Mixing
Understanding equality regrading expectation of random matrices
$begingroup$
I'm reading the following article on Latent Tree Structures (I added a link at the end of the post) :
"Spectral Methods for Learning Multivariate Latent Tree Structure".
I'm trying to understand the following equality (w,v,u are random vectors) :
https://i.stack.imgur.com/RR7BS.png
I don't get both equalities.
the following assumption holds -
- The following equality holds between w and v :
E[v|w] = A(v|w)*w
for a fixed matrix A(v|w).
But even with this assumption I can't see how can you get the previous mentioned equality.
Thanks for the help!
The article :
https://arxiv.org/pdf/1107.1283.pdf
matrices random expected-value
asked Jan 12 at 13:30
Ori KelnerOri Kelner
12
$endgroup$
add a comment |
$begingroup$
I'm reading the following article on Latent Tree Structures (I added a link at the end of the post) :
"Spectral Methods for Learning Multivariate Latent Tree Structure".
I'm trying to understand the following equality (w,v,u are random vectors) :
https://i.stack.imgur.com/RR7BS.png
I don't get both equalities.
the following assumption holds -
- The following equality holds between w and v :
E[v|w] = A(v|w)*w
for a fixed matrix A(v|w).
But even with this assumption I can't see how can you get the previous mentioned equality.
Thanks for the help!
The article :
https://arxiv.org/pdf/1107.1283.pdf
matrices random expected-value
asked Jan 12 at 13:30
Ori KelnerOri Kelner
12
$endgroup$
add a comment |
$begingroup$
I'm reading the following article on Latent Tree Structures (I added a link at the end of the post) :
"Spectral Methods for Learning Multivariate Latent Tree Structure".
I'm trying to understand the following equality (w,v,u are random vectors) :
https://i.stack.imgur.com/RR7BS.png
I don't get both equalities.
the following assumption holds -
- The following equality holds between w and v :
E[v|w] = A(v|w)*w
for a fixed matrix A(v|w).
But even with this assumption I can't see how can you get the previous mentioned equality.
Thanks for the help!
The article :
https://arxiv.org/pdf/1107.1283.pdf
matrices random expected-value
asked Jan 12 at 13:30
Ori KelnerOri Kelner
12
$endgroup$
I'm reading the following article on Latent Tree Structures (I added a link at the end of the post) :
"Spectral Methods for Learning Multivariate Latent Tree Structure".
I'm trying to understand the following equality (w,v,u are random vectors) :
https://i.stack.imgur.com/RR7BS.png
I don't get both equalities.
the following assumption holds -
- The following equality holds between w and v :
E[v|w] = A(v|w)*w
for a fixed matrix A(v|w).
But even with this assumption I can't see how can you get the previous mentioned equality.
Thanks for the help!
The article :
https://arxiv.org/pdf/1107.1283.pdf
matrices random expected-value
matrices random expected-value
asked Jan 12 at 13:30
Ori KelnerOri Kelner
12
asked Jan 12 at 13:30
Ori KelnerOri Kelner
12
edited Jan 12 at 13:39
Ori Kelner
asked Jan 12 at 13:30
Ori KelnerOri Kelner
12
asked Jan 12 at 13:30
Ori KelnerOri Kelner
12
asked Jan 12 at 13:30
Ori KelnerOri Kelner
12
12
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%2f3070897%2funderstanding-equality-regrading-expectation-of-random-matrices%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.
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%2f3070897%2funderstanding-equality-regrading-expectation-of-random-matrices%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
