Expectation inequality of a function with standard normal variable as input
The article "PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming" gives the proof of obtaining the solution for phase retrieval. Here, he used the result
$
boldsymbol{E}|(z_1^2 -1)1_{z_1^2 leq 2beta log(n)} | leq (2beta log(n))^{k-2}boldsymbol{E}(z_1^2 -1)^2
$
Where $boldsymbol{E} $ is the expectation and $ z_1 sim mathcal{N}(0,1)$. $beta $ is a constant and $n$ is the number of measurements taken which is also constant. It is present in page 19 of the article. How is this inequality obtained?
The link to the article https://arxiv.org/pdf/1109.4499.pdf
Edit:The inequality is used in page 19 of the paper
normal-distribution expected-value
asked Nov 27 '18 at 9:15
vi11
11
add a comment |
The article "PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming" gives the proof of obtaining the solution for phase retrieval. Here, he used the result
$
boldsymbol{E}|(z_1^2 -1)1_{z_1^2 leq 2beta log(n)} | leq (2beta log(n))^{k-2}boldsymbol{E}(z_1^2 -1)^2
$
Where $boldsymbol{E} $ is the expectation and $ z_1 sim mathcal{N}(0,1)$. $beta $ is a constant and $n$ is the number of measurements taken which is also constant. It is present in page 19 of the article. How is this inequality obtained?
The link to the article https://arxiv.org/pdf/1109.4499.pdf
Edit:The inequality is used in page 19 of the paper
normal-distribution expected-value
asked Nov 27 '18 at 9:15
vi11
11
Can you give us an idea where in the paper you're looking? I personally can't be bothered to look through 31 pages to try and get some context.
– MRobinson
Nov 27 '18 at 9:21
Its on page 19. Sorry, I forgot to add that detail.
– vi11
Nov 27 '18 at 9:24
add a comment |
The article "PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming" gives the proof of obtaining the solution for phase retrieval. Here, he used the result
$
boldsymbol{E}|(z_1^2 -1)1_{z_1^2 leq 2beta log(n)} | leq (2beta log(n))^{k-2}boldsymbol{E}(z_1^2 -1)^2
$
Where $boldsymbol{E} $ is the expectation and $ z_1 sim mathcal{N}(0,1)$. $beta $ is a constant and $n$ is the number of measurements taken which is also constant. It is present in page 19 of the article. How is this inequality obtained?
The link to the article https://arxiv.org/pdf/1109.4499.pdf
Edit:The inequality is used in page 19 of the paper
normal-distribution expected-value
asked Nov 27 '18 at 9:15
vi11
11
The article "PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming" gives the proof of obtaining the solution for phase retrieval. Here, he used the result
$
boldsymbol{E}|(z_1^2 -1)1_{z_1^2 leq 2beta log(n)} | leq (2beta log(n))^{k-2}boldsymbol{E}(z_1^2 -1)^2
$
Where $boldsymbol{E} $ is the expectation and $ z_1 sim mathcal{N}(0,1)$. $beta $ is a constant and $n$ is the number of measurements taken which is also constant. It is present in page 19 of the article. How is this inequality obtained?
The link to the article https://arxiv.org/pdf/1109.4499.pdf
Edit:The inequality is used in page 19 of the paper
normal-distribution expected-value
normal-distribution expected-value
asked Nov 27 '18 at 9:15
vi11
11
asked Nov 27 '18 at 9:15
vi11
11
edited Nov 28 '18 at 11:47
asked Nov 27 '18 at 9:15
vi11
11
asked Nov 27 '18 at 9:15
vi11
11
asked Nov 27 '18 at 9:15
vi11
11
11
Can you give us an idea where in the paper you're looking? I personally can't be bothered to look through 31 pages to try and get some context.
– MRobinson
Nov 27 '18 at 9:21
Its on page 19. Sorry, I forgot to add that detail.
– vi11
Nov 27 '18 at 9:24
add a comment |
Can you give us an idea where in the paper you're looking? I personally can't be bothered to look through 31 pages to try and get some context.
– MRobinson
Nov 27 '18 at 9:21
Its on page 19. Sorry, I forgot to add that detail.
– vi11
Nov 27 '18 at 9:24
Can you give us an idea where in the paper you're looking? I personally can't be bothered to look through 31 pages to try and get some context.
– MRobinson
Nov 27 '18 at 9:21
Can you give us an idea where in the paper you're looking? I personally can't be bothered to look through 31 pages to try and get some context.
– MRobinson
Nov 27 '18 at 9:21
Its on page 19. Sorry, I forgot to add that detail.
– vi11
Nov 27 '18 at 9:24
Its on page 19. Sorry, I forgot to add that detail.
– vi11
Nov 27 '18 at 9:24
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%2f3015541%2fexpectation-inequality-of-a-function-with-standard-normal-variable-as-input%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%2f3015541%2fexpectation-inequality-of-a-function-with-standard-normal-variable-as-input%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
Can you give us an idea where in the paper you're looking? I personally can't be bothered to look through 31 pages to try and get some context.
– MRobinson
Nov 27 '18 at 9:21
Its on page 19. Sorry, I forgot to add that detail.
– vi11
Nov 27 '18 at 9:24