Algorithm for forward stepwise regression
$begingroup$
I am trying to implement the algorithm for forward stepwise selection following the book "Introduction to Statistical learning":
The steps listed in the book are:
Algorithm 6.2 Forward stepwise selection
1. Let M0 denote the null model, which contains no predictors.
2. For k = 0, . . . , p − 1:
(a) Consider all p − k models that augment the predictors in Mk
with one additional predictor.
(b) Choose the best among these p − k models, and call it Mk+1.
Here best is defined as having smallest RSS or highest R2.
3. Select a single best model from among M0, . . . ,Mp using crossvalidated
prediction error, Cp (AIC), BIC, or adjusted R2.
My question is I am not quite clear on whether or not cross validation should be used in step2. If so, why? or else why not?
regression cross-validation
asked Jan 21 at 4:57
southwindsouthwind
84
$endgroup$
add a comment |
$begingroup$
I am trying to implement the algorithm for forward stepwise selection following the book "Introduction to Statistical learning":
The steps listed in the book are:
Algorithm 6.2 Forward stepwise selection
1. Let M0 denote the null model, which contains no predictors.
2. For k = 0, . . . , p − 1:
(a) Consider all p − k models that augment the predictors in Mk
with one additional predictor.
(b) Choose the best among these p − k models, and call it Mk+1.
Here best is defined as having smallest RSS or highest R2.
3. Select a single best model from among M0, . . . ,Mp using crossvalidated
prediction error, Cp (AIC), BIC, or adjusted R2.
My question is I am not quite clear on whether or not cross validation should be used in step2. If so, why? or else why not?
regression cross-validation
asked Jan 21 at 4:57
southwindsouthwind
84
$endgroup$
add a comment |
$begingroup$
I am trying to implement the algorithm for forward stepwise selection following the book "Introduction to Statistical learning":
The steps listed in the book are:
Algorithm 6.2 Forward stepwise selection
1. Let M0 denote the null model, which contains no predictors.
2. For k = 0, . . . , p − 1:
(a) Consider all p − k models that augment the predictors in Mk
with one additional predictor.
(b) Choose the best among these p − k models, and call it Mk+1.
Here best is defined as having smallest RSS or highest R2.
3. Select a single best model from among M0, . . . ,Mp using crossvalidated
prediction error, Cp (AIC), BIC, or adjusted R2.
My question is I am not quite clear on whether or not cross validation should be used in step2. If so, why? or else why not?
regression cross-validation
asked Jan 21 at 4:57
southwindsouthwind
84
$endgroup$
I am trying to implement the algorithm for forward stepwise selection following the book "Introduction to Statistical learning":
The steps listed in the book are:
Algorithm 6.2 Forward stepwise selection
1. Let M0 denote the null model, which contains no predictors.
2. For k = 0, . . . , p − 1:
(a) Consider all p − k models that augment the predictors in Mk
with one additional predictor.
(b) Choose the best among these p − k models, and call it Mk+1.
Here best is defined as having smallest RSS or highest R2.
3. Select a single best model from among M0, . . . ,Mp using crossvalidated
prediction error, Cp (AIC), BIC, or adjusted R2.
My question is I am not quite clear on whether or not cross validation should be used in step2. If so, why? or else why not?
regression cross-validation
regression cross-validation
asked Jan 21 at 4:57
southwindsouthwind
84
asked Jan 21 at 4:57
southwindsouthwind
84
asked Jan 21 at 4:57
southwindsouthwind
84
asked Jan 21 at 4:57
southwindsouthwind
84
asked Jan 21 at 4:57
southwindsouthwind
84
84
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
best is defined as having smallest RSS or highest R2.
Cross-validation is not mentioned here, so per the text, you would simply choose the model based on in-sample RSS or $R^2$.
Overfitting is (hopefully) controlled by the cross-validation in step 3.
Of course, nothing keeps you from modifying the algorithm given in the book. Just note that you will then do a lot of cross-validation, since you would cross-validate $p-k$ models in each of $p$ iterations of step 2.
answered Jan 21 at 6:07
Stephan KolassaStephan Kolassa
46k695167
$endgroup$
$begingroup$
If I perform cross-validation in step 2, do I still need step 3 since I can just select the model with the smallest error from step 2?
$endgroup$
– southwind
Jan 21 at 6:39
$begingroup$
I would still do step 3. Even with cross-validation in step 2, adding another predictor may overfit. Note also that the result from step 2 is an entire collection of $p$ models with $0, dots, p-1$ predictors, and step 3 consists of choosing one of these models, for which you need some criterion, and cross-validation is a good one.
$endgroup$
– Stephan Kolassa
Jan 21 at 9:27
add a comment |
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$begingroup$
best is defined as having smallest RSS or highest R2.
Cross-validation is not mentioned here, so per the text, you would simply choose the model based on in-sample RSS or $R^2$.
Overfitting is (hopefully) controlled by the cross-validation in step 3.
Of course, nothing keeps you from modifying the algorithm given in the book. Just note that you will then do a lot of cross-validation, since you would cross-validate $p-k$ models in each of $p$ iterations of step 2.
answered Jan 21 at 6:07
Stephan KolassaStephan Kolassa
46k695167
$endgroup$
$begingroup$
If I perform cross-validation in step 2, do I still need step 3 since I can just select the model with the smallest error from step 2?
$endgroup$
– southwind
Jan 21 at 6:39
$begingroup$
I would still do step 3. Even with cross-validation in step 2, adding another predictor may overfit. Note also that the result from step 2 is an entire collection of $p$ models with $0, dots, p-1$ predictors, and step 3 consists of choosing one of these models, for which you need some criterion, and cross-validation is a good one.
$endgroup$
– Stephan Kolassa
Jan 21 at 9:27
add a comment |
$begingroup$
best is defined as having smallest RSS or highest R2.
Cross-validation is not mentioned here, so per the text, you would simply choose the model based on in-sample RSS or $R^2$.
Overfitting is (hopefully) controlled by the cross-validation in step 3.
Of course, nothing keeps you from modifying the algorithm given in the book. Just note that you will then do a lot of cross-validation, since you would cross-validate $p-k$ models in each of $p$ iterations of step 2.
answered Jan 21 at 6:07
Stephan KolassaStephan Kolassa
46k695167
$endgroup$
$begingroup$
If I perform cross-validation in step 2, do I still need step 3 since I can just select the model with the smallest error from step 2?
$endgroup$
– southwind
Jan 21 at 6:39
$begingroup$
I would still do step 3. Even with cross-validation in step 2, adding another predictor may overfit. Note also that the result from step 2 is an entire collection of $p$ models with $0, dots, p-1$ predictors, and step 3 consists of choosing one of these models, for which you need some criterion, and cross-validation is a good one.
$endgroup$
– Stephan Kolassa
Jan 21 at 9:27
add a comment |
$begingroup$
best is defined as having smallest RSS or highest R2.
Cross-validation is not mentioned here, so per the text, you would simply choose the model based on in-sample RSS or $R^2$.
Overfitting is (hopefully) controlled by the cross-validation in step 3.
Of course, nothing keeps you from modifying the algorithm given in the book. Just note that you will then do a lot of cross-validation, since you would cross-validate $p-k$ models in each of $p$ iterations of step 2.
answered Jan 21 at 6:07
Stephan KolassaStephan Kolassa
46k695167
$endgroup$
best is defined as having smallest RSS or highest R2.
Cross-validation is not mentioned here, so per the text, you would simply choose the model based on in-sample RSS or $R^2$.
Overfitting is (hopefully) controlled by the cross-validation in step 3.
Of course, nothing keeps you from modifying the algorithm given in the book. Just note that you will then do a lot of cross-validation, since you would cross-validate $p-k$ models in each of $p$ iterations of step 2.
answered Jan 21 at 6:07
Stephan KolassaStephan Kolassa
46k695167
answered Jan 21 at 6:07
Stephan KolassaStephan Kolassa
46k695167
answered Jan 21 at 6:07
Stephan KolassaStephan Kolassa
46k695167
answered Jan 21 at 6:07
Stephan KolassaStephan Kolassa
46k695167
46k695167
$begingroup$
If I perform cross-validation in step 2, do I still need step 3 since I can just select the model with the smallest error from step 2?
$endgroup$
– southwind
Jan 21 at 6:39
$begingroup$
I would still do step 3. Even with cross-validation in step 2, adding another predictor may overfit. Note also that the result from step 2 is an entire collection of $p$ models with $0, dots, p-1$ predictors, and step 3 consists of choosing one of these models, for which you need some criterion, and cross-validation is a good one.
$endgroup$
– Stephan Kolassa
Jan 21 at 9:27
add a comment |
$begingroup$
If I perform cross-validation in step 2, do I still need step 3 since I can just select the model with the smallest error from step 2?
$endgroup$
– southwind
Jan 21 at 6:39
$begingroup$
I would still do step 3. Even with cross-validation in step 2, adding another predictor may overfit. Note also that the result from step 2 is an entire collection of $p$ models with $0, dots, p-1$ predictors, and step 3 consists of choosing one of these models, for which you need some criterion, and cross-validation is a good one.
$endgroup$
– Stephan Kolassa
Jan 21 at 9:27
$begingroup$
If I perform cross-validation in step 2, do I still need step 3 since I can just select the model with the smallest error from step 2?
$endgroup$
– southwind
Jan 21 at 6:39
$begingroup$
If I perform cross-validation in step 2, do I still need step 3 since I can just select the model with the smallest error from step 2?
$endgroup$
– southwind
Jan 21 at 6:39
$begingroup$
I would still do step 3. Even with cross-validation in step 2, adding another predictor may overfit. Note also that the result from step 2 is an entire collection of $p$ models with $0, dots, p-1$ predictors, and step 3 consists of choosing one of these models, for which you need some criterion, and cross-validation is a good one.
$endgroup$
– Stephan Kolassa
Jan 21 at 9:27
$begingroup$
I would still do step 3. Even with cross-validation in step 2, adding another predictor may overfit. Note also that the result from step 2 is an entire collection of $p$ models with $0, dots, p-1$ predictors, and step 3 consists of choosing one of these models, for which you need some criterion, and cross-validation is a good one.
$endgroup$
– Stephan Kolassa
Jan 21 at 9:27
add a comment |
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