player but I believe this refers to the possibility of selecting a card from each of the four suits. For each of the five cards in the straight, this can be done in $\binom{4}{1} | Ways to make a straight in poker
I am not a keen poker player but I believe this refers to the possibility of selecting a card from each of the four suits. For each of the five cards in the straight, this can be done in $\binom{4}{1} = 4$ ways . For instance, for a straight of 1,2,3,4,5 there are four fives among which... | Ways to make a straight in poker
I am not a keen poker player but I believe this refers to the possibility of selecting a card from each of the four suits. For each of the five cards in the straight, this can be done in $\binom{4}{1} |
49,944 | How to justify a "complicated" regression model over a simpler model to a non-technical audience? | I need a good, intuitive explanation for why not explicitly accounting for these potential sources of variation will lead to a worse model
In my experience it is fairly easy to justify the use of mixed models to a non-techincal audience, at a level that they will be able to understand. I generally try to do this with ... | How to justify a "complicated" regression model over a simpler model to a non-technical audience? | I need a good, intuitive explanation for why not explicitly accounting for these potential sources of variation will lead to a worse model
In my experience it is fairly easy to justify the use of mix | How to justify a "complicated" regression model over a simpler model to a non-technical audience?
I need a good, intuitive explanation for why not explicitly accounting for these potential sources of variation will lead to a worse model
In my experience it is fairly easy to justify the use of mixed models to a non-tec... | How to justify a "complicated" regression model over a simpler model to a non-technical audience?
I need a good, intuitive explanation for why not explicitly accounting for these potential sources of variation will lead to a worse model
In my experience it is fairly easy to justify the use of mix |
49,945 | Producing samples from exponential family conditional on minimal sufficient statistic | Given that the vector $\mathbf{T}(X)=(T_1(X),\ldots,T_K(X))$ is sufficient, this means that the distribution of $X$ conditional on $\mathbf{T}(X)$ does not depend on the parameters $\eta_k$.
If $$p(x)\propto h(x)\exp\left\{-\sum_k \eta_k T_k(x)\right\}$$ the distribution of $X$ given $\mathbf{T}(X)=t$ will have a densi... | Producing samples from exponential family conditional on minimal sufficient statistic | Given that the vector $\mathbf{T}(X)=(T_1(X),\ldots,T_K(X))$ is sufficient, this means that the distribution of $X$ conditional on $\mathbf{T}(X)$ does not depend on the parameters $\eta_k$.
If $$p(x) | Producing samples from exponential family conditional on minimal sufficient statistic
Given that the vector $\mathbf{T}(X)=(T_1(X),\ldots,T_K(X))$ is sufficient, this means that the distribution of $X$ conditional on $\mathbf{T}(X)$ does not depend on the parameters $\eta_k$.
If $$p(x)\propto h(x)\exp\left\{-\sum_k \et... | Producing samples from exponential family conditional on minimal sufficient statistic
Given that the vector $\mathbf{T}(X)=(T_1(X),\ldots,T_K(X))$ is sufficient, this means that the distribution of $X$ conditional on $\mathbf{T}(X)$ does not depend on the parameters $\eta_k$.
If $$p(x) |
49,946 | R - Approach to find outliers/artefacts in blood pressure curve | I'd suggest looking at the changepoint package, in particular cpt.var. At least based on your three examples, it looks like your artifacts involve breaks in variance (first two examples lower, last example higher).
On a more empirical note, you could also try the runmad (windowed MAD) from the caTools package. | R - Approach to find outliers/artefacts in blood pressure curve | I'd suggest looking at the changepoint package, in particular cpt.var. At least based on your three examples, it looks like your artifacts involve breaks in variance (first two examples lower, last ex | R - Approach to find outliers/artefacts in blood pressure curve
I'd suggest looking at the changepoint package, in particular cpt.var. At least based on your three examples, it looks like your artifacts involve breaks in variance (first two examples lower, last example higher).
On a more empirical note, you could also ... | R - Approach to find outliers/artefacts in blood pressure curve
I'd suggest looking at the changepoint package, in particular cpt.var. At least based on your three examples, it looks like your artifacts involve breaks in variance (first two examples lower, last ex |
49,947 | R - Approach to find outliers/artefacts in blood pressure curve | Blood pressure traces have the advantage of containing a well defined nearly periodic structure. As I recall from my long-ago training in physiology there is a substantial history of frequency analysis of blood pressure traces.
So you might consider an application of time series frequency analysis. The artifacts seem t... | R - Approach to find outliers/artefacts in blood pressure curve | Blood pressure traces have the advantage of containing a well defined nearly periodic structure. As I recall from my long-ago training in physiology there is a substantial history of frequency analysi | R - Approach to find outliers/artefacts in blood pressure curve
Blood pressure traces have the advantage of containing a well defined nearly periodic structure. As I recall from my long-ago training in physiology there is a substantial history of frequency analysis of blood pressure traces.
So you might consider an app... | R - Approach to find outliers/artefacts in blood pressure curve
Blood pressure traces have the advantage of containing a well defined nearly periodic structure. As I recall from my long-ago training in physiology there is a substantial history of frequency analysi |
49,948 | Unable to reproduce paper results (sample size) | Maybe the author's
implementation - despite the description - starts with a large n and
works back and stops at the first time we are above alpha, thus
returning the last n where the sum was below alpha? At least an
implementation of such an algo would be consistent with the results of the paper
(test code below).
The... | Unable to reproduce paper results (sample size) | Maybe the author's
implementation - despite the description - starts with a large n and
works back and stops at the first time we are above alpha, thus
returning the last n where the sum was below al | Unable to reproduce paper results (sample size)
Maybe the author's
implementation - despite the description - starts with a large n and
works back and stops at the first time we are above alpha, thus
returning the last n where the sum was below alpha? At least an
implementation of such an algo would be consistent with... | Unable to reproduce paper results (sample size)
Maybe the author's
implementation - despite the description - starts with a large n and
works back and stops at the first time we are above alpha, thus
returning the last n where the sum was below al |
49,949 | Is this a mistake in my exercise? A density for a transformed variable | It's a mistake in the exercise: you made all the progress one can.
After all, suppose there exists a continuous version of the marginal density $\tilde f$ with $\tilde{f}(0)\ne 0$ and $g(x,y)=\tilde{f}(x)\tilde{f}(y)$. (The standard bivariate Normal distribution has this property.)
Modify $\tilde f$ to a new density ... | Is this a mistake in my exercise? A density for a transformed variable | It's a mistake in the exercise: you made all the progress one can.
After all, suppose there exists a continuous version of the marginal density $\tilde f$ with $\tilde{f}(0)\ne 0$ and $g(x,y)=\tilde{ | Is this a mistake in my exercise? A density for a transformed variable
It's a mistake in the exercise: you made all the progress one can.
After all, suppose there exists a continuous version of the marginal density $\tilde f$ with $\tilde{f}(0)\ne 0$ and $g(x,y)=\tilde{f}(x)\tilde{f}(y)$. (The standard bivariate Norm... | Is this a mistake in my exercise? A density for a transformed variable
It's a mistake in the exercise: you made all the progress one can.
After all, suppose there exists a continuous version of the marginal density $\tilde f$ with $\tilde{f}(0)\ne 0$ and $g(x,y)=\tilde{ |
49,950 | Random Forests for predictor importance (Matlab) | What you describe would be one approach. For classification, TreeBagger by default randomly selects sqrt(p) predictors for each decision split (setting recommended by Breiman). Depending on your data and tree depth, some of your 50 predictors could be considered fewer times than others for splits just because they get ... | Random Forests for predictor importance (Matlab) | What you describe would be one approach. For classification, TreeBagger by default randomly selects sqrt(p) predictors for each decision split (setting recommended by Breiman). Depending on your data | Random Forests for predictor importance (Matlab)
What you describe would be one approach. For classification, TreeBagger by default randomly selects sqrt(p) predictors for each decision split (setting recommended by Breiman). Depending on your data and tree depth, some of your 50 predictors could be considered fewer ti... | Random Forests for predictor importance (Matlab)
What you describe would be one approach. For classification, TreeBagger by default randomly selects sqrt(p) predictors for each decision split (setting recommended by Breiman). Depending on your data |
49,951 | Random Forests for predictor importance (Matlab) | Yes, sampling all predictors would typically hurt the model accuracy. It is predictor importance values we are after, not accuracy. Either way, this is a heuristic procedure. Using random forest to estimate predictor importance for SVM can only give you a notion of what predictors could be important. One can construct ... | Random Forests for predictor importance (Matlab) | Yes, sampling all predictors would typically hurt the model accuracy. It is predictor importance values we are after, not accuracy. Either way, this is a heuristic procedure. Using random forest to es | Random Forests for predictor importance (Matlab)
Yes, sampling all predictors would typically hurt the model accuracy. It is predictor importance values we are after, not accuracy. Either way, this is a heuristic procedure. Using random forest to estimate predictor importance for SVM can only give you a notion of what ... | Random Forests for predictor importance (Matlab)
Yes, sampling all predictors would typically hurt the model accuracy. It is predictor importance values we are after, not accuracy. Either way, this is a heuristic procedure. Using random forest to es |
49,952 | How exactly does one marginalize over parameters in an N-dimensional likelihood? | Say you have the state of Information $I$, some observations $\{y_i\}$ and some parameters $\theta_p$ where $p \in \{1,2, \ldots n\}$ then in the continuous case you get the marginal likelihoods from the joint likelihood $p(\theta_1,\theta_2, \ldots \theta_n |\{y_i\},I)$ by integration:
\begin{align*}
p(\theta_k|\{y_i\... | How exactly does one marginalize over parameters in an N-dimensional likelihood? | Say you have the state of Information $I$, some observations $\{y_i\}$ and some parameters $\theta_p$ where $p \in \{1,2, \ldots n\}$ then in the continuous case you get the marginal likelihoods from | How exactly does one marginalize over parameters in an N-dimensional likelihood?
Say you have the state of Information $I$, some observations $\{y_i\}$ and some parameters $\theta_p$ where $p \in \{1,2, \ldots n\}$ then in the continuous case you get the marginal likelihoods from the joint likelihood $p(\theta_1,\theta... | How exactly does one marginalize over parameters in an N-dimensional likelihood?
Say you have the state of Information $I$, some observations $\{y_i\}$ and some parameters $\theta_p$ where $p \in \{1,2, \ldots n\}$ then in the continuous case you get the marginal likelihoods from |
49,953 | How exactly does one marginalize over parameters in an N-dimensional likelihood? | You should always reference your quotes.
The only reference on the Internet I found with this quote
"For each model, we determine the best fit parameters from the peak of
the N-dimensional likelihood surface. For each parameter in the model
we also compute its one dimensional likelihood function by
marginalizin... | How exactly does one marginalize over parameters in an N-dimensional likelihood? | You should always reference your quotes.
The only reference on the Internet I found with this quote
"For each model, we determine the best fit parameters from the peak of
the N-dimensional likelih | How exactly does one marginalize over parameters in an N-dimensional likelihood?
You should always reference your quotes.
The only reference on the Internet I found with this quote
"For each model, we determine the best fit parameters from the peak of
the N-dimensional likelihood surface. For each parameter in the ... | How exactly does one marginalize over parameters in an N-dimensional likelihood?
You should always reference your quotes.
The only reference on the Internet I found with this quote
"For each model, we determine the best fit parameters from the peak of
the N-dimensional likelih |
49,954 | overtrain the CNN? | CNN, like any other neural network, overfits to the training data if it is trained for too long on the same training dataset. The purpose of the validation set is to stop training when performance on validation set starts decreasing, indicating that the model is overfitting the training data. Check this for more info. | overtrain the CNN? | CNN, like any other neural network, overfits to the training data if it is trained for too long on the same training dataset. The purpose of the validation set is to stop training when performance on | overtrain the CNN?
CNN, like any other neural network, overfits to the training data if it is trained for too long on the same training dataset. The purpose of the validation set is to stop training when performance on validation set starts decreasing, indicating that the model is overfitting the training data. Check t... | overtrain the CNN?
CNN, like any other neural network, overfits to the training data if it is trained for too long on the same training dataset. The purpose of the validation set is to stop training when performance on |
49,955 | Stationarity Tests in R, checking mean, variance and covariance | I also asked myself a similar question.
There is a stationarity() from {fractal} package in R; which uses PSR test based on spectral analysis; and hwtos2 from {locits}, which uses wavelet spectrum test.
That answer can be found on the following link:
http://www.maths.bris.ac.uk/~guy/Research/LSTS/TOS.html | Stationarity Tests in R, checking mean, variance and covariance | I also asked myself a similar question.
There is a stationarity() from {fractal} package in R; which uses PSR test based on spectral analysis; and hwtos2 from {locits}, which uses wavelet spectrum te | Stationarity Tests in R, checking mean, variance and covariance
I also asked myself a similar question.
There is a stationarity() from {fractal} package in R; which uses PSR test based on spectral analysis; and hwtos2 from {locits}, which uses wavelet spectrum test.
That answer can be found on the following link:
http... | Stationarity Tests in R, checking mean, variance and covariance
I also asked myself a similar question.
There is a stationarity() from {fractal} package in R; which uses PSR test based on spectral analysis; and hwtos2 from {locits}, which uses wavelet spectrum te |
49,956 | Scaling vs Offsetting in Quasi-Poisson GLM | We can consider the GLM as having two components, model for the mean and a model for the variance. This is even more explicit with the quasi-GLM case.
The mean is assumed proportional to the exposure; with a log-link (which is what I presume you have), you could try to adjust for the effect of exposure on the mean eith... | Scaling vs Offsetting in Quasi-Poisson GLM | We can consider the GLM as having two components, model for the mean and a model for the variance. This is even more explicit with the quasi-GLM case.
The mean is assumed proportional to the exposure; | Scaling vs Offsetting in Quasi-Poisson GLM
We can consider the GLM as having two components, model for the mean and a model for the variance. This is even more explicit with the quasi-GLM case.
The mean is assumed proportional to the exposure; with a log-link (which is what I presume you have), you could try to adjust ... | Scaling vs Offsetting in Quasi-Poisson GLM
We can consider the GLM as having two components, model for the mean and a model for the variance. This is even more explicit with the quasi-GLM case.
The mean is assumed proportional to the exposure; |
49,957 | igraph betweenness depends on order of edges | The following is based on the response of Tamás under the bug report I filed for this.
Betweenness is a property of the graph, so it does not depend on representation details such as edge ordering.
Why does igraph's result depend on ordering then?
As part of betweenness calculations, we must do equality comparisons bet... | igraph betweenness depends on order of edges | The following is based on the response of Tamás under the bug report I filed for this.
Betweenness is a property of the graph, so it does not depend on representation details such as edge ordering.
Wh | igraph betweenness depends on order of edges
The following is based on the response of Tamás under the bug report I filed for this.
Betweenness is a property of the graph, so it does not depend on representation details such as edge ordering.
Why does igraph's result depend on ordering then?
As part of betweenness calc... | igraph betweenness depends on order of edges
The following is based on the response of Tamás under the bug report I filed for this.
Betweenness is a property of the graph, so it does not depend on representation details such as edge ordering.
Wh |
49,958 | When is Markov chain a generator for iid sequences | Q1: The above statement means that the probability of a random variable X being equal to some value x at time n + 1, given all the x values that came before it in the sequence, is equal to the probability of X being equal to some value x at time n + 1 given just the value of x that came before it. In other words, X at ... | When is Markov chain a generator for iid sequences | Q1: The above statement means that the probability of a random variable X being equal to some value x at time n + 1, given all the x values that came before it in the sequence, is equal to the probabi | When is Markov chain a generator for iid sequences
Q1: The above statement means that the probability of a random variable X being equal to some value x at time n + 1, given all the x values that came before it in the sequence, is equal to the probability of X being equal to some value x at time n + 1 given just the va... | When is Markov chain a generator for iid sequences
Q1: The above statement means that the probability of a random variable X being equal to some value x at time n + 1, given all the x values that came before it in the sequence, is equal to the probabi |
49,959 | Conventional wisdom for designing and training neural networks | In addition, to the paper by Le Cun outlined in the comments, two more recent practical guides by pioneers in the area are:
Practical Recommendations for Gradient-Based Training of Deep
Architectures. Yoshua Bengio. 2012.
A Practical Guide to Training Restricted Boltzmann Machines. Geoffrey Hinton. 2010.
Both of thes... | Conventional wisdom for designing and training neural networks | In addition, to the paper by Le Cun outlined in the comments, two more recent practical guides by pioneers in the area are:
Practical Recommendations for Gradient-Based Training of Deep
Architectures | Conventional wisdom for designing and training neural networks
In addition, to the paper by Le Cun outlined in the comments, two more recent practical guides by pioneers in the area are:
Practical Recommendations for Gradient-Based Training of Deep
Architectures. Yoshua Bengio. 2012.
A Practical Guide to Training Rest... | Conventional wisdom for designing and training neural networks
In addition, to the paper by Le Cun outlined in the comments, two more recent practical guides by pioneers in the area are:
Practical Recommendations for Gradient-Based Training of Deep
Architectures |
49,960 | Conventional wisdom for designing and training neural networks | The advice given verbatim from Aurélien Géron' "Hands-On Machine Learning with Scikit-Learn and TensorFlow" on DNN Architecture:
- Initialization: He initialization
- Activation function: ELU
- Normalization: Batch Normalization
- Regularization: Dropout
- Optimizer: Adam
- Learning rate schedule: None
... | Conventional wisdom for designing and training neural networks | The advice given verbatim from Aurélien Géron' "Hands-On Machine Learning with Scikit-Learn and TensorFlow" on DNN Architecture:
- Initialization: He initialization
- Activation function: ELU
- | Conventional wisdom for designing and training neural networks
The advice given verbatim from Aurélien Géron' "Hands-On Machine Learning with Scikit-Learn and TensorFlow" on DNN Architecture:
- Initialization: He initialization
- Activation function: ELU
- Normalization: Batch Normalization
- Regularization: Dr... | Conventional wisdom for designing and training neural networks
The advice given verbatim from Aurélien Géron' "Hands-On Machine Learning with Scikit-Learn and TensorFlow" on DNN Architecture:
- Initialization: He initialization
- Activation function: ELU
- |
49,961 | CART for unsupervised learning - clustering | I think this will only work on toy data sets like this, and where there is plenty of dead space. It relies on a shuffled object $(x_1,y_2)$ being totally different than the real data.
Try the same on a toy data set with four clusters, at (5,5), (5,15), (15,5), (5,5) and it will no longer work. Clusters and dense areas ... | CART for unsupervised learning - clustering | I think this will only work on toy data sets like this, and where there is plenty of dead space. It relies on a shuffled object $(x_1,y_2)$ being totally different than the real data.
Try the same on | CART for unsupervised learning - clustering
I think this will only work on toy data sets like this, and where there is plenty of dead space. It relies on a shuffled object $(x_1,y_2)$ being totally different than the real data.
Try the same on a toy data set with four clusters, at (5,5), (5,15), (15,5), (5,5) and it wi... | CART for unsupervised learning - clustering
I think this will only work on toy data sets like this, and where there is plenty of dead space. It relies on a shuffled object $(x_1,y_2)$ being totally different than the real data.
Try the same on |
49,962 | Bootstrapping to Test for Homogeneity of Variance between Samples | A test proper could be devised by assuming that the two groups differ only in location $\mu$ & scale $\sigma$, so that their distribution functions are $$F_1(x_1) = F((x_1-\mu_1)/\sigma_1)$$ & $$F_2(x_2) = F((x_2-\mu_2)/\sigma_2)$$; then under the null hypothesis of a common scale $\sigma=\sigma_1=\sigma_2$, the centre... | Bootstrapping to Test for Homogeneity of Variance between Samples | A test proper could be devised by assuming that the two groups differ only in location $\mu$ & scale $\sigma$, so that their distribution functions are $$F_1(x_1) = F((x_1-\mu_1)/\sigma_1)$$ & $$F_2(x | Bootstrapping to Test for Homogeneity of Variance between Samples
A test proper could be devised by assuming that the two groups differ only in location $\mu$ & scale $\sigma$, so that their distribution functions are $$F_1(x_1) = F((x_1-\mu_1)/\sigma_1)$$ & $$F_2(x_2) = F((x_2-\mu_2)/\sigma_2)$$; then under the null h... | Bootstrapping to Test for Homogeneity of Variance between Samples
A test proper could be devised by assuming that the two groups differ only in location $\mu$ & scale $\sigma$, so that their distribution functions are $$F_1(x_1) = F((x_1-\mu_1)/\sigma_1)$$ & $$F_2(x |
49,963 | Bayesian modeling and FDR correction | I am not sure to fully answer your question but think that the following can help.
What you can try is to a design multilevel model including a partial pooling of the $\lambda_i$ by considering for example:
$$ \begin{align} c_i &\sim P(\lambda_i) \\ λ_i &\sim Gamma(a,b) \\ a &\sim \text{Find a good prior here} \\ b &\s... | Bayesian modeling and FDR correction | I am not sure to fully answer your question but think that the following can help.
What you can try is to a design multilevel model including a partial pooling of the $\lambda_i$ by considering for ex | Bayesian modeling and FDR correction
I am not sure to fully answer your question but think that the following can help.
What you can try is to a design multilevel model including a partial pooling of the $\lambda_i$ by considering for example:
$$ \begin{align} c_i &\sim P(\lambda_i) \\ λ_i &\sim Gamma(a,b) \\ a &\sim \... | Bayesian modeling and FDR correction
I am not sure to fully answer your question but think that the following can help.
What you can try is to a design multilevel model including a partial pooling of the $\lambda_i$ by considering for ex |
49,964 | Choosing a model for classification: decision tree or naive bayes | Don't make a choice based on believes try both! Once you developed a cross validation framework it is not very hard to feed it with various models and pick the best one. Sometimes, these cross validation framework already exists (caret in R, but there must be plenty of others!)
The paper : "Do we Need Hundreds of Class... | Choosing a model for classification: decision tree or naive bayes | Don't make a choice based on believes try both! Once you developed a cross validation framework it is not very hard to feed it with various models and pick the best one. Sometimes, these cross validat | Choosing a model for classification: decision tree or naive bayes
Don't make a choice based on believes try both! Once you developed a cross validation framework it is not very hard to feed it with various models and pick the best one. Sometimes, these cross validation framework already exists (caret in R, but there mu... | Choosing a model for classification: decision tree or naive bayes
Don't make a choice based on believes try both! Once you developed a cross validation framework it is not very hard to feed it with various models and pick the best one. Sometimes, these cross validat |
49,965 | Assessing the relationship between continuous variables | There are examples of using Multiple Linear Regression for similar studies[1]
Here is an notebook example of doing this in R.
[1] Genomic ancestry and somatic alterations correlate with age at diagnosis in Hispanic children with B-cell ALL | Assessing the relationship between continuous variables | There are examples of using Multiple Linear Regression for similar studies[1]
Here is an notebook example of doing this in R.
[1] Genomic ancestry and somatic alterations correlate with age at diagnos | Assessing the relationship between continuous variables
There are examples of using Multiple Linear Regression for similar studies[1]
Here is an notebook example of doing this in R.
[1] Genomic ancestry and somatic alterations correlate with age at diagnosis in Hispanic children with B-cell ALL | Assessing the relationship between continuous variables
There are examples of using Multiple Linear Regression for similar studies[1]
Here is an notebook example of doing this in R.
[1] Genomic ancestry and somatic alterations correlate with age at diagnos |
49,966 | Assessing the relationship between continuous variables | Here is a somewhat simplistic (Bayesian) model for your problem. I did not complete it (I am not 100% positive I can). Let me know if this seems reasonable, it looks like a nice problem!
Imagine a human being is made of three independent parts: a native american part (1), a european part (2) and an african part (3). Th... | Assessing the relationship between continuous variables | Here is a somewhat simplistic (Bayesian) model for your problem. I did not complete it (I am not 100% positive I can). Let me know if this seems reasonable, it looks like a nice problem!
Imagine a hum | Assessing the relationship between continuous variables
Here is a somewhat simplistic (Bayesian) model for your problem. I did not complete it (I am not 100% positive I can). Let me know if this seems reasonable, it looks like a nice problem!
Imagine a human being is made of three independent parts: a native american p... | Assessing the relationship between continuous variables
Here is a somewhat simplistic (Bayesian) model for your problem. I did not complete it (I am not 100% positive I can). Let me know if this seems reasonable, it looks like a nice problem!
Imagine a hum |
49,967 | Why do we need to use the Markov property in solving this PDE? | In applying the Feynman-Kac formula, there is no need to use the Markov property.
In proving the Feynman-Kac formula, the Markov property is needed.
Showing that $G(t,x)$ indeed satisfies the PDE requires showing that $G(t,X_t)$ is a martingale which relies on $X_t$ having the Markov property, which it has because it i... | Why do we need to use the Markov property in solving this PDE? | In applying the Feynman-Kac formula, there is no need to use the Markov property.
In proving the Feynman-Kac formula, the Markov property is needed.
Showing that $G(t,x)$ indeed satisfies the PDE requ | Why do we need to use the Markov property in solving this PDE?
In applying the Feynman-Kac formula, there is no need to use the Markov property.
In proving the Feynman-Kac formula, the Markov property is needed.
Showing that $G(t,x)$ indeed satisfies the PDE requires showing that $G(t,X_t)$ is a martingale which relies... | Why do we need to use the Markov property in solving this PDE?
In applying the Feynman-Kac formula, there is no need to use the Markov property.
In proving the Feynman-Kac formula, the Markov property is needed.
Showing that $G(t,x)$ indeed satisfies the PDE requ |
49,968 | Why do we need to use the Markov property in solving this PDE? | Perhaps what's meant here is that since $\mathcal{F}_t$ is a filtration, then for $s\leq t$, $\mathcal{F}_s\subseteq \mathcal{F}_t$. In other words the filtration contains all information up to time $t$ so that you really are invoking the Markov property since $X_t$ really just specifies $X_t$ at time $t$ only. | Why do we need to use the Markov property in solving this PDE? | Perhaps what's meant here is that since $\mathcal{F}_t$ is a filtration, then for $s\leq t$, $\mathcal{F}_s\subseteq \mathcal{F}_t$. In other words the filtration contains all information up to time $ | Why do we need to use the Markov property in solving this PDE?
Perhaps what's meant here is that since $\mathcal{F}_t$ is a filtration, then for $s\leq t$, $\mathcal{F}_s\subseteq \mathcal{F}_t$. In other words the filtration contains all information up to time $t$ so that you really are invoking the Markov property si... | Why do we need to use the Markov property in solving this PDE?
Perhaps what's meant here is that since $\mathcal{F}_t$ is a filtration, then for $s\leq t$, $\mathcal{F}_s\subseteq \mathcal{F}_t$. In other words the filtration contains all information up to time $ |
49,969 | How do I determine whether my data is spherically separable? | I think the best and easiest thing you can do when you have data is to just implement your model (k-means), train your model, and then validate your model on unseen data. The validation error tells you how good your model is. You can safely compare any number of models this way.
Visualization might work for small mod... | How do I determine whether my data is spherically separable? | I think the best and easiest thing you can do when you have data is to just implement your model (k-means), train your model, and then validate your model on unseen data. The validation error tells y | How do I determine whether my data is spherically separable?
I think the best and easiest thing you can do when you have data is to just implement your model (k-means), train your model, and then validate your model on unseen data. The validation error tells you how good your model is. You can safely compare any numb... | How do I determine whether my data is spherically separable?
I think the best and easiest thing you can do when you have data is to just implement your model (k-means), train your model, and then validate your model on unseen data. The validation error tells y |
49,970 | How do I determine whether my data is spherically separable? | The two main approaches are:
Visualize (yes, there are methods)
try clustering and evaluate carefully on your data
Do not rely on any automatic method or statistic. | How do I determine whether my data is spherically separable? | The two main approaches are:
Visualize (yes, there are methods)
try clustering and evaluate carefully on your data
Do not rely on any automatic method or statistic. | How do I determine whether my data is spherically separable?
The two main approaches are:
Visualize (yes, there are methods)
try clustering and evaluate carefully on your data
Do not rely on any automatic method or statistic. | How do I determine whether my data is spherically separable?
The two main approaches are:
Visualize (yes, there are methods)
try clustering and evaluate carefully on your data
Do not rely on any automatic method or statistic. |
49,971 | How do I determine whether my data is spherically separable? | Using this blog post as a reference it appears that it's possible to do better than 'try clustering' and 'visualize':
1) all variables should have the same variance so I can use Bartlett's test on all variables.
2) the prior probability for all k clusters are the same (i.e. each cluster has roughly equal number of ob... | How do I determine whether my data is spherically separable? | Using this blog post as a reference it appears that it's possible to do better than 'try clustering' and 'visualize':
1) all variables should have the same variance so I can use Bartlett's test on al | How do I determine whether my data is spherically separable?
Using this blog post as a reference it appears that it's possible to do better than 'try clustering' and 'visualize':
1) all variables should have the same variance so I can use Bartlett's test on all variables.
2) the prior probability for all k clusters a... | How do I determine whether my data is spherically separable?
Using this blog post as a reference it appears that it's possible to do better than 'try clustering' and 'visualize':
1) all variables should have the same variance so I can use Bartlett's test on al |
49,972 | What is the difference between Support Vector Machines and Conditional Random Fields models in the context of Named Entity Recognition? | Assume that for our data, we have observations (each observation is a set of features) and labels (1 label for each observation). In the case of NER, we have a set of features about a word (observation) and the labels are commonly a BIO scheme, where we might have B-Loc for beginning of location, I-Loc inside location,... | What is the difference between Support Vector Machines and Conditional Random Fields models in the c | Assume that for our data, we have observations (each observation is a set of features) and labels (1 label for each observation). In the case of NER, we have a set of features about a word (observatio | What is the difference between Support Vector Machines and Conditional Random Fields models in the context of Named Entity Recognition?
Assume that for our data, we have observations (each observation is a set of features) and labels (1 label for each observation). In the case of NER, we have a set of features about a ... | What is the difference between Support Vector Machines and Conditional Random Fields models in the c
Assume that for our data, we have observations (each observation is a set of features) and labels (1 label for each observation). In the case of NER, we have a set of features about a word (observatio |
49,973 | Adaboost - update of weights | For 1), yes on both counts. You can view training a new classifier as selecting the best classifier from the "pool" defined as the range (i.e. the collection of all possible resultant classifiers) of the classification algorithm.
For 2), this re-weighting scheme is simply part of the definition of the adaboost algorit... | Adaboost - update of weights | For 1), yes on both counts. You can view training a new classifier as selecting the best classifier from the "pool" defined as the range (i.e. the collection of all possible resultant classifiers) of | Adaboost - update of weights
For 1), yes on both counts. You can view training a new classifier as selecting the best classifier from the "pool" defined as the range (i.e. the collection of all possible resultant classifiers) of the classification algorithm.
For 2), this re-weighting scheme is simply part of the defin... | Adaboost - update of weights
For 1), yes on both counts. You can view training a new classifier as selecting the best classifier from the "pool" defined as the range (i.e. the collection of all possible resultant classifiers) of |
49,974 | Justification for invoking Maximum Entropy | First of all, I tried to comment on the question but I couldn't because I didn't have (still don't) 50 reputation, so I'm posting my opinion as an answer despite knowing it is not a complete answer to what's asked..
On a Bayesian probabilistic framework, probabilities are considered as "degrees of belief", that is, th... | Justification for invoking Maximum Entropy | First of all, I tried to comment on the question but I couldn't because I didn't have (still don't) 50 reputation, so I'm posting my opinion as an answer despite knowing it is not a complete answer to | Justification for invoking Maximum Entropy
First of all, I tried to comment on the question but I couldn't because I didn't have (still don't) 50 reputation, so I'm posting my opinion as an answer despite knowing it is not a complete answer to what's asked..
On a Bayesian probabilistic framework, probabilities are con... | Justification for invoking Maximum Entropy
First of all, I tried to comment on the question but I couldn't because I didn't have (still don't) 50 reputation, so I'm posting my opinion as an answer despite knowing it is not a complete answer to |
49,975 | Dunn's test p-values in R are exactly half those in SPSS and GraphPad for the same data | The dunn.test package in R uses a one-sided test, whereas SPSS and GraphPad use two-sided tests. There is no facility in the dunn.test package or its function dunn.test() to change to a two-sided test, but the p-values can be multiplied by 2 if a two-sided test is required.
A two-sided Dunn's test is available from the... | Dunn's test p-values in R are exactly half those in SPSS and GraphPad for the same data | The dunn.test package in R uses a one-sided test, whereas SPSS and GraphPad use two-sided tests. There is no facility in the dunn.test package or its function dunn.test() to change to a two-sided test | Dunn's test p-values in R are exactly half those in SPSS and GraphPad for the same data
The dunn.test package in R uses a one-sided test, whereas SPSS and GraphPad use two-sided tests. There is no facility in the dunn.test package or its function dunn.test() to change to a two-sided test, but the p-values can be multip... | Dunn's test p-values in R are exactly half those in SPSS and GraphPad for the same data
The dunn.test package in R uses a one-sided test, whereas SPSS and GraphPad use two-sided tests. There is no facility in the dunn.test package or its function dunn.test() to change to a two-sided test |
49,976 | Serially Correlated Regressors | I see it as a special case of Structural Vector AutoRegression (SVAR). A standard SVAR model is:
$$
\textbf{A}(L)X_t = \mu +\textbf{e}_t
$$
where $X_t$ is a vector of k endogenous variables, $\mu$ is a vector of k constant parameters $\textbf{e}_t = N(0,I) $
is
a
random
vector
and
$A(L)$ is
a
matrix polynomial of orde... | Serially Correlated Regressors | I see it as a special case of Structural Vector AutoRegression (SVAR). A standard SVAR model is:
$$
\textbf{A}(L)X_t = \mu +\textbf{e}_t
$$
where $X_t$ is a vector of k endogenous variables, $\mu$ is | Serially Correlated Regressors
I see it as a special case of Structural Vector AutoRegression (SVAR). A standard SVAR model is:
$$
\textbf{A}(L)X_t = \mu +\textbf{e}_t
$$
where $X_t$ is a vector of k endogenous variables, $\mu$ is a vector of k constant parameters $\textbf{e}_t = N(0,I) $
is
a
random
vector
and
$A(L)$... | Serially Correlated Regressors
I see it as a special case of Structural Vector AutoRegression (SVAR). A standard SVAR model is:
$$
\textbf{A}(L)X_t = \mu +\textbf{e}_t
$$
where $X_t$ is a vector of k endogenous variables, $\mu$ is |
49,977 | Serially Correlated Regressors | After the moving average, the regressor in your model becomes more persistent, i.e. having stronger serial correlations. The OLS estimate would still be asymptotically consistent, but the finite-sample bias likely becomes larger. You could run a simple simulation study to see the finite-sample bias.
In finance, there i... | Serially Correlated Regressors | After the moving average, the regressor in your model becomes more persistent, i.e. having stronger serial correlations. The OLS estimate would still be asymptotically consistent, but the finite-sampl | Serially Correlated Regressors
After the moving average, the regressor in your model becomes more persistent, i.e. having stronger serial correlations. The OLS estimate would still be asymptotically consistent, but the finite-sample bias likely becomes larger. You could run a simple simulation study to see the finite-s... | Serially Correlated Regressors
After the moving average, the regressor in your model becomes more persistent, i.e. having stronger serial correlations. The OLS estimate would still be asymptotically consistent, but the finite-sampl |
49,978 | Serially Correlated Regressors | I would look into multivariate ARMA modeling for generic models of this form. (It's a sort of hacky way to approach regression, but it'll work.) | Serially Correlated Regressors | I would look into multivariate ARMA modeling for generic models of this form. (It's a sort of hacky way to approach regression, but it'll work.) | Serially Correlated Regressors
I would look into multivariate ARMA modeling for generic models of this form. (It's a sort of hacky way to approach regression, but it'll work.) | Serially Correlated Regressors
I would look into multivariate ARMA modeling for generic models of this form. (It's a sort of hacky way to approach regression, but it'll work.) |
49,979 | A closed form formula for the normalizing constant in standard normal auto-regressive series? | It's not strange you didn't calculate the AR(3) case. It's rather complicated! And no, there is no closed form for the AR(n)-case. For the AR(3) we start with the Yule-Walker equationsAR-model wikipedia(where $\gamma_j=\gamma_{-j}$):
$\gamma_1=c_1\gamma_0+c_2\gamma_{-1}+c_3\gamma_{-2}=c_1\gamma_0+c_2\gamma_{1}+c_3\gam... | A closed form formula for the normalizing constant in standard normal auto-regressive series? | It's not strange you didn't calculate the AR(3) case. It's rather complicated! And no, there is no closed form for the AR(n)-case. For the AR(3) we start with the Yule-Walker equationsAR-model wikiped | A closed form formula for the normalizing constant in standard normal auto-regressive series?
It's not strange you didn't calculate the AR(3) case. It's rather complicated! And no, there is no closed form for the AR(n)-case. For the AR(3) we start with the Yule-Walker equationsAR-model wikipedia(where $\gamma_j=\gamma_... | A closed form formula for the normalizing constant in standard normal auto-regressive series?
It's not strange you didn't calculate the AR(3) case. It's rather complicated! And no, there is no closed form for the AR(n)-case. For the AR(3) we start with the Yule-Walker equationsAR-model wikiped |
49,980 | Bar plots with variable bases (intensive and extensive variables at once) | Apparently they are called cascade charts, see:
Variable Width Column Charts (Cascade Charts) - Excel
The Cascade Chart Creator add-in for Microsoft Excel
Cascade chart (graph with variable width bars) - Statalist
As a bonus, ggplot2: Variable Width Column Chart.
However, sometimes cascade chart is used as a synonymo... | Bar plots with variable bases (intensive and extensive variables at once) | Apparently they are called cascade charts, see:
Variable Width Column Charts (Cascade Charts) - Excel
The Cascade Chart Creator add-in for Microsoft Excel
Cascade chart (graph with variable width bar | Bar plots with variable bases (intensive and extensive variables at once)
Apparently they are called cascade charts, see:
Variable Width Column Charts (Cascade Charts) - Excel
The Cascade Chart Creator add-in for Microsoft Excel
Cascade chart (graph with variable width bars) - Statalist
As a bonus, ggplot2: Variable ... | Bar plots with variable bases (intensive and extensive variables at once)
Apparently they are called cascade charts, see:
Variable Width Column Charts (Cascade Charts) - Excel
The Cascade Chart Creator add-in for Microsoft Excel
Cascade chart (graph with variable width bar |
49,981 | Whether to use a hierarchical linear model | While I agree that multi-level modeling is an option for data with this structure, it's not the only option, especially given the lone time series dimension. Typically, the nestings within a heterarchical model are by category, e.g., students within classes or teachers, classes within schools, and so on, not ordinal di... | Whether to use a hierarchical linear model | While I agree that multi-level modeling is an option for data with this structure, it's not the only option, especially given the lone time series dimension. Typically, the nestings within a heterarch | Whether to use a hierarchical linear model
While I agree that multi-level modeling is an option for data with this structure, it's not the only option, especially given the lone time series dimension. Typically, the nestings within a heterarchical model are by category, e.g., students within classes or teachers, classe... | Whether to use a hierarchical linear model
While I agree that multi-level modeling is an option for data with this structure, it's not the only option, especially given the lone time series dimension. Typically, the nestings within a heterarch |
49,982 | Whether to use a hierarchical linear model | I would say that using a hierarchical model is suitable in your case.
Following this guide, BRAND would be your Level-2-term and Year could be your Level-1-term, used as random slope.
You should also check the ICC afterwards to see whether hierarchical models give you any benefits over normal linear regression. | Whether to use a hierarchical linear model | I would say that using a hierarchical model is suitable in your case.
Following this guide, BRAND would be your Level-2-term and Year could be your Level-1-term, used as random slope.
You should also | Whether to use a hierarchical linear model
I would say that using a hierarchical model is suitable in your case.
Following this guide, BRAND would be your Level-2-term and Year could be your Level-1-term, used as random slope.
You should also check the ICC afterwards to see whether hierarchical models give you any bene... | Whether to use a hierarchical linear model
I would say that using a hierarchical model is suitable in your case.
Following this guide, BRAND would be your Level-2-term and Year could be your Level-1-term, used as random slope.
You should also |
49,983 | Whether to use a hierarchical linear model | Yes, you should probably use multilevel modeling, possibly with company at level 3 and year at level 2. This would be a multilevel growth curve approach. You could then analyze the different kinds of changes in x different types of companies had over time. | Whether to use a hierarchical linear model | Yes, you should probably use multilevel modeling, possibly with company at level 3 and year at level 2. This would be a multilevel growth curve approach. You could then analyze the different kinds of | Whether to use a hierarchical linear model
Yes, you should probably use multilevel modeling, possibly with company at level 3 and year at level 2. This would be a multilevel growth curve approach. You could then analyze the different kinds of changes in x different types of companies had over time. | Whether to use a hierarchical linear model
Yes, you should probably use multilevel modeling, possibly with company at level 3 and year at level 2. This would be a multilevel growth curve approach. You could then analyze the different kinds of |
49,984 | regression with circular response variable | The pattern in the residuals is not necessarily a problem. One way to check this is to simulate a set of responses from the model that you just fitted (that is, under the assumption that the model is correct), fit a new model to the results, and plot its residuals. This gives you a measure of how weird you would expect... | regression with circular response variable | The pattern in the residuals is not necessarily a problem. One way to check this is to simulate a set of responses from the model that you just fitted (that is, under the assumption that the model is | regression with circular response variable
The pattern in the residuals is not necessarily a problem. One way to check this is to simulate a set of responses from the model that you just fitted (that is, under the assumption that the model is correct), fit a new model to the results, and plot its residuals. This gives ... | regression with circular response variable
The pattern in the residuals is not necessarily a problem. One way to check this is to simulate a set of responses from the model that you just fitted (that is, under the assumption that the model is |
49,985 | How was public opinion survey sampling done in early 20th century? | In his book, Théorie des Sondages (Dunod, 2001, written in French), Yves Tillé tells the history of survey sampling. According to him, A.N. Kiaer introduced in 1895 at an IIS (International Institute for Statistics) congress the idea of conducting a survey to measure certain variables on the population, instead of doin... | How was public opinion survey sampling done in early 20th century? | In his book, Théorie des Sondages (Dunod, 2001, written in French), Yves Tillé tells the history of survey sampling. According to him, A.N. Kiaer introduced in 1895 at an IIS (International Institute | How was public opinion survey sampling done in early 20th century?
In his book, Théorie des Sondages (Dunod, 2001, written in French), Yves Tillé tells the history of survey sampling. According to him, A.N. Kiaer introduced in 1895 at an IIS (International Institute for Statistics) congress the idea of conducting a sur... | How was public opinion survey sampling done in early 20th century?
In his book, Théorie des Sondages (Dunod, 2001, written in French), Yves Tillé tells the history of survey sampling. According to him, A.N. Kiaer introduced in 1895 at an IIS (International Institute |
49,986 | How was public opinion survey sampling done in early 20th century? | To the best of my knowledge, in 1936, George Gallup used a version of quota sampling. It worked in some cases, like in 1936, and failed in others, like just 12 years later in 1948, when Gallup, like some others, said that "Dewey defeats Truman". | How was public opinion survey sampling done in early 20th century? | To the best of my knowledge, in 1936, George Gallup used a version of quota sampling. It worked in some cases, like in 1936, and failed in others, like just 12 years later in 1948, when Gallup, like s | How was public opinion survey sampling done in early 20th century?
To the best of my knowledge, in 1936, George Gallup used a version of quota sampling. It worked in some cases, like in 1936, and failed in others, like just 12 years later in 1948, when Gallup, like some others, said that "Dewey defeats Truman". | How was public opinion survey sampling done in early 20th century?
To the best of my knowledge, in 1936, George Gallup used a version of quota sampling. It worked in some cases, like in 1936, and failed in others, like just 12 years later in 1948, when Gallup, like s |
49,987 | Estimating bias in surveys | Here's a solution using survey sampling theory ("frequentist" solution).
Let's assume that the estimate of males and females in the entire country is a good one (its variance is sufficiently low). Then the estimate in each city can be improved using calibration techniques (such as post-stratification or Deville and Sär... | Estimating bias in surveys | Here's a solution using survey sampling theory ("frequentist" solution).
Let's assume that the estimate of males and females in the entire country is a good one (its variance is sufficiently low). The | Estimating bias in surveys
Here's a solution using survey sampling theory ("frequentist" solution).
Let's assume that the estimate of males and females in the entire country is a good one (its variance is sufficiently low). Then the estimate in each city can be improved using calibration techniques (such as post-strati... | Estimating bias in surveys
Here's a solution using survey sampling theory ("frequentist" solution).
Let's assume that the estimate of males and females in the entire country is a good one (its variance is sufficiently low). The |
49,988 | Binomial data: Null Hypothesis $p = 0$ when all Sample Values are 0 - testing and power analysis | Before assessing the power, we have to make it clear what the test is.
This null hypothesis $H_0:p=0$ posits that successes have no chance of occurring. Observing even a single success would be convincing evidence against the null. But what if no successes (in $n$ independent trials) are observed?
For a test at level... | Binomial data: Null Hypothesis $p = 0$ when all Sample Values are 0 - testing and power analysis | Before assessing the power, we have to make it clear what the test is.
This null hypothesis $H_0:p=0$ posits that successes have no chance of occurring. Observing even a single success would be convi | Binomial data: Null Hypothesis $p = 0$ when all Sample Values are 0 - testing and power analysis
Before assessing the power, we have to make it clear what the test is.
This null hypothesis $H_0:p=0$ posits that successes have no chance of occurring. Observing even a single success would be convincing evidence against ... | Binomial data: Null Hypothesis $p = 0$ when all Sample Values are 0 - testing and power analysis
Before assessing the power, we have to make it clear what the test is.
This null hypothesis $H_0:p=0$ posits that successes have no chance of occurring. Observing even a single success would be convi |
49,989 | Two equivalent forms of logistic regression | I think you lost (or added) a minus sign in one of the formulations (maybe going from log-lik to neg-log-lik?).
Using $z=\beta x$, if we write the losses as:
$l_{01} = -y_{01} z + \log (1+e^z)$
$l_{\pm1} = \log (1+e^{-y_{\pm1}z})$
Then when $y_{01} = y_{\pm1} = 1$, we have:
$$-z + \log (1 + e^z) \quad \text{and} \qua... | Two equivalent forms of logistic regression | I think you lost (or added) a minus sign in one of the formulations (maybe going from log-lik to neg-log-lik?).
Using $z=\beta x$, if we write the losses as:
$l_{01} = -y_{01} z + \log (1+e^z)$
$l_{\ | Two equivalent forms of logistic regression
I think you lost (or added) a minus sign in one of the formulations (maybe going from log-lik to neg-log-lik?).
Using $z=\beta x$, if we write the losses as:
$l_{01} = -y_{01} z + \log (1+e^z)$
$l_{\pm1} = \log (1+e^{-y_{\pm1}z})$
Then when $y_{01} = y_{\pm1} = 1$, we have:... | Two equivalent forms of logistic regression
I think you lost (or added) a minus sign in one of the formulations (maybe going from log-lik to neg-log-lik?).
Using $z=\beta x$, if we write the losses as:
$l_{01} = -y_{01} z + \log (1+e^z)$
$l_{\ |
49,990 | MANOVA multiple comparisons with equivalence testing | For an R package, you might take a look at lsmeans. For mlm models, it sets up the multivariate response as if it were a factor whose levels are the dimenstions of the response. Then you can do estimates or contrasts of those, with or without other factors being involved. See the example for the MOats dataset that acco... | MANOVA multiple comparisons with equivalence testing | For an R package, you might take a look at lsmeans. For mlm models, it sets up the multivariate response as if it were a factor whose levels are the dimenstions of the response. Then you can do estima | MANOVA multiple comparisons with equivalence testing
For an R package, you might take a look at lsmeans. For mlm models, it sets up the multivariate response as if it were a factor whose levels are the dimenstions of the response. Then you can do estimates or contrasts of those, with or without other factors being invo... | MANOVA multiple comparisons with equivalence testing
For an R package, you might take a look at lsmeans. For mlm models, it sets up the multivariate response as if it were a factor whose levels are the dimenstions of the response. Then you can do estima |
49,991 | conditional probability, change of variable and Jacobian | Ok. I just figured out that
$$
f_{X|Z}(x|z) = f_{X|Y}(x|A^Tz+\mu).
$$
To see this, first, the change of variable technique shows that:
$$
f_{X,Z}(x,z) = f_{X,Y}(x,A^Tz+\mu) |A|.
$$
The change of variable technique also shows that:
$$
f_{Z}(z) = f_{Y}(A^Tz+\mu) |A|.
$$
(You can get this result by simply integrating o... | conditional probability, change of variable and Jacobian | Ok. I just figured out that
$$
f_{X|Z}(x|z) = f_{X|Y}(x|A^Tz+\mu).
$$
To see this, first, the change of variable technique shows that:
$$
f_{X,Z}(x,z) = f_{X,Y}(x,A^Tz+\mu) |A|.
$$
The change of va | conditional probability, change of variable and Jacobian
Ok. I just figured out that
$$
f_{X|Z}(x|z) = f_{X|Y}(x|A^Tz+\mu).
$$
To see this, first, the change of variable technique shows that:
$$
f_{X,Z}(x,z) = f_{X,Y}(x,A^Tz+\mu) |A|.
$$
The change of variable technique also shows that:
$$
f_{Z}(z) = f_{Y}(A^Tz+\mu)... | conditional probability, change of variable and Jacobian
Ok. I just figured out that
$$
f_{X|Z}(x|z) = f_{X|Y}(x|A^Tz+\mu).
$$
To see this, first, the change of variable technique shows that:
$$
f_{X,Z}(x,z) = f_{X,Y}(x,A^Tz+\mu) |A|.
$$
The change of va |
49,992 | Can a 1-D risk score (binary outcome) be sensibly used to create multiple treatment groups? | What would be the most convincing argument for a layperson to hear?
Different types of treatments carry different risks.
Here is an example:
A sample model:
For sick patients:
No treatment has a success rate (spontaneous recovery) of 0.01
Treatment A has a success rate of 0.80
Treatment B has a success rate of 0.95
... | Can a 1-D risk score (binary outcome) be sensibly used to create multiple treatment groups? | What would be the most convincing argument for a layperson to hear?
Different types of treatments carry different risks.
Here is an example:
A sample model:
For sick patients:
No treatment has a suc | Can a 1-D risk score (binary outcome) be sensibly used to create multiple treatment groups?
What would be the most convincing argument for a layperson to hear?
Different types of treatments carry different risks.
Here is an example:
A sample model:
For sick patients:
No treatment has a success rate (spontaneous recov... | Can a 1-D risk score (binary outcome) be sensibly used to create multiple treatment groups?
What would be the most convincing argument for a layperson to hear?
Different types of treatments carry different risks.
Here is an example:
A sample model:
For sick patients:
No treatment has a suc |
49,993 | Can a 1-D risk score (binary outcome) be sensibly used to create multiple treatment groups? | Consider you have two treatments available:
1. costs 1000 but has a 99% chance of helping
2. costs 10 but has a 90% chance of working
Would you rather treat 1 with the first, or 100 with the second?
Assume your risk distribution is 1, 0, ..., 0 then you should treat only the first.
If your risk distribution is 0.60,0.5... | Can a 1-D risk score (binary outcome) be sensibly used to create multiple treatment groups? | Consider you have two treatments available:
1. costs 1000 but has a 99% chance of helping
2. costs 10 but has a 90% chance of working
Would you rather treat 1 with the first, or 100 with the second?
A | Can a 1-D risk score (binary outcome) be sensibly used to create multiple treatment groups?
Consider you have two treatments available:
1. costs 1000 but has a 99% chance of helping
2. costs 10 but has a 90% chance of working
Would you rather treat 1 with the first, or 100 with the second?
Assume your risk distribution... | Can a 1-D risk score (binary outcome) be sensibly used to create multiple treatment groups?
Consider you have two treatments available:
1. costs 1000 but has a 99% chance of helping
2. costs 10 but has a 90% chance of working
Would you rather treat 1 with the first, or 100 with the second?
A |
49,994 | Can a 1-D risk score (binary outcome) be sensibly used to create multiple treatment groups? | Suppose there were three kinds of patient:
Patients with risk 0 will never catch the virus
Patients with risk 1 will catch the virus only if untreated
Patients with risk 2 will always catch the virus
Then the optimal strategy would be to use multiple cutpoints and only treat patients of risk 1.
I came up with that p... | Can a 1-D risk score (binary outcome) be sensibly used to create multiple treatment groups? | Suppose there were three kinds of patient:
Patients with risk 0 will never catch the virus
Patients with risk 1 will catch the virus only if untreated
Patients with risk 2 will always catch the virus | Can a 1-D risk score (binary outcome) be sensibly used to create multiple treatment groups?
Suppose there were three kinds of patient:
Patients with risk 0 will never catch the virus
Patients with risk 1 will catch the virus only if untreated
Patients with risk 2 will always catch the virus
Then the optimal strategy ... | Can a 1-D risk score (binary outcome) be sensibly used to create multiple treatment groups?
Suppose there were three kinds of patient:
Patients with risk 0 will never catch the virus
Patients with risk 1 will catch the virus only if untreated
Patients with risk 2 will always catch the virus |
49,995 | Distribution of test statistic under null and alternative | First, review some basic properties of expectation and variance:
Expectation (in particular, linearity, so $E(\Sigma_i X_i)=\sum_i E(X_i)$ and $E(aX)=aE(X)$)
Variance (in particular, that $\text{Var}(aX)=a^2\text{Var}(X)$), and
Variance of a sum of uncorrelated variables so $\text{Var}(\Sigma_i X_i)=\sum_i \text{Var}(... | Distribution of test statistic under null and alternative | First, review some basic properties of expectation and variance:
Expectation (in particular, linearity, so $E(\Sigma_i X_i)=\sum_i E(X_i)$ and $E(aX)=aE(X)$)
Variance (in particular, that $\text{Var} | Distribution of test statistic under null and alternative
First, review some basic properties of expectation and variance:
Expectation (in particular, linearity, so $E(\Sigma_i X_i)=\sum_i E(X_i)$ and $E(aX)=aE(X)$)
Variance (in particular, that $\text{Var}(aX)=a^2\text{Var}(X)$), and
Variance of a sum of uncorrelated... | Distribution of test statistic under null and alternative
First, review some basic properties of expectation and variance:
Expectation (in particular, linearity, so $E(\Sigma_i X_i)=\sum_i E(X_i)$ and $E(aX)=aE(X)$)
Variance (in particular, that $\text{Var} |
49,996 | Variance Inflation Factor less than 1 in ridge regression? | I would like to suggest that you calculate the diagonal elements of matrix directly.
It is assumed that the design matrix is centered and scaled.
We can adopt the eigen value decomposition $R_{XX}=X'X=T\Lambda T'$.
$\begin{align} (R_{XX}+cI)^{-1}R_{XX}(R_{XX}+cI)^{-1}&=(R_{XX}+cI)^{-1}(R_{XX}+cI)(R_{XX}+cI)^{-1}-c(R_... | Variance Inflation Factor less than 1 in ridge regression? | I would like to suggest that you calculate the diagonal elements of matrix directly.
It is assumed that the design matrix is centered and scaled.
We can adopt the eigen value decomposition $R_{XX}=X | Variance Inflation Factor less than 1 in ridge regression?
I would like to suggest that you calculate the diagonal elements of matrix directly.
It is assumed that the design matrix is centered and scaled.
We can adopt the eigen value decomposition $R_{XX}=X'X=T\Lambda T'$.
$\begin{align} (R_{XX}+cI)^{-1}R_{XX}(R_{XX}... | Variance Inflation Factor less than 1 in ridge regression?
I would like to suggest that you calculate the diagonal elements of matrix directly.
It is assumed that the design matrix is centered and scaled.
We can adopt the eigen value decomposition $R_{XX}=X |
49,997 | Variance Inflation Factor less than 1 in ridge regression? | I was wrestling with this issue myself, and then discovered this article by Garcia et al., where they show how traditional definition of the VIF does in fact lead to values less than unity in the case of ridge regression. They subsequently propose an alternate definition, involving the ridge parameter $k$, which leads ... | Variance Inflation Factor less than 1 in ridge regression? | I was wrestling with this issue myself, and then discovered this article by Garcia et al., where they show how traditional definition of the VIF does in fact lead to values less than unity in the case | Variance Inflation Factor less than 1 in ridge regression?
I was wrestling with this issue myself, and then discovered this article by Garcia et al., where they show how traditional definition of the VIF does in fact lead to values less than unity in the case of ridge regression. They subsequently propose an alternate ... | Variance Inflation Factor less than 1 in ridge regression?
I was wrestling with this issue myself, and then discovered this article by Garcia et al., where they show how traditional definition of the VIF does in fact lead to values less than unity in the case |
49,998 | Variance Inflation Factor less than 1 in ridge regression? | Recall that you are minimizing
$$
\|Ax -y\|^2 + c\|x-0\|^2
$$
So as $c$ increases $x\to 0$ i.e. the bias is such that your estimator approches $0$ as $c$ increases. So when your VIFs are approaching one then stop increasing $c$, that is probably your optimal $c$.
Reference: p. 434 in Applied Statistical Models. | Variance Inflation Factor less than 1 in ridge regression? | Recall that you are minimizing
$$
\|Ax -y\|^2 + c\|x-0\|^2
$$
So as $c$ increases $x\to 0$ i.e. the bias is such that your estimator approches $0$ as $c$ increases. So when your VIFs are approaching | Variance Inflation Factor less than 1 in ridge regression?
Recall that you are minimizing
$$
\|Ax -y\|^2 + c\|x-0\|^2
$$
So as $c$ increases $x\to 0$ i.e. the bias is such that your estimator approches $0$ as $c$ increases. So when your VIFs are approaching one then stop increasing $c$, that is probably your optimal $... | Variance Inflation Factor less than 1 in ridge regression?
Recall that you are minimizing
$$
\|Ax -y\|^2 + c\|x-0\|^2
$$
So as $c$ increases $x\to 0$ i.e. the bias is such that your estimator approches $0$ as $c$ increases. So when your VIFs are approaching |
49,999 | Short term for Probability of Type I error | The pithiest word I've seen is size | Short term for Probability of Type I error | The pithiest word I've seen is size | Short term for Probability of Type I error
The pithiest word I've seen is size | Short term for Probability of Type I error
The pithiest word I've seen is size |
50,000 | Short term for Probability of Type I error | Significance level $\alpha$, see here
Power $1-\beta$, sensitivity or recall rate | Short term for Probability of Type I error | Significance level $\alpha$, see here
Power $1-\beta$, sensitivity or recall rate | Short term for Probability of Type I error
Significance level $\alpha$, see here
Power $1-\beta$, sensitivity or recall rate | Short term for Probability of Type I error
Significance level $\alpha$, see here
Power $1-\beta$, sensitivity or recall rate |
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