Help with Forward Stepwise Selection Algorithm
Below is a simplified forward stepwise selection algorithm and I am trying to understand the logic in step 2.
Algorithm:
- Let $M_0$ denote the null model, which contains no predictors. For
- For $k=0,....,p-1:$
- (a) Consider all $p-k$ models that augment the predictors in $M_k$ with one additional predictor.
- (b) Choose the best among these $p-k$ models, and call it $M_{k+1}$. Here best is defined as having smallest RSS or highest $R^2$.
- Select a single best model from among $M_0,....M_p$ using cross-validated prediction error, $C_p$ (AIC), BIC, or adjusted $R^2$.
In step 2(a), what is the significance of $p-k$? My understanding is since there are $p$ predictors, total number of possible models should be $2^p$. If we are iterating $k$, and in the first iteration where $k=0$, shouldn't we consider all the remaining models which would be $2^p-1$? Why are we considering $p-k$?
statistics machine-learning
asked Dec 3 '18 at 0:12
DoLare
112
add a comment |
Below is a simplified forward stepwise selection algorithm and I am trying to understand the logic in step 2.
Algorithm:
- Let $M_0$ denote the null model, which contains no predictors. For
- For $k=0,....,p-1:$
- (a) Consider all $p-k$ models that augment the predictors in $M_k$ with one additional predictor.
- (b) Choose the best among these $p-k$ models, and call it $M_{k+1}$. Here best is defined as having smallest RSS or highest $R^2$.
- Select a single best model from among $M_0,....M_p$ using cross-validated prediction error, $C_p$ (AIC), BIC, or adjusted $R^2$.
In step 2(a), what is the significance of $p-k$? My understanding is since there are $p$ predictors, total number of possible models should be $2^p$. If we are iterating $k$, and in the first iteration where $k=0$, shouldn't we consider all the remaining models which would be $2^p-1$? Why are we considering $p-k$?
statistics machine-learning
asked Dec 3 '18 at 0:12
DoLare
112
add a comment |
Below is a simplified forward stepwise selection algorithm and I am trying to understand the logic in step 2.
Algorithm:
- Let $M_0$ denote the null model, which contains no predictors. For
- For $k=0,....,p-1:$
- (a) Consider all $p-k$ models that augment the predictors in $M_k$ with one additional predictor.
- (b) Choose the best among these $p-k$ models, and call it $M_{k+1}$. Here best is defined as having smallest RSS or highest $R^2$.
- Select a single best model from among $M_0,....M_p$ using cross-validated prediction error, $C_p$ (AIC), BIC, or adjusted $R^2$.
In step 2(a), what is the significance of $p-k$? My understanding is since there are $p$ predictors, total number of possible models should be $2^p$. If we are iterating $k$, and in the first iteration where $k=0$, shouldn't we consider all the remaining models which would be $2^p-1$? Why are we considering $p-k$?
statistics machine-learning
asked Dec 3 '18 at 0:12
DoLare
112
Below is a simplified forward stepwise selection algorithm and I am trying to understand the logic in step 2.
Algorithm:
- Let $M_0$ denote the null model, which contains no predictors. For
- For $k=0,....,p-1:$
- (a) Consider all $p-k$ models that augment the predictors in $M_k$ with one additional predictor.
- (b) Choose the best among these $p-k$ models, and call it $M_{k+1}$. Here best is defined as having smallest RSS or highest $R^2$.
- Select a single best model from among $M_0,....M_p$ using cross-validated prediction error, $C_p$ (AIC), BIC, or adjusted $R^2$.
In step 2(a), what is the significance of $p-k$? My understanding is since there are $p$ predictors, total number of possible models should be $2^p$. If we are iterating $k$, and in the first iteration where $k=0$, shouldn't we consider all the remaining models which would be $2^p-1$? Why are we considering $p-k$?
statistics machine-learning
statistics machine-learning
asked Dec 3 '18 at 0:12
DoLare
112
asked Dec 3 '18 at 0:12
DoLare
112
asked Dec 3 '18 at 0:12
DoLare
112
asked Dec 3 '18 at 0:12
DoLare
112
asked Dec 3 '18 at 0:12
DoLare
112
112
add a comment |
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3023418%2fhelp-with-forward-stepwise-selection-algorithm%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3023418%2fhelp-with-forward-stepwise-selection-algorithm%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
