SRM (structural risk minimization) learning guarantee proof
$begingroup$
I am reading Chapter 4 (Model Selection) in the book "Foundations of Machine Learning Edition 2".
Currently, I am trying to follow the proof of Theorem 4.2 (SRM Learning guarantee), but I cannot understand the derivation of the second inequality in the proof, which is:
$sum_{k=1}^infty P Big[ sup_{hin H_k}R(h)-hat{R}_S(h)-cal{R}_m(H_k)geq epsilon +sqrt{frac{log k}{m}}Big]leq sum_{k=1}^infty exp Big(-2mbig( epsilon +sqrt{frac{log k}{m}}big)^2Big)$
The equations can be found here in page 66:
https://books.google.co.jp/books?id=V2B9DwAAQBAJ&pg=PA66&lpg=PA66
I am guessing I will use some other Theorems that are related to this problem, but could not find any good candidates.
Thank you for reading my question!
machine-learning theory vc-theory
asked 20 hours ago
ML studentML student
594
$endgroup$
add a comment |
$begingroup$
I am reading Chapter 4 (Model Selection) in the book "Foundations of Machine Learning Edition 2".
Currently, I am trying to follow the proof of Theorem 4.2 (SRM Learning guarantee), but I cannot understand the derivation of the second inequality in the proof, which is:
$sum_{k=1}^infty P Big[ sup_{hin H_k}R(h)-hat{R}_S(h)-cal{R}_m(H_k)geq epsilon +sqrt{frac{log k}{m}}Big]leq sum_{k=1}^infty exp Big(-2mbig( epsilon +sqrt{frac{log k}{m}}big)^2Big)$
The equations can be found here in page 66:
https://books.google.co.jp/books?id=V2B9DwAAQBAJ&pg=PA66&lpg=PA66
I am guessing I will use some other Theorems that are related to this problem, but could not find any good candidates.
Thank you for reading my question!
machine-learning theory vc-theory
asked 20 hours ago
ML studentML student
594
$endgroup$
add a comment |
$begingroup$
I am reading Chapter 4 (Model Selection) in the book "Foundations of Machine Learning Edition 2".
Currently, I am trying to follow the proof of Theorem 4.2 (SRM Learning guarantee), but I cannot understand the derivation of the second inequality in the proof, which is:
$sum_{k=1}^infty P Big[ sup_{hin H_k}R(h)-hat{R}_S(h)-cal{R}_m(H_k)geq epsilon +sqrt{frac{log k}{m}}Big]leq sum_{k=1}^infty exp Big(-2mbig( epsilon +sqrt{frac{log k}{m}}big)^2Big)$
The equations can be found here in page 66:
https://books.google.co.jp/books?id=V2B9DwAAQBAJ&pg=PA66&lpg=PA66
I am guessing I will use some other Theorems that are related to this problem, but could not find any good candidates.
Thank you for reading my question!
machine-learning theory vc-theory
asked 20 hours ago
ML studentML student
594
$endgroup$
I am reading Chapter 4 (Model Selection) in the book "Foundations of Machine Learning Edition 2".
Currently, I am trying to follow the proof of Theorem 4.2 (SRM Learning guarantee), but I cannot understand the derivation of the second inequality in the proof, which is:
$sum_{k=1}^infty P Big[ sup_{hin H_k}R(h)-hat{R}_S(h)-cal{R}_m(H_k)geq epsilon +sqrt{frac{log k}{m}}Big]leq sum_{k=1}^infty exp Big(-2mbig( epsilon +sqrt{frac{log k}{m}}big)^2Big)$
The equations can be found here in page 66:
https://books.google.co.jp/books?id=V2B9DwAAQBAJ&pg=PA66&lpg=PA66
I am guessing I will use some other Theorems that are related to this problem, but could not find any good candidates.
Thank you for reading my question!
machine-learning theory vc-theory
machine-learning theory vc-theory
asked 20 hours ago
ML studentML student
594
asked 20 hours ago
ML studentML student
594
asked 20 hours ago
ML studentML student
594
asked 20 hours ago
ML studentML student
594
asked 20 hours ago
ML studentML student
594
594
add a comment |
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "557"
};
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
});
}
});
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%2fdatascience.stackexchange.com%2fquestions%2f49244%2fsrm-structural-risk-minimization-learning-guarantee-proof%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 Data Science 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.
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%2fdatascience.stackexchange.com%2fquestions%2f49244%2fsrm-structural-risk-minimization-learning-guarantee-proof%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
