idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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3,401 | How to visualize what ANOVA does? | Personally, I like introducing linear regression and ANOVA by showing that it is all the same and that linear models amount to partition the total variance: We have some kind of variance in the outcome that can be explained by the factors of interest, plus the unexplained part (called the 'residual'). I generally use t... | How to visualize what ANOVA does? | Personally, I like introducing linear regression and ANOVA by showing that it is all the same and that linear models amount to partition the total variance: We have some kind of variance in the outcom | How to visualize what ANOVA does?
Personally, I like introducing linear regression and ANOVA by showing that it is all the same and that linear models amount to partition the total variance: We have some kind of variance in the outcome that can be explained by the factors of interest, plus the unexplained part (called ... | How to visualize what ANOVA does?
Personally, I like introducing linear regression and ANOVA by showing that it is all the same and that linear models amount to partition the total variance: We have some kind of variance in the outcom |
3,402 | How to visualize what ANOVA does? | How about something like this?
Following Crawley (2005). Statistics. An introduction using R: Wiley. | How to visualize what ANOVA does? | How about something like this?
Following Crawley (2005). Statistics. An introduction using R: Wiley. | How to visualize what ANOVA does?
How about something like this?
Following Crawley (2005). Statistics. An introduction using R: Wiley. | How to visualize what ANOVA does?
How about something like this?
Following Crawley (2005). Statistics. An introduction using R: Wiley. |
3,403 | How to visualize what ANOVA does? | Thank you for your great answer so far. While they where very enlightening, I felt that using them for the course I am currently teaching (well, TA'ing) will be too much for my students. (I help teach the course BioStatistics for students from advanced degrees in medicine sciences)
Therefore, I ended up creating two i... | How to visualize what ANOVA does? | Thank you for your great answer so far. While they where very enlightening, I felt that using them for the course I am currently teaching (well, TA'ing) will be too much for my students. (I help teac | How to visualize what ANOVA does?
Thank you for your great answer so far. While they where very enlightening, I felt that using them for the course I am currently teaching (well, TA'ing) will be too much for my students. (I help teach the course BioStatistics for students from advanced degrees in medicine sciences)
Th... | How to visualize what ANOVA does?
Thank you for your great answer so far. While they where very enlightening, I felt that using them for the course I am currently teaching (well, TA'ing) will be too much for my students. (I help teac |
3,404 | How to visualize what ANOVA does? | Since we gather certain types of nice graphs in this post, here is another one that I recently found and may help you understand how ANOVA works and how the F statistic is generated. The graphic was created using the granova package in R. | How to visualize what ANOVA does? | Since we gather certain types of nice graphs in this post, here is another one that I recently found and may help you understand how ANOVA works and how the F statistic is generated. The graphic was c | How to visualize what ANOVA does?
Since we gather certain types of nice graphs in this post, here is another one that I recently found and may help you understand how ANOVA works and how the F statistic is generated. The graphic was created using the granova package in R. | How to visualize what ANOVA does?
Since we gather certain types of nice graphs in this post, here is another one that I recently found and may help you understand how ANOVA works and how the F statistic is generated. The graphic was c |
3,405 | How to visualize what ANOVA does? | Check out Hadley Wickham's presentation (pdf, mirror) on ggplot.
Starting on pages 23-40 of this document he describes an interesting approach to visualizing ANOVAs.
*Link taken from: http://had.co.nz/ggplot2/ | How to visualize what ANOVA does? | Check out Hadley Wickham's presentation (pdf, mirror) on ggplot.
Starting on pages 23-40 of this document he describes an interesting approach to visualizing ANOVAs.
*Link taken from: http://had.co.nz | How to visualize what ANOVA does?
Check out Hadley Wickham's presentation (pdf, mirror) on ggplot.
Starting on pages 23-40 of this document he describes an interesting approach to visualizing ANOVAs.
*Link taken from: http://had.co.nz/ggplot2/ | How to visualize what ANOVA does?
Check out Hadley Wickham's presentation (pdf, mirror) on ggplot.
Starting on pages 23-40 of this document he describes an interesting approach to visualizing ANOVAs.
*Link taken from: http://had.co.nz |
3,406 | How to visualize what ANOVA does? | Great question. You know, I've struggled myself with wrapping my head around ANOVA for a very long time. I always find myself going back to the "between versus within" intuition, and I've always tried to imagine what this would look like in my head. I'm glad this question came up, and I've been amazed by the varied a... | How to visualize what ANOVA does? | Great question. You know, I've struggled myself with wrapping my head around ANOVA for a very long time. I always find myself going back to the "between versus within" intuition, and I've always trie | How to visualize what ANOVA does?
Great question. You know, I've struggled myself with wrapping my head around ANOVA for a very long time. I always find myself going back to the "between versus within" intuition, and I've always tried to imagine what this would look like in my head. I'm glad this question came up, an... | How to visualize what ANOVA does?
Great question. You know, I've struggled myself with wrapping my head around ANOVA for a very long time. I always find myself going back to the "between versus within" intuition, and I've always trie |
3,407 | How to visualize what ANOVA does? | Here are some representations of situations in which an ANOVA will conclude to different level of fit between $Y$ and $X$. | How to visualize what ANOVA does? | Here are some representations of situations in which an ANOVA will conclude to different level of fit between $Y$ and $X$. | How to visualize what ANOVA does?
Here are some representations of situations in which an ANOVA will conclude to different level of fit between $Y$ and $X$. | How to visualize what ANOVA does?
Here are some representations of situations in which an ANOVA will conclude to different level of fit between $Y$ and $X$. |
3,408 | How to visualize what ANOVA does? | To illustrate what is going on with one-way ANOVA I have sometimes used an applet offered by the authors of "Introduction to the Practice of Statistics", which allows the students to play with within and between variances and observe their effect on the F statistic. Here is the link (the applet is the last one on the p... | How to visualize what ANOVA does? | To illustrate what is going on with one-way ANOVA I have sometimes used an applet offered by the authors of "Introduction to the Practice of Statistics", which allows the students to play with within | How to visualize what ANOVA does?
To illustrate what is going on with one-way ANOVA I have sometimes used an applet offered by the authors of "Introduction to the Practice of Statistics", which allows the students to play with within and between variances and observe their effect on the F statistic. Here is the link (t... | How to visualize what ANOVA does?
To illustrate what is going on with one-way ANOVA I have sometimes used an applet offered by the authors of "Introduction to the Practice of Statistics", which allows the students to play with within |
3,409 | How to visualize what ANOVA does? | It seems the ship has already sailed in terms of an answer, but I think that if this is an introductory course that most of the displays offered here are going to be too difficult to grasp for introductory students... or at the very least too difficult to grasp without an introductory display which provides a very simp... | How to visualize what ANOVA does? | It seems the ship has already sailed in terms of an answer, but I think that if this is an introductory course that most of the displays offered here are going to be too difficult to grasp for introdu | How to visualize what ANOVA does?
It seems the ship has already sailed in terms of an answer, but I think that if this is an introductory course that most of the displays offered here are going to be too difficult to grasp for introductory students... or at the very least too difficult to grasp without an introductory ... | How to visualize what ANOVA does?
It seems the ship has already sailed in terms of an answer, but I think that if this is an introductory course that most of the displays offered here are going to be too difficult to grasp for introdu |
3,410 | Interpreting Residual and Null Deviance in GLM R | Let LL = loglikelihood
Here is a quick summary of what you see from the summary(glm.fit) output,
Null Deviance = 2(LL(Saturated Model) - LL(Null Model)) on df = df_Sat - df_Null
Residual Deviance = 2(LL(Saturated Model) - LL(Proposed Model)) df = df_Sat - df_Proposed
The Saturated Model is a model that assumes each da... | Interpreting Residual and Null Deviance in GLM R | Let LL = loglikelihood
Here is a quick summary of what you see from the summary(glm.fit) output,
Null Deviance = 2(LL(Saturated Model) - LL(Null Model)) on df = df_Sat - df_Null
Residual Deviance = 2 | Interpreting Residual and Null Deviance in GLM R
Let LL = loglikelihood
Here is a quick summary of what you see from the summary(glm.fit) output,
Null Deviance = 2(LL(Saturated Model) - LL(Null Model)) on df = df_Sat - df_Null
Residual Deviance = 2(LL(Saturated Model) - LL(Proposed Model)) df = df_Sat - df_Proposed
Th... | Interpreting Residual and Null Deviance in GLM R
Let LL = loglikelihood
Here is a quick summary of what you see from the summary(glm.fit) output,
Null Deviance = 2(LL(Saturated Model) - LL(Null Model)) on df = df_Sat - df_Null
Residual Deviance = 2 |
3,411 | Interpreting Residual and Null Deviance in GLM R | The null deviance shows how well the response is predicted by the model with nothing but an intercept.
The residual deviance shows how well the response is predicted by the model when the predictors are included. From your example, it can be seen that the deviance goes up by 3443.3 when 22 predictor variables are added... | Interpreting Residual and Null Deviance in GLM R | The null deviance shows how well the response is predicted by the model with nothing but an intercept.
The residual deviance shows how well the response is predicted by the model when the predictors a | Interpreting Residual and Null Deviance in GLM R
The null deviance shows how well the response is predicted by the model with nothing but an intercept.
The residual deviance shows how well the response is predicted by the model when the predictors are included. From your example, it can be seen that the deviance goes u... | Interpreting Residual and Null Deviance in GLM R
The null deviance shows how well the response is predicted by the model with nothing but an intercept.
The residual deviance shows how well the response is predicted by the model when the predictors a |
3,412 | Interpreting Residual and Null Deviance in GLM R | While both answers given here are correct (and really useful resources), from page 432 of Introduction to Linear Regression Analysis (Montgomery, Peck, Vining, 5E), a general rule of thumb is given as if
$$
\frac{D}{n-p} >> 1,
$$
where $p$ is the number of regressors, $n$ is the number of observations and $D$ is the ... | Interpreting Residual and Null Deviance in GLM R | While both answers given here are correct (and really useful resources), from page 432 of Introduction to Linear Regression Analysis (Montgomery, Peck, Vining, 5E), a general rule of thumb is given as | Interpreting Residual and Null Deviance in GLM R
While both answers given here are correct (and really useful resources), from page 432 of Introduction to Linear Regression Analysis (Montgomery, Peck, Vining, 5E), a general rule of thumb is given as if
$$
\frac{D}{n-p} >> 1,
$$
where $p$ is the number of regressors, ... | Interpreting Residual and Null Deviance in GLM R
While both answers given here are correct (and really useful resources), from page 432 of Introduction to Linear Regression Analysis (Montgomery, Peck, Vining, 5E), a general rule of thumb is given as |
3,413 | Questions about how random effects are specified in lmer | I'm going to describe what model each of your calls to lmer() fits and how they are different and then answer your final question about selecting random effects.
Each of your three models contain fixed effects for practice, context and the interaction between the two. The random effects differ between the models.
lme... | Questions about how random effects are specified in lmer | I'm going to describe what model each of your calls to lmer() fits and how they are different and then answer your final question about selecting random effects.
Each of your three models contain fix | Questions about how random effects are specified in lmer
I'm going to describe what model each of your calls to lmer() fits and how they are different and then answer your final question about selecting random effects.
Each of your three models contain fixed effects for practice, context and the interaction between th... | Questions about how random effects are specified in lmer
I'm going to describe what model each of your calls to lmer() fits and how they are different and then answer your final question about selecting random effects.
Each of your three models contain fix |
3,414 | Questions about how random effects are specified in lmer | @Macro has given a good answer here, I just want to add one small point. If some people in your situation are using:
lmer(ERPindex ~ practice*context + (practice|participants) +
(practice|participants:context), data=base)
I suspect they are making a mistake. Consider: (practice|participants) mean... | Questions about how random effects are specified in lmer | @Macro has given a good answer here, I just want to add one small point. If some people in your situation are using:
lmer(ERPindex ~ practice*context + (practice|participants) +
(p | Questions about how random effects are specified in lmer
@Macro has given a good answer here, I just want to add one small point. If some people in your situation are using:
lmer(ERPindex ~ practice*context + (practice|participants) +
(practice|participants:context), data=base)
I suspect they are ... | Questions about how random effects are specified in lmer
@Macro has given a good answer here, I just want to add one small point. If some people in your situation are using:
lmer(ERPindex ~ practice*context + (practice|participants) +
(p |
3,415 | Questions about how random effects are specified in lmer | In a random effects or mixed effects model, a random effect is used when you want to treat the effect that you observed as if it were drawn from some probability distribution of effects.
One of the best examples I can give is when modeling clinical trial data from a multicentered clinical trial. A site (or center) effe... | Questions about how random effects are specified in lmer | In a random effects or mixed effects model, a random effect is used when you want to treat the effect that you observed as if it were drawn from some probability distribution of effects.
One of the be | Questions about how random effects are specified in lmer
In a random effects or mixed effects model, a random effect is used when you want to treat the effect that you observed as if it were drawn from some probability distribution of effects.
One of the best examples I can give is when modeling clinical trial data fro... | Questions about how random effects are specified in lmer
In a random effects or mixed effects model, a random effect is used when you want to treat the effect that you observed as if it were drawn from some probability distribution of effects.
One of the be |
3,416 | How does one interpret SVM feature weights? | For a general kernel it is difficult to interpret the SVM weights, however for the linear SVM there actually is a useful interpretation:
1) Recall that in linear SVM, the result is a hyperplane that separates the classes as best as possible. The weights represent this hyperplane, by giving you the coordinates of a vect... | How does one interpret SVM feature weights? | For a general kernel it is difficult to interpret the SVM weights, however for the linear SVM there actually is a useful interpretation:
1) Recall that in linear SVM, the result is a hyperplane that s | How does one interpret SVM feature weights?
For a general kernel it is difficult to interpret the SVM weights, however for the linear SVM there actually is a useful interpretation:
1) Recall that in linear SVM, the result is a hyperplane that separates the classes as best as possible. The weights represent this hyperpl... | How does one interpret SVM feature weights?
For a general kernel it is difficult to interpret the SVM weights, however for the linear SVM there actually is a useful interpretation:
1) Recall that in linear SVM, the result is a hyperplane that s |
3,417 | How does one interpret SVM feature weights? | I am trying to interpret the variable weights given by fitting a linear SVM.
A good way to understand how the weights are calculated and how to interpret them in the case of linear SVM is to perform the calculations by hand on a very simple example.
Example
Consider the following dataset which is linearly separable
i... | How does one interpret SVM feature weights? | I am trying to interpret the variable weights given by fitting a linear SVM.
A good way to understand how the weights are calculated and how to interpret them in the case of linear SVM is to perform | How does one interpret SVM feature weights?
I am trying to interpret the variable weights given by fitting a linear SVM.
A good way to understand how the weights are calculated and how to interpret them in the case of linear SVM is to perform the calculations by hand on a very simple example.
Example
Consider the fol... | How does one interpret SVM feature weights?
I am trying to interpret the variable weights given by fitting a linear SVM.
A good way to understand how the weights are calculated and how to interpret them in the case of linear SVM is to perform |
3,418 | How does one interpret SVM feature weights? | The documentation is pretty complete: for the multiclass case, SVC which is based on the libsvm library uses the one-vs-one setting. In the case of a linear kernel, n_classes * (n_classes - 1) / 2 individual linear binary models are fitted for each possible class pair. Hence the aggregate shape of all the primal parame... | How does one interpret SVM feature weights? | The documentation is pretty complete: for the multiclass case, SVC which is based on the libsvm library uses the one-vs-one setting. In the case of a linear kernel, n_classes * (n_classes - 1) / 2 ind | How does one interpret SVM feature weights?
The documentation is pretty complete: for the multiclass case, SVC which is based on the libsvm library uses the one-vs-one setting. In the case of a linear kernel, n_classes * (n_classes - 1) / 2 individual linear binary models are fitted for each possible class pair. Hence ... | How does one interpret SVM feature weights?
The documentation is pretty complete: for the multiclass case, SVC which is based on the libsvm library uses the one-vs-one setting. In the case of a linear kernel, n_classes * (n_classes - 1) / 2 ind |
3,419 | How does one interpret SVM feature weights? | Check this paper on feature selection. The authors use square of weights (of attributes) as assigned by a linear kernel SVM as ranking metric for deciding the relevance of a particular attribute. This is one of the highly cited ways of selecting genes from microarray data. | How does one interpret SVM feature weights? | Check this paper on feature selection. The authors use square of weights (of attributes) as assigned by a linear kernel SVM as ranking metric for deciding the relevance of a particular attribute. This | How does one interpret SVM feature weights?
Check this paper on feature selection. The authors use square of weights (of attributes) as assigned by a linear kernel SVM as ranking metric for deciding the relevance of a particular attribute. This is one of the highly cited ways of selecting genes from microarray data. | How does one interpret SVM feature weights?
Check this paper on feature selection. The authors use square of weights (of attributes) as assigned by a linear kernel SVM as ranking metric for deciding the relevance of a particular attribute. This |
3,420 | How does one interpret SVM feature weights? | A great paper by Guyon and Elisseeff (2003). An introduction to variable and feature selection. Journal of machine learning research, 1157-1182 says:
"Constructing and selecting subsets of features that are useful to build a good predictor contrasts with the problem of finding or ranking all potentially relevant variab... | How does one interpret SVM feature weights? | A great paper by Guyon and Elisseeff (2003). An introduction to variable and feature selection. Journal of machine learning research, 1157-1182 says:
"Constructing and selecting subsets of features th | How does one interpret SVM feature weights?
A great paper by Guyon and Elisseeff (2003). An introduction to variable and feature selection. Journal of machine learning research, 1157-1182 says:
"Constructing and selecting subsets of features that are useful to build a good predictor contrasts with the problem of findin... | How does one interpret SVM feature weights?
A great paper by Guyon and Elisseeff (2003). An introduction to variable and feature selection. Journal of machine learning research, 1157-1182 says:
"Constructing and selecting subsets of features th |
3,421 | Why doesn't Random Forest handle missing values in predictors? | Gradient Boosting Trees uses CART trees (in a standard setup, as it was proposed by its authors). CART trees are also used in Random Forests. What @user777 said is true, that RF trees handles missing values either by imputation with average, either by rough average/mode, either by an averaging/mode based on proximities... | Why doesn't Random Forest handle missing values in predictors? | Gradient Boosting Trees uses CART trees (in a standard setup, as it was proposed by its authors). CART trees are also used in Random Forests. What @user777 said is true, that RF trees handles missing | Why doesn't Random Forest handle missing values in predictors?
Gradient Boosting Trees uses CART trees (in a standard setup, as it was proposed by its authors). CART trees are also used in Random Forests. What @user777 said is true, that RF trees handles missing values either by imputation with average, either by rough... | Why doesn't Random Forest handle missing values in predictors?
Gradient Boosting Trees uses CART trees (in a standard setup, as it was proposed by its authors). CART trees are also used in Random Forests. What @user777 said is true, that RF trees handles missing |
3,422 | Why doesn't Random Forest handle missing values in predictors? | "What are [the] theoretical reasons [for RF] to not handle missing values? Gradient boosting machines, regression trees handle missing values. Why doesn't Random Forest do that?"
RF does handle missing values, just not in the same way that CART and other similar decision tree algorithms do. User777 correctly describes... | Why doesn't Random Forest handle missing values in predictors? | "What are [the] theoretical reasons [for RF] to not handle missing values? Gradient boosting machines, regression trees handle missing values. Why doesn't Random Forest do that?"
RF does handle missi | Why doesn't Random Forest handle missing values in predictors?
"What are [the] theoretical reasons [for RF] to not handle missing values? Gradient boosting machines, regression trees handle missing values. Why doesn't Random Forest do that?"
RF does handle missing values, just not in the same way that CART and other s... | Why doesn't Random Forest handle missing values in predictors?
"What are [the] theoretical reasons [for RF] to not handle missing values? Gradient boosting machines, regression trees handle missing values. Why doesn't Random Forest do that?"
RF does handle missi |
3,423 | Why doesn't Random Forest handle missing values in predictors? | Random forest does handle missing data and there are two distinct ways
it does so:
1) Without imputation of missing data, but providing inference.
2) Imputing the data. Imputed data is then used for inference.
Both methods are implemented in my R-package randomForestSRC
(co-written with Udaya Kogalur). First, it is i... | Why doesn't Random Forest handle missing values in predictors? | Random forest does handle missing data and there are two distinct ways
it does so:
1) Without imputation of missing data, but providing inference.
2) Imputing the data. Imputed data is then used for | Why doesn't Random Forest handle missing values in predictors?
Random forest does handle missing data and there are two distinct ways
it does so:
1) Without imputation of missing data, but providing inference.
2) Imputing the data. Imputed data is then used for inference.
Both methods are implemented in my R-package r... | Why doesn't Random Forest handle missing values in predictors?
Random forest does handle missing data and there are two distinct ways
it does so:
1) Without imputation of missing data, but providing inference.
2) Imputing the data. Imputed data is then used for |
3,424 | Why doesn't Random Forest handle missing values in predictors? | Recursive partitioning uses surrogate splits based on non-missing predictors that are correlated with the predictor possessing the missing value for an observation. It would seem possible in theory for random forests to be implemented that use the same idea. I don't know if any random forest software has done so. | Why doesn't Random Forest handle missing values in predictors? | Recursive partitioning uses surrogate splits based on non-missing predictors that are correlated with the predictor possessing the missing value for an observation. It would seem possible in theory f | Why doesn't Random Forest handle missing values in predictors?
Recursive partitioning uses surrogate splits based on non-missing predictors that are correlated with the predictor possessing the missing value for an observation. It would seem possible in theory for random forests to be implemented that use the same ide... | Why doesn't Random Forest handle missing values in predictors?
Recursive partitioning uses surrogate splits based on non-missing predictors that are correlated with the predictor possessing the missing value for an observation. It would seem possible in theory f |
3,425 | Why doesn't Random Forest handle missing values in predictors? | Random Forest has two methods for handling missing values, according to Leo Breiman and Adele Cutler, who invented it.
The first is quick and dirty: it just fills in the median value for continuous variables, or the most common non-missing value by class.
The second method fills in missing values, then runs RF, then fo... | Why doesn't Random Forest handle missing values in predictors? | Random Forest has two methods for handling missing values, according to Leo Breiman and Adele Cutler, who invented it.
The first is quick and dirty: it just fills in the median value for continuous va | Why doesn't Random Forest handle missing values in predictors?
Random Forest has two methods for handling missing values, according to Leo Breiman and Adele Cutler, who invented it.
The first is quick and dirty: it just fills in the median value for continuous variables, or the most common non-missing value by class.
T... | Why doesn't Random Forest handle missing values in predictors?
Random Forest has two methods for handling missing values, according to Leo Breiman and Adele Cutler, who invented it.
The first is quick and dirty: it just fills in the median value for continuous va |
3,426 | Why doesn't Random Forest handle missing values in predictors? | For CART, you can apply the missing-in-attributes (MIA) approach. That is, for categorical predictors, you code missing as a separate category. For numerical predictors, you create two new variables for every variable with missings: one where you code missings as -Inf and one where you code missings as +Inf. Then you a... | Why doesn't Random Forest handle missing values in predictors? | For CART, you can apply the missing-in-attributes (MIA) approach. That is, for categorical predictors, you code missing as a separate category. For numerical predictors, you create two new variables f | Why doesn't Random Forest handle missing values in predictors?
For CART, you can apply the missing-in-attributes (MIA) approach. That is, for categorical predictors, you code missing as a separate category. For numerical predictors, you create two new variables for every variable with missings: one where you code missi... | Why doesn't Random Forest handle missing values in predictors?
For CART, you can apply the missing-in-attributes (MIA) approach. That is, for categorical predictors, you code missing as a separate category. For numerical predictors, you create two new variables f |
3,427 | Why doesn't Random Forest handle missing values in predictors? | Instead of using median values, etc., I would highly recommend looking at the missRanger package (currently in development on Github) or the R package missForest). Both of these packages use random forests to first impute your data using a method similar to multiple imputation via chained equations (MICE). This would b... | Why doesn't Random Forest handle missing values in predictors? | Instead of using median values, etc., I would highly recommend looking at the missRanger package (currently in development on Github) or the R package missForest). Both of these packages use random fo | Why doesn't Random Forest handle missing values in predictors?
Instead of using median values, etc., I would highly recommend looking at the missRanger package (currently in development on Github) or the R package missForest). Both of these packages use random forests to first impute your data using a method similar to... | Why doesn't Random Forest handle missing values in predictors?
Instead of using median values, etc., I would highly recommend looking at the missRanger package (currently in development on Github) or the R package missForest). Both of these packages use random fo |
3,428 | Why on average does each bootstrap sample contain roughly two thirds of observations? | Essentially, the issue is to show that $\lim_{n\to\infty}(1- 1/n)^n=e^{-1}$
(and of course, $e^{-1} =1/e \approx 1/3$, at least very roughly).
It doesn't work at very small $n$ -- e.g. at $n=2$, $(1- 1/n)^n=\frac{1}{4}$. It passes $\frac{1}{3}$ at $n=6$, passes $0.35$ at $n=11$, and $0.366$ by $n=99$. Once you go beyon... | Why on average does each bootstrap sample contain roughly two thirds of observations? | Essentially, the issue is to show that $\lim_{n\to\infty}(1- 1/n)^n=e^{-1}$
(and of course, $e^{-1} =1/e \approx 1/3$, at least very roughly).
It doesn't work at very small $n$ -- e.g. at $n=2$, $(1- | Why on average does each bootstrap sample contain roughly two thirds of observations?
Essentially, the issue is to show that $\lim_{n\to\infty}(1- 1/n)^n=e^{-1}$
(and of course, $e^{-1} =1/e \approx 1/3$, at least very roughly).
It doesn't work at very small $n$ -- e.g. at $n=2$, $(1- 1/n)^n=\frac{1}{4}$. It passes $\f... | Why on average does each bootstrap sample contain roughly two thirds of observations?
Essentially, the issue is to show that $\lim_{n\to\infty}(1- 1/n)^n=e^{-1}$
(and of course, $e^{-1} =1/e \approx 1/3$, at least very roughly).
It doesn't work at very small $n$ -- e.g. at $n=2$, $(1- |
3,429 | Why on average does each bootstrap sample contain roughly two thirds of observations? | More precisely, each bootstrap sample (or bagged tree) will contain $1-\frac{1}{e} \approx 0.632$ of the sample.
Let's go over how the bootstrap works. We have an original sample $x_1, x_2, \ldots x_n$ with $n$ items in it. We draw items with replacement from this original set until we have another set of size $n$.
Fr... | Why on average does each bootstrap sample contain roughly two thirds of observations? | More precisely, each bootstrap sample (or bagged tree) will contain $1-\frac{1}{e} \approx 0.632$ of the sample.
Let's go over how the bootstrap works. We have an original sample $x_1, x_2, \ldots x_ | Why on average does each bootstrap sample contain roughly two thirds of observations?
More precisely, each bootstrap sample (or bagged tree) will contain $1-\frac{1}{e} \approx 0.632$ of the sample.
Let's go over how the bootstrap works. We have an original sample $x_1, x_2, \ldots x_n$ with $n$ items in it. We draw i... | Why on average does each bootstrap sample contain roughly two thirds of observations?
More precisely, each bootstrap sample (or bagged tree) will contain $1-\frac{1}{e} \approx 0.632$ of the sample.
Let's go over how the bootstrap works. We have an original sample $x_1, x_2, \ldots x_ |
3,430 | Why on average does each bootstrap sample contain roughly two thirds of observations? | Sampling with replacement can be modeled as a sequence of binomial trials where "success" is an instance being selected. For an original dataset of $n$ instances, the probability of "success" is $1/n$, and the probability of "failure" is $(n-1)/n$. For a sample size of $b$, the odds of selecting an instance exactly $x... | Why on average does each bootstrap sample contain roughly two thirds of observations? | Sampling with replacement can be modeled as a sequence of binomial trials where "success" is an instance being selected. For an original dataset of $n$ instances, the probability of "success" is $1/n$ | Why on average does each bootstrap sample contain roughly two thirds of observations?
Sampling with replacement can be modeled as a sequence of binomial trials where "success" is an instance being selected. For an original dataset of $n$ instances, the probability of "success" is $1/n$, and the probability of "failure"... | Why on average does each bootstrap sample contain roughly two thirds of observations?
Sampling with replacement can be modeled as a sequence of binomial trials where "success" is an instance being selected. For an original dataset of $n$ instances, the probability of "success" is $1/n$ |
3,431 | Why on average does each bootstrap sample contain roughly two thirds of observations? | Just adding to @retsreg's answer this can also be demonstrated quite easily via numerical simulation in R:
N <- 1e7 # number of instances and sample size
bootstrap <- sample(c(1:N), N, replace = TRUE)
round((length(unique(bootstrap))) / N, 3)
## [1] 0.632 | Why on average does each bootstrap sample contain roughly two thirds of observations? | Just adding to @retsreg's answer this can also be demonstrated quite easily via numerical simulation in R:
N <- 1e7 # number of instances and sample size
bootstrap <- sample(c(1:N), N, replace = TRUE) | Why on average does each bootstrap sample contain roughly two thirds of observations?
Just adding to @retsreg's answer this can also be demonstrated quite easily via numerical simulation in R:
N <- 1e7 # number of instances and sample size
bootstrap <- sample(c(1:N), N, replace = TRUE)
round((length(unique(bootstrap)))... | Why on average does each bootstrap sample contain roughly two thirds of observations?
Just adding to @retsreg's answer this can also be demonstrated quite easily via numerical simulation in R:
N <- 1e7 # number of instances and sample size
bootstrap <- sample(c(1:N), N, replace = TRUE) |
3,432 | Why on average does each bootstrap sample contain roughly two thirds of observations? | If you want to look deeper into the sample coverage of the bootstrap, it is worth noting that simple-random-sampling with replacement gives an "occupancy number" that follows the classical occupancy distribution (see e.g., O'Neill 2019). Suppose we have an original sample containing $n$ data points and we take a boots... | Why on average does each bootstrap sample contain roughly two thirds of observations? | If you want to look deeper into the sample coverage of the bootstrap, it is worth noting that simple-random-sampling with replacement gives an "occupancy number" that follows the classical occupancy d | Why on average does each bootstrap sample contain roughly two thirds of observations?
If you want to look deeper into the sample coverage of the bootstrap, it is worth noting that simple-random-sampling with replacement gives an "occupancy number" that follows the classical occupancy distribution (see e.g., O'Neill 201... | Why on average does each bootstrap sample contain roughly two thirds of observations?
If you want to look deeper into the sample coverage of the bootstrap, it is worth noting that simple-random-sampling with replacement gives an "occupancy number" that follows the classical occupancy d |
3,433 | Why on average does each bootstrap sample contain roughly two thirds of observations? | This can be easily seen by counting. How many total possible samples? n^n. How many NOT containing a specific value? (n-1)^n. Probability of a sample not having a specific value - (1-1/n)^n, which is about 1/3 in the limit. | Why on average does each bootstrap sample contain roughly two thirds of observations? | This can be easily seen by counting. How many total possible samples? n^n. How many NOT containing a specific value? (n-1)^n. Probability of a sample not having a specific value - (1-1/n)^n, which is | Why on average does each bootstrap sample contain roughly two thirds of observations?
This can be easily seen by counting. How many total possible samples? n^n. How many NOT containing a specific value? (n-1)^n. Probability of a sample not having a specific value - (1-1/n)^n, which is about 1/3 in the limit. | Why on average does each bootstrap sample contain roughly two thirds of observations?
This can be easily seen by counting. How many total possible samples? n^n. How many NOT containing a specific value? (n-1)^n. Probability of a sample not having a specific value - (1-1/n)^n, which is |
3,434 | What is the difference in Bayesian estimate and maximum likelihood estimate? | It is a very broad question and my answer here only begins to scratch the surface a bit. I will use the Bayes's rule to explain the concepts.
Let’s assume that a set of probability distribution parameters, $\theta$, best explains the dataset $D$. We may wish to estimate the parameters $\theta$ with the help of the Ba... | What is the difference in Bayesian estimate and maximum likelihood estimate? | It is a very broad question and my answer here only begins to scratch the surface a bit. I will use the Bayes's rule to explain the concepts.
Let’s assume that a set of probability distribution param | What is the difference in Bayesian estimate and maximum likelihood estimate?
It is a very broad question and my answer here only begins to scratch the surface a bit. I will use the Bayes's rule to explain the concepts.
Let’s assume that a set of probability distribution parameters, $\theta$, best explains the dataset... | What is the difference in Bayesian estimate and maximum likelihood estimate?
It is a very broad question and my answer here only begins to scratch the surface a bit. I will use the Bayes's rule to explain the concepts.
Let’s assume that a set of probability distribution param |
3,435 | What is the difference in Bayesian estimate and maximum likelihood estimate? | I think you're talking about point estimation as in parametric inference, so that we can assume a parametric probability model for a data generating mechanism but the actual value of the parameter is unknown.
Maximum likelihood estimation refers to using a probability model for data and optimizing the joint likelihood ... | What is the difference in Bayesian estimate and maximum likelihood estimate? | I think you're talking about point estimation as in parametric inference, so that we can assume a parametric probability model for a data generating mechanism but the actual value of the parameter is | What is the difference in Bayesian estimate and maximum likelihood estimate?
I think you're talking about point estimation as in parametric inference, so that we can assume a parametric probability model for a data generating mechanism but the actual value of the parameter is unknown.
Maximum likelihood estimation refe... | What is the difference in Bayesian estimate and maximum likelihood estimate?
I think you're talking about point estimation as in parametric inference, so that we can assume a parametric probability model for a data generating mechanism but the actual value of the parameter is |
3,436 | What is the difference in Bayesian estimate and maximum likelihood estimate? | The Bayesian estimate is Bayesian inference while the MLE is a type of frequentist inference method.
According to the Bayesian inference, $f(x_1,...,x_n; \theta) = \frac{f(\theta; x_1,...,x_n) * f(x_1,...,x_n)}{f(\theta)}$ holds, that is $likelihood = \frac{posterior * evidence}{prior}$. Notice that the maximum likelih... | What is the difference in Bayesian estimate and maximum likelihood estimate? | The Bayesian estimate is Bayesian inference while the MLE is a type of frequentist inference method.
According to the Bayesian inference, $f(x_1,...,x_n; \theta) = \frac{f(\theta; x_1,...,x_n) * f(x_1 | What is the difference in Bayesian estimate and maximum likelihood estimate?
The Bayesian estimate is Bayesian inference while the MLE is a type of frequentist inference method.
According to the Bayesian inference, $f(x_1,...,x_n; \theta) = \frac{f(\theta; x_1,...,x_n) * f(x_1,...,x_n)}{f(\theta)}$ holds, that is $like... | What is the difference in Bayesian estimate and maximum likelihood estimate?
The Bayesian estimate is Bayesian inference while the MLE is a type of frequentist inference method.
According to the Bayesian inference, $f(x_1,...,x_n; \theta) = \frac{f(\theta; x_1,...,x_n) * f(x_1 |
3,437 | What is the difference in Bayesian estimate and maximum likelihood estimate? | In principle the difference is precisely 0 - asymptotically speaking :) | What is the difference in Bayesian estimate and maximum likelihood estimate? | In principle the difference is precisely 0 - asymptotically speaking :) | What is the difference in Bayesian estimate and maximum likelihood estimate?
In principle the difference is precisely 0 - asymptotically speaking :) | What is the difference in Bayesian estimate and maximum likelihood estimate?
In principle the difference is precisely 0 - asymptotically speaking :) |
3,438 | Is it true that the percentile bootstrap should never be used? | There are some difficulties that are common to all nonparametric bootstrapping estimates of confidence intervals (CI), some that are more of an issue with both the "empirical" (called "basic" in the boot.ci() function of the R boot package and in Ref. 1) and the "percentile" CI estimates (as described in Ref. 2), and s... | Is it true that the percentile bootstrap should never be used? | There are some difficulties that are common to all nonparametric bootstrapping estimates of confidence intervals (CI), some that are more of an issue with both the "empirical" (called "basic" in the b | Is it true that the percentile bootstrap should never be used?
There are some difficulties that are common to all nonparametric bootstrapping estimates of confidence intervals (CI), some that are more of an issue with both the "empirical" (called "basic" in the boot.ci() function of the R boot package and in Ref. 1) an... | Is it true that the percentile bootstrap should never be used?
There are some difficulties that are common to all nonparametric bootstrapping estimates of confidence intervals (CI), some that are more of an issue with both the "empirical" (called "basic" in the b |
3,439 | Is it true that the percentile bootstrap should never be used? | Some comments on different terminology between MIT / Rice and Efron's book
I think that EdM's answer does a fantastic job in answering the OPs original question, in relation to the MIT lecture notes. However, the OP also quotes the book from Efrom (2016) Computer Age Statistical Inference which uses slightly different ... | Is it true that the percentile bootstrap should never be used? | Some comments on different terminology between MIT / Rice and Efron's book
I think that EdM's answer does a fantastic job in answering the OPs original question, in relation to the MIT lecture notes. | Is it true that the percentile bootstrap should never be used?
Some comments on different terminology between MIT / Rice and Efron's book
I think that EdM's answer does a fantastic job in answering the OPs original question, in relation to the MIT lecture notes. However, the OP also quotes the book from Efrom (2016) Co... | Is it true that the percentile bootstrap should never be used?
Some comments on different terminology between MIT / Rice and Efron's book
I think that EdM's answer does a fantastic job in answering the OPs original question, in relation to the MIT lecture notes. |
3,440 | Is it true that the percentile bootstrap should never be used? | I'm following your guideline: "Looking for an answer drawing from credible and/or official sources."
The bootstrap was invented by Brad Efron. I think it's fair to say that he's a distinguished statistician. It is a fact that he is a professor at Stanford. I think that makes his opinions credible and official.
I b... | Is it true that the percentile bootstrap should never be used? | I'm following your guideline: "Looking for an answer drawing from credible and/or official sources."
The bootstrap was invented by Brad Efron. I think it's fair to say that he's a distinguished stati | Is it true that the percentile bootstrap should never be used?
I'm following your guideline: "Looking for an answer drawing from credible and/or official sources."
The bootstrap was invented by Brad Efron. I think it's fair to say that he's a distinguished statistician. It is a fact that he is a professor at Stanford... | Is it true that the percentile bootstrap should never be used?
I'm following your guideline: "Looking for an answer drawing from credible and/or official sources."
The bootstrap was invented by Brad Efron. I think it's fair to say that he's a distinguished stati |
3,441 | Is it true that the percentile bootstrap should never be used? | As already noted in earlier replies, the "empirical bootstrap" is called "basic bootstrap" in other sources (including the R function boot.ci), which is identical to the "percentile bootstrap" flipped at the point estimate. Venables and Ripley write ("Modern Applied Statstics with S", 4th ed., Springer, 2002, p. 136):
... | Is it true that the percentile bootstrap should never be used? | As already noted in earlier replies, the "empirical bootstrap" is called "basic bootstrap" in other sources (including the R function boot.ci), which is identical to the "percentile bootstrap" flipped | Is it true that the percentile bootstrap should never be used?
As already noted in earlier replies, the "empirical bootstrap" is called "basic bootstrap" in other sources (including the R function boot.ci), which is identical to the "percentile bootstrap" flipped at the point estimate. Venables and Ripley write ("Moder... | Is it true that the percentile bootstrap should never be used?
As already noted in earlier replies, the "empirical bootstrap" is called "basic bootstrap" in other sources (including the R function boot.ci), which is identical to the "percentile bootstrap" flipped |
3,442 | Is it true that the percentile bootstrap should never be used? | As noted in cdalitz's answer, the percentile bootstrap gives better confidence intervals than the empirical/basic bootstrap quite often. I'd now like to offer a justification as to why this is the case.
I'm unaware of a frequentist justification for the percentile bootstrap. However, the percentile bootstrap (or a clos... | Is it true that the percentile bootstrap should never be used? | As noted in cdalitz's answer, the percentile bootstrap gives better confidence intervals than the empirical/basic bootstrap quite often. I'd now like to offer a justification as to why this is the cas | Is it true that the percentile bootstrap should never be used?
As noted in cdalitz's answer, the percentile bootstrap gives better confidence intervals than the empirical/basic bootstrap quite often. I'd now like to offer a justification as to why this is the case.
I'm unaware of a frequentist justification for the per... | Is it true that the percentile bootstrap should never be used?
As noted in cdalitz's answer, the percentile bootstrap gives better confidence intervals than the empirical/basic bootstrap quite often. I'd now like to offer a justification as to why this is the cas |
3,443 | Data normalization and standardization in neural networks | A standard approach is to scale the inputs to have mean 0 and a variance of 1. Also linear decorrelation/whitening/pca helps a lot.
If you are interested in the tricks of the trade, I can recommend LeCun's efficient backprop paper. | Data normalization and standardization in neural networks | A standard approach is to scale the inputs to have mean 0 and a variance of 1. Also linear decorrelation/whitening/pca helps a lot.
If you are interested in the tricks of the trade, I can recommend Le | Data normalization and standardization in neural networks
A standard approach is to scale the inputs to have mean 0 and a variance of 1. Also linear decorrelation/whitening/pca helps a lot.
If you are interested in the tricks of the trade, I can recommend LeCun's efficient backprop paper. | Data normalization and standardization in neural networks
A standard approach is to scale the inputs to have mean 0 and a variance of 1. Also linear decorrelation/whitening/pca helps a lot.
If you are interested in the tricks of the trade, I can recommend Le |
3,444 | Data normalization and standardization in neural networks | 1- Min-max normalization retains the original distribution of scores except for a scaling factor and transforms all the scores into a common range [0, 1]. However, this method is not robust (i.e., the method is highly sensitive to outliers.
2- Standardization (Z-score normalization) The most commonly used technique, wh... | Data normalization and standardization in neural networks | 1- Min-max normalization retains the original distribution of scores except for a scaling factor and transforms all the scores into a common range [0, 1]. However, this method is not robust (i.e., the | Data normalization and standardization in neural networks
1- Min-max normalization retains the original distribution of scores except for a scaling factor and transforms all the scores into a common range [0, 1]. However, this method is not robust (i.e., the method is highly sensitive to outliers.
2- Standardization (Z... | Data normalization and standardization in neural networks
1- Min-max normalization retains the original distribution of scores except for a scaling factor and transforms all the scores into a common range [0, 1]. However, this method is not robust (i.e., the |
3,445 | Data normalization and standardization in neural networks | You could do
min-max normalization (Normalize inputs/targets to fall in the range [−1,1]), or
mean-standard deviation normalization (Normalize inputs/targets to have zero mean and unity variance/standard deviation) | Data normalization and standardization in neural networks | You could do
min-max normalization (Normalize inputs/targets to fall in the range [−1,1]), or
mean-standard deviation normalization (Normalize inputs/targets to have zero mean and unity variance/st | Data normalization and standardization in neural networks
You could do
min-max normalization (Normalize inputs/targets to fall in the range [−1,1]), or
mean-standard deviation normalization (Normalize inputs/targets to have zero mean and unity variance/standard deviation) | Data normalization and standardization in neural networks
You could do
min-max normalization (Normalize inputs/targets to fall in the range [−1,1]), or
mean-standard deviation normalization (Normalize inputs/targets to have zero mean and unity variance/st |
3,446 | Data normalization and standardization in neural networks | Rank guass scaler is a scikit-learn style transformer that scales numeric variables to normal distributions. Its based on rank transformation. First step is to assign a linspace to the sorted features from 0..1, then apply the inverse of error function ErfInv to shape them like gaussians, then I substract the mean.
Bin... | Data normalization and standardization in neural networks | Rank guass scaler is a scikit-learn style transformer that scales numeric variables to normal distributions. Its based on rank transformation. First step is to assign a linspace to the sorted features | Data normalization and standardization in neural networks
Rank guass scaler is a scikit-learn style transformer that scales numeric variables to normal distributions. Its based on rank transformation. First step is to assign a linspace to the sorted features from 0..1, then apply the inverse of error function ErfInv to... | Data normalization and standardization in neural networks
Rank guass scaler is a scikit-learn style transformer that scales numeric variables to normal distributions. Its based on rank transformation. First step is to assign a linspace to the sorted features |
3,447 | Data normalization and standardization in neural networks | If you are working in python, sklearn has a method for doing this using different techniques in their preprocessing module (plus a nifty pipeline feature, with an example in their docs):
import sklearn
# Normalize X, shape (n_samples, n_features)
X_norm = sklearn.preprocessing.normalize(X) | Data normalization and standardization in neural networks | If you are working in python, sklearn has a method for doing this using different techniques in their preprocessing module (plus a nifty pipeline feature, with an example in their docs):
import sklear | Data normalization and standardization in neural networks
If you are working in python, sklearn has a method for doing this using different techniques in their preprocessing module (plus a nifty pipeline feature, with an example in their docs):
import sklearn
# Normalize X, shape (n_samples, n_features)
X_norm = sklea... | Data normalization and standardization in neural networks
If you are working in python, sklearn has a method for doing this using different techniques in their preprocessing module (plus a nifty pipeline feature, with an example in their docs):
import sklear |
3,448 | Data normalization and standardization in neural networks | Well, [0,1] is the standard approach.
For Neural Networks, works best in the range 0-1.
Min-Max scaling (or Normalization) is the approach to follow.
Now on the outliers, in most scenarios we have to clip those, as outliers are not common, you don't want outliers to affect your model (unless Anomaly detection is the pr... | Data normalization and standardization in neural networks | Well, [0,1] is the standard approach.
For Neural Networks, works best in the range 0-1.
Min-Max scaling (or Normalization) is the approach to follow.
Now on the outliers, in most scenarios we have to | Data normalization and standardization in neural networks
Well, [0,1] is the standard approach.
For Neural Networks, works best in the range 0-1.
Min-Max scaling (or Normalization) is the approach to follow.
Now on the outliers, in most scenarios we have to clip those, as outliers are not common, you don't want outlier... | Data normalization and standardization in neural networks
Well, [0,1] is the standard approach.
For Neural Networks, works best in the range 0-1.
Min-Max scaling (or Normalization) is the approach to follow.
Now on the outliers, in most scenarios we have to |
3,449 | Data normalization and standardization in neural networks | "Accepted" is whatever works best for you -- then you accept it.
In my experience fitting a distribution from the Johnson family of distributions to each of the continuous features works well because the distributions are highly flexible and can transform most uni-modal features into standard normal distributions. I... | Data normalization and standardization in neural networks | "Accepted" is whatever works best for you -- then you accept it.
In my experience fitting a distribution from the Johnson family of distributions to each of the continuous features works well becaus | Data normalization and standardization in neural networks
"Accepted" is whatever works best for you -- then you accept it.
In my experience fitting a distribution from the Johnson family of distributions to each of the continuous features works well because the distributions are highly flexible and can transform most... | Data normalization and standardization in neural networks
"Accepted" is whatever works best for you -- then you accept it.
In my experience fitting a distribution from the Johnson family of distributions to each of the continuous features works well becaus |
3,450 | What is a contrast matrix? | In their nice answer, @Gus_est, undertook a mathematical explanation of the essence of the contrast coefficient matrix L (notated there a C). $\bf Lb=k$ is the fundamental formula for testing hypotheses in univariate general linear modeling (where $\bf b$ are parameters and $\bf k$ are estimable function representing a... | What is a contrast matrix? | In their nice answer, @Gus_est, undertook a mathematical explanation of the essence of the contrast coefficient matrix L (notated there a C). $\bf Lb=k$ is the fundamental formula for testing hypothes | What is a contrast matrix?
In their nice answer, @Gus_est, undertook a mathematical explanation of the essence of the contrast coefficient matrix L (notated there a C). $\bf Lb=k$ is the fundamental formula for testing hypotheses in univariate general linear modeling (where $\bf b$ are parameters and $\bf k$ are estima... | What is a contrast matrix?
In their nice answer, @Gus_est, undertook a mathematical explanation of the essence of the contrast coefficient matrix L (notated there a C). $\bf Lb=k$ is the fundamental formula for testing hypothes |
3,451 | What is a contrast matrix? | I'll use lower-case letters for vectors and upper-case letters for matrices.
In case of a linear model of the form:
$$
\mathbf{y}=\mathbf{X} \boldsymbol{\beta} + \boldsymbol{\varepsilon}
$$
where $\bf{X}$ is a $n \times (k+1)$ matrix of rank $k+1 \leq n$, and we assume $\boldsymbol{\varepsilon} \sim \mathcal N(0,\sigma... | What is a contrast matrix? | I'll use lower-case letters for vectors and upper-case letters for matrices.
In case of a linear model of the form:
$$
\mathbf{y}=\mathbf{X} \boldsymbol{\beta} + \boldsymbol{\varepsilon}
$$
where $\bf | What is a contrast matrix?
I'll use lower-case letters for vectors and upper-case letters for matrices.
In case of a linear model of the form:
$$
\mathbf{y}=\mathbf{X} \boldsymbol{\beta} + \boldsymbol{\varepsilon}
$$
where $\bf{X}$ is a $n \times (k+1)$ matrix of rank $k+1 \leq n$, and we assume $\boldsymbol{\varepsilo... | What is a contrast matrix?
I'll use lower-case letters for vectors and upper-case letters for matrices.
In case of a linear model of the form:
$$
\mathbf{y}=\mathbf{X} \boldsymbol{\beta} + \boldsymbol{\varepsilon}
$$
where $\bf |
3,452 | What is a contrast matrix? | "Contrast matrix" is not a standard term in the statistical literature. It can have [at least] two related by distinct meanings:
A matrix specifying a particular null hypothesis in an ANOVA regression (unrelated to the coding scheme), where each row is a contrast. This is not a standard usage of the term. I used full... | What is a contrast matrix? | "Contrast matrix" is not a standard term in the statistical literature. It can have [at least] two related by distinct meanings:
A matrix specifying a particular null hypothesis in an ANOVA regressio | What is a contrast matrix?
"Contrast matrix" is not a standard term in the statistical literature. It can have [at least] two related by distinct meanings:
A matrix specifying a particular null hypothesis in an ANOVA regression (unrelated to the coding scheme), where each row is a contrast. This is not a standard usa... | What is a contrast matrix?
"Contrast matrix" is not a standard term in the statistical literature. It can have [at least] two related by distinct meanings:
A matrix specifying a particular null hypothesis in an ANOVA regressio |
3,453 | What is a contrast matrix? | A contrast compares two groups by comparing their difference with zero.
In a contrast matrix the rows are the contrasts and must add to zero, the columns are the groups. For example:
Let's say you have 4 groups A,B,C,D that you want to compare, then the contrast matrix would be:
Group: A B C D
A vs B: 1 -1 0 0
C... | What is a contrast matrix? | A contrast compares two groups by comparing their difference with zero.
In a contrast matrix the rows are the contrasts and must add to zero, the columns are the groups. For example:
Let's say you ha | What is a contrast matrix?
A contrast compares two groups by comparing their difference with zero.
In a contrast matrix the rows are the contrasts and must add to zero, the columns are the groups. For example:
Let's say you have 4 groups A,B,C,D that you want to compare, then the contrast matrix would be:
Group: A ... | What is a contrast matrix?
A contrast compares two groups by comparing their difference with zero.
In a contrast matrix the rows are the contrasts and must add to zero, the columns are the groups. For example:
Let's say you ha |
3,454 | What is a contrast matrix? | I wanted to add some more basic information to the previous (great) responses, and clarify a little (also for myself) how contrast coding works in R, and why we need to calculate the inverse of the contrast coding matrix to understand which comparisons are performed.
I'll start with the description of the linear model ... | What is a contrast matrix? | I wanted to add some more basic information to the previous (great) responses, and clarify a little (also for myself) how contrast coding works in R, and why we need to calculate the inverse of the co | What is a contrast matrix?
I wanted to add some more basic information to the previous (great) responses, and clarify a little (also for myself) how contrast coding works in R, and why we need to calculate the inverse of the contrast coding matrix to understand which comparisons are performed.
I'll start with the descr... | What is a contrast matrix?
I wanted to add some more basic information to the previous (great) responses, and clarify a little (also for myself) how contrast coding works in R, and why we need to calculate the inverse of the co |
3,455 | What is the difference between a partial likelihood, profile likelihood and marginal likelihood? | The likelihood function usually depends on many parameters. Depending on the application, we are usually interested in only a subset of these parameters. For example, in linear regression, interest typically lies in the slope coefficients and not on the error variance.
Denote the parameters we are interested in as $\b... | What is the difference between a partial likelihood, profile likelihood and marginal likelihood? | The likelihood function usually depends on many parameters. Depending on the application, we are usually interested in only a subset of these parameters. For example, in linear regression, interest ty | What is the difference between a partial likelihood, profile likelihood and marginal likelihood?
The likelihood function usually depends on many parameters. Depending on the application, we are usually interested in only a subset of these parameters. For example, in linear regression, interest typically lies in the slo... | What is the difference between a partial likelihood, profile likelihood and marginal likelihood?
The likelihood function usually depends on many parameters. Depending on the application, we are usually interested in only a subset of these parameters. For example, in linear regression, interest ty |
3,456 | What is the difference between a partial likelihood, profile likelihood and marginal likelihood? | All three are used when dealing with nuisance parameters in the completely specified likelihood function.
The marginal likelihood is the primary method to eliminate nuisance parameters in theory. It's a true likelihood function (i.e. it's proportional to the (marginal) probability of the observed data).
The partial... | What is the difference between a partial likelihood, profile likelihood and marginal likelihood? | All three are used when dealing with nuisance parameters in the completely specified likelihood function.
The marginal likelihood is the primary method to eliminate nuisance parameters in theory. | What is the difference between a partial likelihood, profile likelihood and marginal likelihood?
All three are used when dealing with nuisance parameters in the completely specified likelihood function.
The marginal likelihood is the primary method to eliminate nuisance parameters in theory. It's a true likelihood ... | What is the difference between a partial likelihood, profile likelihood and marginal likelihood?
All three are used when dealing with nuisance parameters in the completely specified likelihood function.
The marginal likelihood is the primary method to eliminate nuisance parameters in theory. |
3,457 | What does orthogonal mean in the context of statistics? | It means they [the random variables X,Y] are 'independent' to each other. Independent random variables are often considered to be at 'right angles' to each other, where by 'right angles' is meant that the inner product of the two is 0 (an equivalent condition from linear algebra).
For example on the X-Y plane the X ... | What does orthogonal mean in the context of statistics? | It means they [the random variables X,Y] are 'independent' to each other. Independent random variables are often considered to be at 'right angles' to each other, where by 'right angles' is meant tha | What does orthogonal mean in the context of statistics?
It means they [the random variables X,Y] are 'independent' to each other. Independent random variables are often considered to be at 'right angles' to each other, where by 'right angles' is meant that the inner product of the two is 0 (an equivalent condition fro... | What does orthogonal mean in the context of statistics?
It means they [the random variables X,Y] are 'independent' to each other. Independent random variables are often considered to be at 'right angles' to each other, where by 'right angles' is meant tha |
3,458 | What does orthogonal mean in the context of statistics? | I can't make a comment because I don't have enough points, so I'm forced to speak my mind as an answer, please forgive me. From the little I know, I disagree with the selected answer by @crazyjoe because orthogonality is defined as
$$E[XY^{\star}] = 0$$
So:
If $Y=X^2$ with symmetric pdf they they are dependent yet or... | What does orthogonal mean in the context of statistics? | I can't make a comment because I don't have enough points, so I'm forced to speak my mind as an answer, please forgive me. From the little I know, I disagree with the selected answer by @crazyjoe bec | What does orthogonal mean in the context of statistics?
I can't make a comment because I don't have enough points, so I'm forced to speak my mind as an answer, please forgive me. From the little I know, I disagree with the selected answer by @crazyjoe because orthogonality is defined as
$$E[XY^{\star}] = 0$$
So:
If $... | What does orthogonal mean in the context of statistics?
I can't make a comment because I don't have enough points, so I'm forced to speak my mind as an answer, please forgive me. From the little I know, I disagree with the selected answer by @crazyjoe bec |
3,459 | What does orthogonal mean in the context of statistics? | If X and Y are independent then they are Orthogonal. But the converse is not true as pointed out by the clever example of user497804. For the exact definitions refer to
Orthogonal :
Complex-valued random variables $C_1$ and $C_2$ are called orthogonal if they satisfy ${\rm cov}(C_1,C_2)=0$
(Pg 376, Probability and Ran... | What does orthogonal mean in the context of statistics? | If X and Y are independent then they are Orthogonal. But the converse is not true as pointed out by the clever example of user497804. For the exact definitions refer to
Orthogonal :
Complex-valued ra | What does orthogonal mean in the context of statistics?
If X and Y are independent then they are Orthogonal. But the converse is not true as pointed out by the clever example of user497804. For the exact definitions refer to
Orthogonal :
Complex-valued random variables $C_1$ and $C_2$ are called orthogonal if they sat... | What does orthogonal mean in the context of statistics?
If X and Y are independent then they are Orthogonal. But the converse is not true as pointed out by the clever example of user497804. For the exact definitions refer to
Orthogonal :
Complex-valued ra |
3,460 | What does orthogonal mean in the context of statistics? | @Mien already provided an answer, and, as pointed out by @whuber, orthogonal means uncorrelated. However, I really wish people would provide some references. You might consider the following links helpful since they explain the concept of correlation from a geometric perspective.
The Geometry of Vectors (see p. 7)
Lin... | What does orthogonal mean in the context of statistics? | @Mien already provided an answer, and, as pointed out by @whuber, orthogonal means uncorrelated. However, I really wish people would provide some references. You might consider the following links hel | What does orthogonal mean in the context of statistics?
@Mien already provided an answer, and, as pointed out by @whuber, orthogonal means uncorrelated. However, I really wish people would provide some references. You might consider the following links helpful since they explain the concept of correlation from a geomet... | What does orthogonal mean in the context of statistics?
@Mien already provided an answer, and, as pointed out by @whuber, orthogonal means uncorrelated. However, I really wish people would provide some references. You might consider the following links hel |
3,461 | What does orthogonal mean in the context of statistics? | A NIST website (ref below) defines orthogonal as follows, "An experimental design is orthogonal if the effects of any factor balance out (sum to zero) across the effects of the other factors."
In statistical deisgn, I understand orthogonal to mean "not cofounded" or "not aliased". This is important when designing and ... | What does orthogonal mean in the context of statistics? | A NIST website (ref below) defines orthogonal as follows, "An experimental design is orthogonal if the effects of any factor balance out (sum to zero) across the effects of the other factors."
In sta | What does orthogonal mean in the context of statistics?
A NIST website (ref below) defines orthogonal as follows, "An experimental design is orthogonal if the effects of any factor balance out (sum to zero) across the effects of the other factors."
In statistical deisgn, I understand orthogonal to mean "not cofounded"... | What does orthogonal mean in the context of statistics?
A NIST website (ref below) defines orthogonal as follows, "An experimental design is orthogonal if the effects of any factor balance out (sum to zero) across the effects of the other factors."
In sta |
3,462 | What does orthogonal mean in the context of statistics? | It's most likely they mean 'unrelated' if they say 'orthogonal'; if two factors are orthogonal (e.g. in factor analysis), they are unrelated, their correlation is zero. | What does orthogonal mean in the context of statistics? | It's most likely they mean 'unrelated' if they say 'orthogonal'; if two factors are orthogonal (e.g. in factor analysis), they are unrelated, their correlation is zero. | What does orthogonal mean in the context of statistics?
It's most likely they mean 'unrelated' if they say 'orthogonal'; if two factors are orthogonal (e.g. in factor analysis), they are unrelated, their correlation is zero. | What does orthogonal mean in the context of statistics?
It's most likely they mean 'unrelated' if they say 'orthogonal'; if two factors are orthogonal (e.g. in factor analysis), they are unrelated, their correlation is zero. |
3,463 | What does orthogonal mean in the context of statistics? | I asked a similar question What is the relationship between orthogonality and the expectation of the product of RVs, and I reproduce the answer here. Although orthogonality is a concept from Linear Algebra, and it means that the dot-product of two vectors is zero, the term is sometimes loosely used in statistics and me... | What does orthogonal mean in the context of statistics? | I asked a similar question What is the relationship between orthogonality and the expectation of the product of RVs, and I reproduce the answer here. Although orthogonality is a concept from Linear Al | What does orthogonal mean in the context of statistics?
I asked a similar question What is the relationship between orthogonality and the expectation of the product of RVs, and I reproduce the answer here. Although orthogonality is a concept from Linear Algebra, and it means that the dot-product of two vectors is zero,... | What does orthogonal mean in the context of statistics?
I asked a similar question What is the relationship between orthogonality and the expectation of the product of RVs, and I reproduce the answer here. Although orthogonality is a concept from Linear Al |
3,464 | What does orthogonal mean in the context of statistics? | According to https://web.archive.org/web/20160705135417/http://terpconnect.umd.edu/~bmomen/BIOM621/LineardepCorrOrthogonal.pdf, linear independency is a necessary condition for orthogonality or uncorrelatedness. But there are finer distinctions, in particular, orthogonality is not uncorrelatedness. | What does orthogonal mean in the context of statistics? | According to https://web.archive.org/web/20160705135417/http://terpconnect.umd.edu/~bmomen/BIOM621/LineardepCorrOrthogonal.pdf, linear independency is a necessary condition for orthogonality or uncorr | What does orthogonal mean in the context of statistics?
According to https://web.archive.org/web/20160705135417/http://terpconnect.umd.edu/~bmomen/BIOM621/LineardepCorrOrthogonal.pdf, linear independency is a necessary condition for orthogonality or uncorrelatedness. But there are finer distinctions, in particular, ort... | What does orthogonal mean in the context of statistics?
According to https://web.archive.org/web/20160705135417/http://terpconnect.umd.edu/~bmomen/BIOM621/LineardepCorrOrthogonal.pdf, linear independency is a necessary condition for orthogonality or uncorr |
3,465 | What does orthogonal mean in the context of statistics? | In econometrics, the orthogonality assumption means the expected value of the sum of all errors is 0. All variables of a regressor is orthogonal to their current error terms.
Mathematically, the orthogonality assumption is $E(x_{i}·ε_{i}) = 0$.
In simpler terms, it means a regressor is "perpendicular" to the error term... | What does orthogonal mean in the context of statistics? | In econometrics, the orthogonality assumption means the expected value of the sum of all errors is 0. All variables of a regressor is orthogonal to their current error terms.
Mathematically, the ortho | What does orthogonal mean in the context of statistics?
In econometrics, the orthogonality assumption means the expected value of the sum of all errors is 0. All variables of a regressor is orthogonal to their current error terms.
Mathematically, the orthogonality assumption is $E(x_{i}·ε_{i}) = 0$.
In simpler terms, i... | What does orthogonal mean in the context of statistics?
In econometrics, the orthogonality assumption means the expected value of the sum of all errors is 0. All variables of a regressor is orthogonal to their current error terms.
Mathematically, the ortho |
3,466 | What does orthogonal mean in the context of statistics? | Assume a random process x(t), hence y1=cos(x(t)) and y2= sin(x(t)), both are random processes. It is clear that y1 is orthogonal on y2, i.e., E[y1.y2] = 0. However, indeed they are dependent on each other. Actually, both are based on the same random process. Therefore, it is not necessary for orthogonal processes to be... | What does orthogonal mean in the context of statistics? | Assume a random process x(t), hence y1=cos(x(t)) and y2= sin(x(t)), both are random processes. It is clear that y1 is orthogonal on y2, i.e., E[y1.y2] = 0. However, indeed they are dependent on each o | What does orthogonal mean in the context of statistics?
Assume a random process x(t), hence y1=cos(x(t)) and y2= sin(x(t)), both are random processes. It is clear that y1 is orthogonal on y2, i.e., E[y1.y2] = 0. However, indeed they are dependent on each other. Actually, both are based on the same random process. There... | What does orthogonal mean in the context of statistics?
Assume a random process x(t), hence y1=cos(x(t)) and y2= sin(x(t)), both are random processes. It is clear that y1 is orthogonal on y2, i.e., E[y1.y2] = 0. However, indeed they are dependent on each o |
3,467 | What does orthogonal mean in the context of statistics? | The related random variables mean the variables say X and Y can have any relationship; may be linear or non-linear. The independence and orthogonal properties are the same if the two variables are linearly related. | What does orthogonal mean in the context of statistics? | The related random variables mean the variables say X and Y can have any relationship; may be linear or non-linear. The independence and orthogonal properties are the same if the two variables are lin | What does orthogonal mean in the context of statistics?
The related random variables mean the variables say X and Y can have any relationship; may be linear or non-linear. The independence and orthogonal properties are the same if the two variables are linearly related. | What does orthogonal mean in the context of statistics?
The related random variables mean the variables say X and Y can have any relationship; may be linear or non-linear. The independence and orthogonal properties are the same if the two variables are lin |
3,468 | What does orthogonal mean in the context of statistics? | Two or more IV's unrelated (independent) to one another but both having an influence on the DV. Each IV separately contributes a distinct value to the outcome , while both or all IV's also contribute in an additive fashion in the prediction of income (orthogonal=non-intersecting IV's influence on a DV). IV's are non-c... | What does orthogonal mean in the context of statistics? | Two or more IV's unrelated (independent) to one another but both having an influence on the DV. Each IV separately contributes a distinct value to the outcome , while both or all IV's also contribute | What does orthogonal mean in the context of statistics?
Two or more IV's unrelated (independent) to one another but both having an influence on the DV. Each IV separately contributes a distinct value to the outcome , while both or all IV's also contribute in an additive fashion in the prediction of income (orthogonal=... | What does orthogonal mean in the context of statistics?
Two or more IV's unrelated (independent) to one another but both having an influence on the DV. Each IV separately contributes a distinct value to the outcome , while both or all IV's also contribute |
3,469 | Efficient online linear regression | Maindonald describes a sequential method based on Givens rotations. (A Givens rotation is an orthogonal transformation of two vectors that zeros out a given entry in one of the vectors.) At the previous step you have decomposed the design matrix $\mathbf{X}$ into a triangular matrix $\mathbf{T}$ via an orthogonal tra... | Efficient online linear regression | Maindonald describes a sequential method based on Givens rotations. (A Givens rotation is an orthogonal transformation of two vectors that zeros out a given entry in one of the vectors.) At the prev | Efficient online linear regression
Maindonald describes a sequential method based on Givens rotations. (A Givens rotation is an orthogonal transformation of two vectors that zeros out a given entry in one of the vectors.) At the previous step you have decomposed the design matrix $\mathbf{X}$ into a triangular matrix... | Efficient online linear regression
Maindonald describes a sequential method based on Givens rotations. (A Givens rotation is an orthogonal transformation of two vectors that zeros out a given entry in one of the vectors.) At the prev |
3,470 | Efficient online linear regression | I think recasting your linear regression model into a state-space model will give you what you are after. If you use R, you may want to use package dlm
and have a look at the companion book by Petris et al. | Efficient online linear regression | I think recasting your linear regression model into a state-space model will give you what you are after. If you use R, you may want to use package dlm
and have a look at the companion book by Petris | Efficient online linear regression
I think recasting your linear regression model into a state-space model will give you what you are after. If you use R, you may want to use package dlm
and have a look at the companion book by Petris et al. | Efficient online linear regression
I think recasting your linear regression model into a state-space model will give you what you are after. If you use R, you may want to use package dlm
and have a look at the companion book by Petris |
3,471 | Efficient online linear regression | You can always just perform gradient descent on the sum of squares cost $E$ wrt the parameters of your model $W$. Just take the gradient of it but don't go for the closed form solution but only for the search direction instead.
Let $E(i; W)$ be the cost of the i'th training sample given the parameters $W$. Your updat... | Efficient online linear regression | You can always just perform gradient descent on the sum of squares cost $E$ wrt the parameters of your model $W$. Just take the gradient of it but don't go for the closed form solution but only for t | Efficient online linear regression
You can always just perform gradient descent on the sum of squares cost $E$ wrt the parameters of your model $W$. Just take the gradient of it but don't go for the closed form solution but only for the search direction instead.
Let $E(i; W)$ be the cost of the i'th training sample g... | Efficient online linear regression
You can always just perform gradient descent on the sum of squares cost $E$ wrt the parameters of your model $W$. Just take the gradient of it but don't go for the closed form solution but only for t |
3,472 | Efficient online linear regression | Surprised no one else touched on this so far. Linear regression has a quadratic objective function. So, a newton Raphson step from any starting point leads you straight to the optima. Now, let's say you already did your linear regression. The objective function is:
$$ L(\beta) = (y - X \beta)^t (y - X \beta) $$
The gra... | Efficient online linear regression | Surprised no one else touched on this so far. Linear regression has a quadratic objective function. So, a newton Raphson step from any starting point leads you straight to the optima. Now, let's say y | Efficient online linear regression
Surprised no one else touched on this so far. Linear regression has a quadratic objective function. So, a newton Raphson step from any starting point leads you straight to the optima. Now, let's say you already did your linear regression. The objective function is:
$$ L(\beta) = (y - ... | Efficient online linear regression
Surprised no one else touched on this so far. Linear regression has a quadratic objective function. So, a newton Raphson step from any starting point leads you straight to the optima. Now, let's say y |
3,473 | Efficient online linear regression | The standard least-square fit gives regression coefficients
$
\beta = ( X^T X )^{-1} X^T Y
$
where X is a matrix of M values for each of N data points, and is NXM in size. Y is a NX1 matrix of outputs. $\beta$ of course is a MX1 matrix of coefficients. (If you want an intercept just make one set of x's equal always to ... | Efficient online linear regression | The standard least-square fit gives regression coefficients
$
\beta = ( X^T X )^{-1} X^T Y
$
where X is a matrix of M values for each of N data points, and is NXM in size. Y is a NX1 matrix of outputs | Efficient online linear regression
The standard least-square fit gives regression coefficients
$
\beta = ( X^T X )^{-1} X^T Y
$
where X is a matrix of M values for each of N data points, and is NXM in size. Y is a NX1 matrix of outputs. $\beta$ of course is a MX1 matrix of coefficients. (If you want an intercept just m... | Efficient online linear regression
The standard least-square fit gives regression coefficients
$
\beta = ( X^T X )^{-1} X^T Y
$
where X is a matrix of M values for each of N data points, and is NXM in size. Y is a NX1 matrix of outputs |
3,474 | Efficient online linear regression | The problem is more easily solved when you rewrite things a little bit:
Y = y
X = [x, 1 ]
then
Y = A*X
A one time-solution is found by calculating
V = X' * X
and
C = X' * Y
note the V should have size N-by-N and C a size of N-by-M.
The parameters you're looking for are then given by:
A = inv(V) * C
Since both V and C ... | Efficient online linear regression | The problem is more easily solved when you rewrite things a little bit:
Y = y
X = [x, 1 ]
then
Y = A*X
A one time-solution is found by calculating
V = X' * X
and
C = X' * Y
note the V should have siz | Efficient online linear regression
The problem is more easily solved when you rewrite things a little bit:
Y = y
X = [x, 1 ]
then
Y = A*X
A one time-solution is found by calculating
V = X' * X
and
C = X' * Y
note the V should have size N-by-N and C a size of N-by-M.
The parameters you're looking for are then given by:... | Efficient online linear regression
The problem is more easily solved when you rewrite things a little bit:
Y = y
X = [x, 1 ]
then
Y = A*X
A one time-solution is found by calculating
V = X' * X
and
C = X' * Y
note the V should have siz |
3,475 | Perform feature normalization before or within model validation? | Your approach is entirely correct. Although data transformations are often undervalued as "preprocessing", one cannot emphasize enough that transformations in order to optimize model performance can and should be treated as part of the model building process.
Reasoning: A model shall be applied on unseen data which is ... | Perform feature normalization before or within model validation? | Your approach is entirely correct. Although data transformations are often undervalued as "preprocessing", one cannot emphasize enough that transformations in order to optimize model performance can a | Perform feature normalization before or within model validation?
Your approach is entirely correct. Although data transformations are often undervalued as "preprocessing", one cannot emphasize enough that transformations in order to optimize model performance can and should be treated as part of the model building proc... | Perform feature normalization before or within model validation?
Your approach is entirely correct. Although data transformations are often undervalued as "preprocessing", one cannot emphasize enough that transformations in order to optimize model performance can a |
3,476 | Perform feature normalization before or within model validation? | Feature normalization is to make different features in the same scale. The scaling speeds up gradient descent by avoiding many extra iterations that are required when one or more features take on much larger values than the rest(Without scaling, the cost function that is visualized will show a great asymmetry).
I thi... | Perform feature normalization before or within model validation? | Feature normalization is to make different features in the same scale. The scaling speeds up gradient descent by avoiding many extra iterations that are required when one or more features take on much | Perform feature normalization before or within model validation?
Feature normalization is to make different features in the same scale. The scaling speeds up gradient descent by avoiding many extra iterations that are required when one or more features take on much larger values than the rest(Without scaling, the cost ... | Perform feature normalization before or within model validation?
Feature normalization is to make different features in the same scale. The scaling speeds up gradient descent by avoiding many extra iterations that are required when one or more features take on much |
3,477 | Perform feature normalization before or within model validation? | The methodology you have described is sound as others have said. You should perform the exact same transformation on your test set features as you do on features from your training set.
I think it's worth adding that another reason for feature normalization is to enhance the performance of certain processes that are se... | Perform feature normalization before or within model validation? | The methodology you have described is sound as others have said. You should perform the exact same transformation on your test set features as you do on features from your training set.
I think it's w | Perform feature normalization before or within model validation?
The methodology you have described is sound as others have said. You should perform the exact same transformation on your test set features as you do on features from your training set.
I think it's worth adding that another reason for feature normalizati... | Perform feature normalization before or within model validation?
The methodology you have described is sound as others have said. You should perform the exact same transformation on your test set features as you do on features from your training set.
I think it's w |
3,478 | Perform feature normalization before or within model validation? | Let me illustrate as to why we have to do normalization only on training data set.Say we extract features of different characteristics of apples like length,breath of the bounding box surrounding the apples,color,etc.,Let's say we normalize the feature length on the whole data and we have got mean length as 7 cm and va... | Perform feature normalization before or within model validation? | Let me illustrate as to why we have to do normalization only on training data set.Say we extract features of different characteristics of apples like length,breath of the bounding box surrounding the | Perform feature normalization before or within model validation?
Let me illustrate as to why we have to do normalization only on training data set.Say we extract features of different characteristics of apples like length,breath of the bounding box surrounding the apples,color,etc.,Let's say we normalize the feature le... | Perform feature normalization before or within model validation?
Let me illustrate as to why we have to do normalization only on training data set.Say we extract features of different characteristics of apples like length,breath of the bounding box surrounding the |
3,479 | What is the effect of having correlated predictors in a multiple regression model? | The topic you are asking about is multicollinearity. You might want to read some of the threads on CV categorized under the multicollinearity tag. @whuber's answer linked above in particular is also worth your time.
The assertion that "if two predictors are correlated and both are included in a model, one will be ... | What is the effect of having correlated predictors in a multiple regression model? | The topic you are asking about is multicollinearity. You might want to read some of the threads on CV categorized under the multicollinearity tag. @whuber's answer linked above in particular is also | What is the effect of having correlated predictors in a multiple regression model?
The topic you are asking about is multicollinearity. You might want to read some of the threads on CV categorized under the multicollinearity tag. @whuber's answer linked above in particular is also worth your time.
The assertion th... | What is the effect of having correlated predictors in a multiple regression model?
The topic you are asking about is multicollinearity. You might want to read some of the threads on CV categorized under the multicollinearity tag. @whuber's answer linked above in particular is also |
3,480 | What is the effect of having correlated predictors in a multiple regression model? | This is more of comment, but I wanted to include a graph and some code.
I think the statement "if two predictors are correlated and both are included in a model, one will be insignificant" is false if you mean "only one." Binary statistical significance cannot be used for variable selection.
Here's my counterexample u... | What is the effect of having correlated predictors in a multiple regression model? | This is more of comment, but I wanted to include a graph and some code.
I think the statement "if two predictors are correlated and both are included in a model, one will be insignificant" is false if | What is the effect of having correlated predictors in a multiple regression model?
This is more of comment, but I wanted to include a graph and some code.
I think the statement "if two predictors are correlated and both are included in a model, one will be insignificant" is false if you mean "only one." Binary statisti... | What is the effect of having correlated predictors in a multiple regression model?
This is more of comment, but I wanted to include a graph and some code.
I think the statement "if two predictors are correlated and both are included in a model, one will be insignificant" is false if |
3,481 | What is the effect of having correlated predictors in a multiple regression model? | As @whuber noted, this is a complex question. However, the first sentence of your post is a vast simplification. It is often the case that two (or more) variables will be correlated and both related to the dependent variable. Whether they are significant or not depends on both effect size and cell size.
In your example... | What is the effect of having correlated predictors in a multiple regression model? | As @whuber noted, this is a complex question. However, the first sentence of your post is a vast simplification. It is often the case that two (or more) variables will be correlated and both related t | What is the effect of having correlated predictors in a multiple regression model?
As @whuber noted, this is a complex question. However, the first sentence of your post is a vast simplification. It is often the case that two (or more) variables will be correlated and both related to the dependent variable. Whether the... | What is the effect of having correlated predictors in a multiple regression model?
As @whuber noted, this is a complex question. However, the first sentence of your post is a vast simplification. It is often the case that two (or more) variables will be correlated and both related t |
3,482 | References containing arguments against null hypothesis significance testing? | Chris Fraley has taught a whole course on the history of the debate (the link seems to be broken, even though it's still on his official site; here is a copy in Internet Archive). His summary/conclusion is here (again, archived copy). According to Fraley's homepage, the last time he taught this course was in 2003.
He ... | References containing arguments against null hypothesis significance testing? | Chris Fraley has taught a whole course on the history of the debate (the link seems to be broken, even though it's still on his official site; here is a copy in Internet Archive). His summary/conclus | References containing arguments against null hypothesis significance testing?
Chris Fraley has taught a whole course on the history of the debate (the link seems to be broken, even though it's still on his official site; here is a copy in Internet Archive). His summary/conclusion is here (again, archived copy). Accord... | References containing arguments against null hypothesis significance testing?
Chris Fraley has taught a whole course on the history of the debate (the link seems to be broken, even though it's still on his official site; here is a copy in Internet Archive). His summary/conclus |
3,483 | References containing arguments against null hypothesis significance testing? | These are excellent references. I have a perhaps useful handout at http://hbiostat.org/bayes | References containing arguments against null hypothesis significance testing? | These are excellent references. I have a perhaps useful handout at http://hbiostat.org/bayes | References containing arguments against null hypothesis significance testing?
These are excellent references. I have a perhaps useful handout at http://hbiostat.org/bayes | References containing arguments against null hypothesis significance testing?
These are excellent references. I have a perhaps useful handout at http://hbiostat.org/bayes |
3,484 | References containing arguments against null hypothesis significance testing? | 402 Citations Questioning the Indiscriminate Use of
Null Hypothesis Significance Tests in Observational Studies:
http://warnercnr.colostate.edu/~anderson/thompson1.html | References containing arguments against null hypothesis significance testing? | 402 Citations Questioning the Indiscriminate Use of
Null Hypothesis Significance Tests in Observational Studies:
http://warnercnr.colostate.edu/~anderson/thompson1.html | References containing arguments against null hypothesis significance testing?
402 Citations Questioning the Indiscriminate Use of
Null Hypothesis Significance Tests in Observational Studies:
http://warnercnr.colostate.edu/~anderson/thompson1.html | References containing arguments against null hypothesis significance testing?
402 Citations Questioning the Indiscriminate Use of
Null Hypothesis Significance Tests in Observational Studies:
http://warnercnr.colostate.edu/~anderson/thompson1.html |
3,485 | Why is the square root transformation recommended for count data? | The square root is approximately variance-stabilizing for the Poisson. There are a number of variations on the square root that improve the properties, such as adding $\frac{3}{8}$ before taking the square root, or the Freeman-Tukey ($\sqrt{X}+\sqrt{X+1}$ - though it's often adjusted for the mean as well).
In the plots... | Why is the square root transformation recommended for count data? | The square root is approximately variance-stabilizing for the Poisson. There are a number of variations on the square root that improve the properties, such as adding $\frac{3}{8}$ before taking the s | Why is the square root transformation recommended for count data?
The square root is approximately variance-stabilizing for the Poisson. There are a number of variations on the square root that improve the properties, such as adding $\frac{3}{8}$ before taking the square root, or the Freeman-Tukey ($\sqrt{X}+\sqrt{X+1}... | Why is the square root transformation recommended for count data?
The square root is approximately variance-stabilizing for the Poisson. There are a number of variations on the square root that improve the properties, such as adding $\frac{3}{8}$ before taking the s |
3,486 | Real-life examples of moving average processes | One very common cause is mis-specification. For example, let $y$ be grocery sales and $\varepsilon$ be an unobserved (to the analyst) coupon campaign that varies in intensity over time. At any point in time, there may be several "vintages" of coupons circulating as people use them, throw them away, and receive new ones... | Real-life examples of moving average processes | One very common cause is mis-specification. For example, let $y$ be grocery sales and $\varepsilon$ be an unobserved (to the analyst) coupon campaign that varies in intensity over time. At any point i | Real-life examples of moving average processes
One very common cause is mis-specification. For example, let $y$ be grocery sales and $\varepsilon$ be an unobserved (to the analyst) coupon campaign that varies in intensity over time. At any point in time, there may be several "vintages" of coupons circulating as people ... | Real-life examples of moving average processes
One very common cause is mis-specification. For example, let $y$ be grocery sales and $\varepsilon$ be an unobserved (to the analyst) coupon campaign that varies in intensity over time. At any point i |
3,487 | Real-life examples of moving average processes | Suppose you are producing some good, stockpiling some of it and selling the rest. Your production in time period $t$ is $x_t=m+\varepsilon_t$ with $\mathbb{E}(\varepsilon_t)=0$ and your stock is $y_t$. The sequence of $\varepsilon$s is i.i.d. A $1-\theta$ fraction of the period's production is sold during the next peri... | Real-life examples of moving average processes | Suppose you are producing some good, stockpiling some of it and selling the rest. Your production in time period $t$ is $x_t=m+\varepsilon_t$ with $\mathbb{E}(\varepsilon_t)=0$ and your stock is $y_t$ | Real-life examples of moving average processes
Suppose you are producing some good, stockpiling some of it and selling the rest. Your production in time period $t$ is $x_t=m+\varepsilon_t$ with $\mathbb{E}(\varepsilon_t)=0$ and your stock is $y_t$. The sequence of $\varepsilon$s is i.i.d. A $1-\theta$ fraction of the p... | Real-life examples of moving average processes
Suppose you are producing some good, stockpiling some of it and selling the rest. Your production in time period $t$ is $x_t=m+\varepsilon_t$ with $\mathbb{E}(\varepsilon_t)=0$ and your stock is $y_t$ |
3,488 | Real-life examples of moving average processes | in our article
Scaling portfolio volatility and calculating risk contributions in the presence of serial
cross-correlations we analyze a multivariate model of asset returns. Due to different closing times of the stock exchanges a dependence structure (by the covariance) appears. This dependence only holds for one peri... | Real-life examples of moving average processes | in our article
Scaling portfolio volatility and calculating risk contributions in the presence of serial
cross-correlations we analyze a multivariate model of asset returns. Due to different closing | Real-life examples of moving average processes
in our article
Scaling portfolio volatility and calculating risk contributions in the presence of serial
cross-correlations we analyze a multivariate model of asset returns. Due to different closing times of the stock exchanges a dependence structure (by the covariance) a... | Real-life examples of moving average processes
in our article
Scaling portfolio volatility and calculating risk contributions in the presence of serial
cross-correlations we analyze a multivariate model of asset returns. Due to different closing |
3,489 | Real-life examples of moving average processes | It is true that MA processes are more difficult to explain to users than AR processes. However they are very ubiquitous. The most common MA type of the process that you didn't know about is a low pass filter.
The active versions would be a "TREBLE" knob on your car stereo, or a tone control knob on your guitar.
Here'... | Real-life examples of moving average processes | It is true that MA processes are more difficult to explain to users than AR processes. However they are very ubiquitous. The most common MA type of the process that you didn't know about is a low pass | Real-life examples of moving average processes
It is true that MA processes are more difficult to explain to users than AR processes. However they are very ubiquitous. The most common MA type of the process that you didn't know about is a low pass filter.
The active versions would be a "TREBLE" knob on your car stereo... | Real-life examples of moving average processes
It is true that MA processes are more difficult to explain to users than AR processes. However they are very ubiquitous. The most common MA type of the process that you didn't know about is a low pass |
3,490 | Real-life examples of moving average processes | Consecutive multiple-step-ahead forecast errors from optimal forecasts will be MA processes.
For example, suppose the data generating process is a random walk: $X_t=X_{t-1}+\varepsilon_t$ where $\varepsilon_t\sim\text{i.i.d.}(0,\sigma_\varepsilon^2)$.
If you are at time $t$ predicting the value of the process at time $... | Real-life examples of moving average processes | Consecutive multiple-step-ahead forecast errors from optimal forecasts will be MA processes.
For example, suppose the data generating process is a random walk: $X_t=X_{t-1}+\varepsilon_t$ where $\vare | Real-life examples of moving average processes
Consecutive multiple-step-ahead forecast errors from optimal forecasts will be MA processes.
For example, suppose the data generating process is a random walk: $X_t=X_{t-1}+\varepsilon_t$ where $\varepsilon_t\sim\text{i.i.d.}(0,\sigma_\varepsilon^2)$.
If you are at time $t... | Real-life examples of moving average processes
Consecutive multiple-step-ahead forecast errors from optimal forecasts will be MA processes.
For example, suppose the data generating process is a random walk: $X_t=X_{t-1}+\varepsilon_t$ where $\vare |
3,491 | Real-life examples of moving average processes | Increments of cumulative processes measured over overlapping periods of time are MA processes when increments are i.i.d. If
$$
x_t=\sum_{\tau=0}^t\varepsilon_\tau
$$
where $\varepsilon_\tau\sim i.i.d.$, then
$$
(x_t-x_{t-s},x_{t+1}-x_{t+1-s},\dots)=(\sum_{\tau=s}^t\varepsilon_\tau,\sum_{\tau=s+1}^{t+1}\varepsilon_\tau,... | Real-life examples of moving average processes | Increments of cumulative processes measured over overlapping periods of time are MA processes when increments are i.i.d. If
$$
x_t=\sum_{\tau=0}^t\varepsilon_\tau
$$
where $\varepsilon_\tau\sim i.i.d. | Real-life examples of moving average processes
Increments of cumulative processes measured over overlapping periods of time are MA processes when increments are i.i.d. If
$$
x_t=\sum_{\tau=0}^t\varepsilon_\tau
$$
where $\varepsilon_\tau\sim i.i.d.$, then
$$
(x_t-x_{t-s},x_{t+1}-x_{t+1-s},\dots)=(\sum_{\tau=s}^t\varepsi... | Real-life examples of moving average processes
Increments of cumulative processes measured over overlapping periods of time are MA processes when increments are i.i.d. If
$$
x_t=\sum_{\tau=0}^t\varepsilon_\tau
$$
where $\varepsilon_\tau\sim i.i.d. |
3,492 | Why do neural networks need so many training examples to perform? | I caution against expecting strong resemblance between biological and artificial neural networks. I think the name "neural networks" is a bit dangerous, because it tricks people into expecting that neurological processes and machine learning should be the same. The differences between biological and artificial neural n... | Why do neural networks need so many training examples to perform? | I caution against expecting strong resemblance between biological and artificial neural networks. I think the name "neural networks" is a bit dangerous, because it tricks people into expecting that ne | Why do neural networks need so many training examples to perform?
I caution against expecting strong resemblance between biological and artificial neural networks. I think the name "neural networks" is a bit dangerous, because it tricks people into expecting that neurological processes and machine learning should be th... | Why do neural networks need so many training examples to perform?
I caution against expecting strong resemblance between biological and artificial neural networks. I think the name "neural networks" is a bit dangerous, because it tricks people into expecting that ne |
3,493 | Why do neural networks need so many training examples to perform? | First of all, at age two, a child knows a lot about the world and actively applies this knowledge. A child does a lot of "transfer learning" by applying this knowledge to new concepts.
Second, before seeing those five "labeled" examples of cars, a child sees a lot of cars on the street, on TV, toy cars, etc., so also a... | Why do neural networks need so many training examples to perform? | First of all, at age two, a child knows a lot about the world and actively applies this knowledge. A child does a lot of "transfer learning" by applying this knowledge to new concepts.
Second, before | Why do neural networks need so many training examples to perform?
First of all, at age two, a child knows a lot about the world and actively applies this knowledge. A child does a lot of "transfer learning" by applying this knowledge to new concepts.
Second, before seeing those five "labeled" examples of cars, a child ... | Why do neural networks need so many training examples to perform?
First of all, at age two, a child knows a lot about the world and actively applies this knowledge. A child does a lot of "transfer learning" by applying this knowledge to new concepts.
Second, before |
3,494 | Why do neural networks need so many training examples to perform? | One major aspect that I don't see in current answers is evolution.
A child's brain does not learn from scratch. It's similar to asking how deer and giraffe babies can walk a few minutes after birth. Because they are born with their brains already wired for this task. There is some fine-tuning needed of course, but the ... | Why do neural networks need so many training examples to perform? | One major aspect that I don't see in current answers is evolution.
A child's brain does not learn from scratch. It's similar to asking how deer and giraffe babies can walk a few minutes after birth. B | Why do neural networks need so many training examples to perform?
One major aspect that I don't see in current answers is evolution.
A child's brain does not learn from scratch. It's similar to asking how deer and giraffe babies can walk a few minutes after birth. Because they are born with their brains already wired f... | Why do neural networks need so many training examples to perform?
One major aspect that I don't see in current answers is evolution.
A child's brain does not learn from scratch. It's similar to asking how deer and giraffe babies can walk a few minutes after birth. B |
3,495 | Why do neural networks need so many training examples to perform? | I don't know much about neural networks but I know a fair bit about babies.
Many 2 year olds have a lot of issues with how general words should be. For instance, it is quite common at that age for kids to use "dog" for any four legged animal. That's a more difficult distinction than "car" - just think how different a p... | Why do neural networks need so many training examples to perform? | I don't know much about neural networks but I know a fair bit about babies.
Many 2 year olds have a lot of issues with how general words should be. For instance, it is quite common at that age for kid | Why do neural networks need so many training examples to perform?
I don't know much about neural networks but I know a fair bit about babies.
Many 2 year olds have a lot of issues with how general words should be. For instance, it is quite common at that age for kids to use "dog" for any four legged animal. That's a mo... | Why do neural networks need so many training examples to perform?
I don't know much about neural networks but I know a fair bit about babies.
Many 2 year olds have a lot of issues with how general words should be. For instance, it is quite common at that age for kid |
3,496 | Why do neural networks need so many training examples to perform? | This is an a fascinating question that I've pondered over a lot also, and can come up with a few explanations why.
Neural networks work nothing like the brain. Backpropagation is unique to neural networks, and does not happen in the brain. In that sense, we just don't know the general learning algorithm in our brains.... | Why do neural networks need so many training examples to perform? | This is an a fascinating question that I've pondered over a lot also, and can come up with a few explanations why.
Neural networks work nothing like the brain. Backpropagation is unique to neural net | Why do neural networks need so many training examples to perform?
This is an a fascinating question that I've pondered over a lot also, and can come up with a few explanations why.
Neural networks work nothing like the brain. Backpropagation is unique to neural networks, and does not happen in the brain. In that sense... | Why do neural networks need so many training examples to perform?
This is an a fascinating question that I've pondered over a lot also, and can come up with a few explanations why.
Neural networks work nothing like the brain. Backpropagation is unique to neural net |
3,497 | Why do neural networks need so many training examples to perform? | A human child at age 2 needs around 5 instances of a car to be able to identify it with reasonable accuracy regardless of color, make, etc.
The concept of "instances" gets easily muddied. While a child may have seen 5 unique instances of a car, they have actually seen thousands of thousands of frames, in many differi... | Why do neural networks need so many training examples to perform? | A human child at age 2 needs around 5 instances of a car to be able to identify it with reasonable accuracy regardless of color, make, etc.
The concept of "instances" gets easily muddied. While a ch | Why do neural networks need so many training examples to perform?
A human child at age 2 needs around 5 instances of a car to be able to identify it with reasonable accuracy regardless of color, make, etc.
The concept of "instances" gets easily muddied. While a child may have seen 5 unique instances of a car, they ha... | Why do neural networks need so many training examples to perform?
A human child at age 2 needs around 5 instances of a car to be able to identify it with reasonable accuracy regardless of color, make, etc.
The concept of "instances" gets easily muddied. While a ch |
3,498 | Why do neural networks need so many training examples to perform? | As pointed out by others, the data-efficiency of artificial neural networks varies quite substantially, depending on the details. As a matter of fact, there are many so called one-shot learning methods, that can solve the task of labelling trams with quite good accuracy, using only a single labelled sample.
One way to... | Why do neural networks need so many training examples to perform? | As pointed out by others, the data-efficiency of artificial neural networks varies quite substantially, depending on the details. As a matter of fact, there are many so called one-shot learning method | Why do neural networks need so many training examples to perform?
As pointed out by others, the data-efficiency of artificial neural networks varies quite substantially, depending on the details. As a matter of fact, there are many so called one-shot learning methods, that can solve the task of labelling trams with qui... | Why do neural networks need so many training examples to perform?
As pointed out by others, the data-efficiency of artificial neural networks varies quite substantially, depending on the details. As a matter of fact, there are many so called one-shot learning method |
3,499 | Why do neural networks need so many training examples to perform? | One thing that I haven't seen in the answers so far is the fact that one 'instance' of a real world object that is seen by a human child does not corresponds to an instance in the context of NN training.
Suppose you're standing at a railway intersection with a 5 year old child and watch 5 trains pass within 10 minutes... | Why do neural networks need so many training examples to perform? | One thing that I haven't seen in the answers so far is the fact that one 'instance' of a real world object that is seen by a human child does not corresponds to an instance in the context of NN traini | Why do neural networks need so many training examples to perform?
One thing that I haven't seen in the answers so far is the fact that one 'instance' of a real world object that is seen by a human child does not corresponds to an instance in the context of NN training.
Suppose you're standing at a railway intersection... | Why do neural networks need so many training examples to perform?
One thing that I haven't seen in the answers so far is the fact that one 'instance' of a real world object that is seen by a human child does not corresponds to an instance in the context of NN traini |
3,500 | Why do neural networks need so many training examples to perform? | One way to train a deep neural network is to treat it as a stack of auto-encoders (Restricted Boltzmann Machines).
In theory, an auto-encoder learns in an unsupervised manner: It takes arbitrary, unlabelled input data and processes it to generate output data. Then it takes that output data, and tries to regenerate it... | Why do neural networks need so many training examples to perform? | One way to train a deep neural network is to treat it as a stack of auto-encoders (Restricted Boltzmann Machines).
In theory, an auto-encoder learns in an unsupervised manner: It takes arbitrary, unl | Why do neural networks need so many training examples to perform?
One way to train a deep neural network is to treat it as a stack of auto-encoders (Restricted Boltzmann Machines).
In theory, an auto-encoder learns in an unsupervised manner: It takes arbitrary, unlabelled input data and processes it to generate output... | Why do neural networks need so many training examples to perform?
One way to train a deep neural network is to treat it as a stack of auto-encoders (Restricted Boltzmann Machines).
In theory, an auto-encoder learns in an unsupervised manner: It takes arbitrary, unl |
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