Can the alpha, lambda values of a glmnet object output determine whether ridge or Lasso?
$begingroup$
Given a glmnet object using train() where trControl method is "cv" and number of iterations is 5, I obtained that the bestTune alpha and lambda values are alpha=0.1 and lambda= 0.007688342. On running the glmnet object, I notice that the alpha values start from 0.1.
Can the inference here be that the method used is Lasso and not ridge because of the non-negative alpha value?
In general, can the values of alpha, lambda indicate which model is being used?
regression generalized-linear-model cross-validation caret
asked 4 hours ago
red4life93red4life93
161
New contributor
red4life93 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
Given a glmnet object using train() where trControl method is "cv" and number of iterations is 5, I obtained that the bestTune alpha and lambda values are alpha=0.1 and lambda= 0.007688342. On running the glmnet object, I notice that the alpha values start from 0.1.
Can the inference here be that the method used is Lasso and not ridge because of the non-negative alpha value?
In general, can the values of alpha, lambda indicate which model is being used?
regression generalized-linear-model cross-validation caret
asked 4 hours ago
red4life93red4life93
161
New contributor
red4life93 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
Given a glmnet object using train() where trControl method is "cv" and number of iterations is 5, I obtained that the bestTune alpha and lambda values are alpha=0.1 and lambda= 0.007688342. On running the glmnet object, I notice that the alpha values start from 0.1.
Can the inference here be that the method used is Lasso and not ridge because of the non-negative alpha value?
In general, can the values of alpha, lambda indicate which model is being used?
regression generalized-linear-model cross-validation caret
asked 4 hours ago
red4life93red4life93
161
New contributor
red4life93 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Given a glmnet object using train() where trControl method is "cv" and number of iterations is 5, I obtained that the bestTune alpha and lambda values are alpha=0.1 and lambda= 0.007688342. On running the glmnet object, I notice that the alpha values start from 0.1.
Can the inference here be that the method used is Lasso and not ridge because of the non-negative alpha value?
In general, can the values of alpha, lambda indicate which model is being used?
regression generalized-linear-model cross-validation caret
regression generalized-linear-model cross-validation caret
asked 4 hours ago
red4life93red4life93
161
New contributor
red4life93 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 4 hours ago
red4life93red4life93
161
New contributor
red4life93 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 4 hours ago
red4life93red4life93
161
New contributor
red4life93 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 4 hours ago
red4life93red4life93
161
asked 4 hours ago
red4life93red4life93
161
161
New contributor
red4life93 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
red4life93 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
red4life93 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
As far as I understand glmnet, $alpha=0$ would actually be a ridge penalty, and $alpha=1$ would be a Lasso penalty (rather than the other way around) and as far as glmnet is concerned you can fit those end cases.
The penalty with $alpha=0.1$ would be fairly similar to the ridge penalty but it is not the ridge penalty; if it's not considering $alpha$ below $0.1$ you can't necessarily infer much more than that just from the fact that you had that endpoint. If you know that an $alpha$ value that was only slightly larger was worse then it would be likely that a larger range might have chosen a smaller $alpha$, but it doesn't suggest it would have been $0$; I expect it would not. If the grid of values is coarse it may well have been that a larger value than $0.1$ would be better.
[You may want to check whether there was some other reason that $alpha$ might have been at an endpoint; e.g. I seem to recall $lambda$ got set to an endpoint in forecasting if coefficients for lambdaOpt were not saved.]
answered 4 hours ago
Glen_b♦Glen_b
213k22412762
$endgroup$
add a comment |
$begingroup$
Absolutely! The $alpha$ parameter can be adjusted to either fit a Lasso or a Ridge regression (or something in between). Recall that the loss function which Elastic Net minimizes is $$frac{1}{2N}sum^N_{i=1}(y_i-beta_0-x_i^tbeta)^2+lambdasum_{j=1}^p(frac{1}{2}(1-alpha)beta_j^2+alpha|beta_j|).$$
Focus on the second big sum (the one multiplied by $lambda$). If you let $alpha=1$, the first term inside this sum becomes $0$, and the whole function becomes exactly the function that Lasso minimizes (or the Lasso loss function). If you let $alpha=0$, the second term becomes $0$ and you are left with Ridge.
You can check the loss for Ridge and Lasso in this book and for elastic net in this paper.
answered 4 hours ago
BananinBananin
1795
$endgroup$
$begingroup$
This looks like a good answer but can you edit to include citations for the hyperlinks? Over time, links die.
$endgroup$
– Sycorax
4 hours ago
add a comment |
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: "65"
};
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: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
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
},
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
red4life93 is a new contributor. Be nice, and check out our Code of Conduct.
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%2fstats.stackexchange.com%2fquestions%2f396748%2fcan-the-alpha-lambda-values-of-a-glmnet-object-output-determine-whether-ridge-o%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
As far as I understand glmnet, $alpha=0$ would actually be a ridge penalty, and $alpha=1$ would be a Lasso penalty (rather than the other way around) and as far as glmnet is concerned you can fit those end cases.
The penalty with $alpha=0.1$ would be fairly similar to the ridge penalty but it is not the ridge penalty; if it's not considering $alpha$ below $0.1$ you can't necessarily infer much more than that just from the fact that you had that endpoint. If you know that an $alpha$ value that was only slightly larger was worse then it would be likely that a larger range might have chosen a smaller $alpha$, but it doesn't suggest it would have been $0$; I expect it would not. If the grid of values is coarse it may well have been that a larger value than $0.1$ would be better.
[You may want to check whether there was some other reason that $alpha$ might have been at an endpoint; e.g. I seem to recall $lambda$ got set to an endpoint in forecasting if coefficients for lambdaOpt were not saved.]
answered 4 hours ago
Glen_b♦Glen_b
213k22412762
$endgroup$
add a comment |
$begingroup$
As far as I understand glmnet, $alpha=0$ would actually be a ridge penalty, and $alpha=1$ would be a Lasso penalty (rather than the other way around) and as far as glmnet is concerned you can fit those end cases.
The penalty with $alpha=0.1$ would be fairly similar to the ridge penalty but it is not the ridge penalty; if it's not considering $alpha$ below $0.1$ you can't necessarily infer much more than that just from the fact that you had that endpoint. If you know that an $alpha$ value that was only slightly larger was worse then it would be likely that a larger range might have chosen a smaller $alpha$, but it doesn't suggest it would have been $0$; I expect it would not. If the grid of values is coarse it may well have been that a larger value than $0.1$ would be better.
[You may want to check whether there was some other reason that $alpha$ might have been at an endpoint; e.g. I seem to recall $lambda$ got set to an endpoint in forecasting if coefficients for lambdaOpt were not saved.]
answered 4 hours ago
Glen_b♦Glen_b
213k22412762
$endgroup$
add a comment |
$begingroup$
As far as I understand glmnet, $alpha=0$ would actually be a ridge penalty, and $alpha=1$ would be a Lasso penalty (rather than the other way around) and as far as glmnet is concerned you can fit those end cases.
The penalty with $alpha=0.1$ would be fairly similar to the ridge penalty but it is not the ridge penalty; if it's not considering $alpha$ below $0.1$ you can't necessarily infer much more than that just from the fact that you had that endpoint. If you know that an $alpha$ value that was only slightly larger was worse then it would be likely that a larger range might have chosen a smaller $alpha$, but it doesn't suggest it would have been $0$; I expect it would not. If the grid of values is coarse it may well have been that a larger value than $0.1$ would be better.
[You may want to check whether there was some other reason that $alpha$ might have been at an endpoint; e.g. I seem to recall $lambda$ got set to an endpoint in forecasting if coefficients for lambdaOpt were not saved.]
answered 4 hours ago
Glen_b♦Glen_b
213k22412762
$endgroup$
As far as I understand glmnet, $alpha=0$ would actually be a ridge penalty, and $alpha=1$ would be a Lasso penalty (rather than the other way around) and as far as glmnet is concerned you can fit those end cases.
The penalty with $alpha=0.1$ would be fairly similar to the ridge penalty but it is not the ridge penalty; if it's not considering $alpha$ below $0.1$ you can't necessarily infer much more than that just from the fact that you had that endpoint. If you know that an $alpha$ value that was only slightly larger was worse then it would be likely that a larger range might have chosen a smaller $alpha$, but it doesn't suggest it would have been $0$; I expect it would not. If the grid of values is coarse it may well have been that a larger value than $0.1$ would be better.
[You may want to check whether there was some other reason that $alpha$ might have been at an endpoint; e.g. I seem to recall $lambda$ got set to an endpoint in forecasting if coefficients for lambdaOpt were not saved.]
answered 4 hours ago
Glen_b♦Glen_b
213k22412762
edited 4 hours ago
answered 4 hours ago
Glen_b♦Glen_b
213k22412762
answered 4 hours ago
Glen_b♦Glen_b
213k22412762
answered 4 hours ago
Glen_b♦Glen_b
213k22412762
213k22412762
add a comment |
add a comment |
$begingroup$
Absolutely! The $alpha$ parameter can be adjusted to either fit a Lasso or a Ridge regression (or something in between). Recall that the loss function which Elastic Net minimizes is $$frac{1}{2N}sum^N_{i=1}(y_i-beta_0-x_i^tbeta)^2+lambdasum_{j=1}^p(frac{1}{2}(1-alpha)beta_j^2+alpha|beta_j|).$$
Focus on the second big sum (the one multiplied by $lambda$). If you let $alpha=1$, the first term inside this sum becomes $0$, and the whole function becomes exactly the function that Lasso minimizes (or the Lasso loss function). If you let $alpha=0$, the second term becomes $0$ and you are left with Ridge.
You can check the loss for Ridge and Lasso in this book and for elastic net in this paper.
answered 4 hours ago
BananinBananin
1795
$endgroup$
$begingroup$
This looks like a good answer but can you edit to include citations for the hyperlinks? Over time, links die.
$endgroup$
– Sycorax
4 hours ago
add a comment |
$begingroup$
Absolutely! The $alpha$ parameter can be adjusted to either fit a Lasso or a Ridge regression (or something in between). Recall that the loss function which Elastic Net minimizes is $$frac{1}{2N}sum^N_{i=1}(y_i-beta_0-x_i^tbeta)^2+lambdasum_{j=1}^p(frac{1}{2}(1-alpha)beta_j^2+alpha|beta_j|).$$
Focus on the second big sum (the one multiplied by $lambda$). If you let $alpha=1$, the first term inside this sum becomes $0$, and the whole function becomes exactly the function that Lasso minimizes (or the Lasso loss function). If you let $alpha=0$, the second term becomes $0$ and you are left with Ridge.
You can check the loss for Ridge and Lasso in this book and for elastic net in this paper.
answered 4 hours ago
BananinBananin
1795
$endgroup$
$begingroup$
This looks like a good answer but can you edit to include citations for the hyperlinks? Over time, links die.
$endgroup$
– Sycorax
4 hours ago
add a comment |
$begingroup$
Absolutely! The $alpha$ parameter can be adjusted to either fit a Lasso or a Ridge regression (or something in between). Recall that the loss function which Elastic Net minimizes is $$frac{1}{2N}sum^N_{i=1}(y_i-beta_0-x_i^tbeta)^2+lambdasum_{j=1}^p(frac{1}{2}(1-alpha)beta_j^2+alpha|beta_j|).$$
Focus on the second big sum (the one multiplied by $lambda$). If you let $alpha=1$, the first term inside this sum becomes $0$, and the whole function becomes exactly the function that Lasso minimizes (or the Lasso loss function). If you let $alpha=0$, the second term becomes $0$ and you are left with Ridge.
You can check the loss for Ridge and Lasso in this book and for elastic net in this paper.
answered 4 hours ago
BananinBananin
1795
$endgroup$
Absolutely! The $alpha$ parameter can be adjusted to either fit a Lasso or a Ridge regression (or something in between). Recall that the loss function which Elastic Net minimizes is $$frac{1}{2N}sum^N_{i=1}(y_i-beta_0-x_i^tbeta)^2+lambdasum_{j=1}^p(frac{1}{2}(1-alpha)beta_j^2+alpha|beta_j|).$$
Focus on the second big sum (the one multiplied by $lambda$). If you let $alpha=1$, the first term inside this sum becomes $0$, and the whole function becomes exactly the function that Lasso minimizes (or the Lasso loss function). If you let $alpha=0$, the second term becomes $0$ and you are left with Ridge.
You can check the loss for Ridge and Lasso in this book and for elastic net in this paper.
answered 4 hours ago
BananinBananin
1795
answered 4 hours ago
BananinBananin
1795
answered 4 hours ago
BananinBananin
1795
answered 4 hours ago
BananinBananin
1795
1795
$begingroup$
This looks like a good answer but can you edit to include citations for the hyperlinks? Over time, links die.
$endgroup$
– Sycorax
4 hours ago
add a comment |
$begingroup$
This looks like a good answer but can you edit to include citations for the hyperlinks? Over time, links die.
$endgroup$
– Sycorax
4 hours ago
$begingroup$
This looks like a good answer but can you edit to include citations for the hyperlinks? Over time, links die.
$endgroup$
– Sycorax
4 hours ago
$begingroup$
This looks like a good answer but can you edit to include citations for the hyperlinks? Over time, links die.
$endgroup$
– Sycorax
4 hours ago
add a comment |
red4life93 is a new contributor. Be nice, and check out our Code of Conduct.
red4life93 is a new contributor. Be nice, and check out our Code of Conduct.
red4life93 is a new contributor. Be nice, and check out our Code of Conduct.
red4life93 is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to Cross Validated!
- 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.
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%2fstats.stackexchange.com%2fquestions%2f396748%2fcan-the-alpha-lambda-values-of-a-glmnet-object-output-determine-whether-ridge-o%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
