How does on test regression for a subspace or matrix factorization?
$begingroup$
I've recently been reading a lot of papers and watching a lot of videos on both subspace learning, and matrix factorization. One thing is particularly eluding me though - how does any of this get tested?
Let's take, straight from Wikipedia, Matrix Factorization Non-Negative.
$$V = WH$$
So, you have a data matrix $V$. Your goal is to learn components $W$ and $H$, which when multiplied together, give a good approximation of $V$. This can be done by minimizing over $W$, $H$
$$| V - WH |$$
That seems fine so far. My problem, theoretically, is understanding when we want to apply this to a problem, like say Regression.
If you wanted to minimize:
$$Y - WH*B$$
How do you do this with a test point? I get confused here, because if we had, say a 100-user test set with 10 features. Then we do a 90/10 split, we get a size of $W*H$ that is different than the size of our test data.
Do people just plug the test data in directly when testing, in place of $W*H$, and just rely on those learned weights $B$?
regression linear-regression matrix-factorisation matrix
edited 3 hours ago
Stephen Rauch
1,52551330
asked 4 hours ago
JibrilJibril
1111
$endgroup$
add a comment |
$begingroup$
I've recently been reading a lot of papers and watching a lot of videos on both subspace learning, and matrix factorization. One thing is particularly eluding me though - how does any of this get tested?
Let's take, straight from Wikipedia, Matrix Factorization Non-Negative.
$$V = WH$$
So, you have a data matrix $V$. Your goal is to learn components $W$ and $H$, which when multiplied together, give a good approximation of $V$. This can be done by minimizing over $W$, $H$
$$| V - WH |$$
That seems fine so far. My problem, theoretically, is understanding when we want to apply this to a problem, like say Regression.
If you wanted to minimize:
$$Y - WH*B$$
How do you do this with a test point? I get confused here, because if we had, say a 100-user test set with 10 features. Then we do a 90/10 split, we get a size of $W*H$ that is different than the size of our test data.
Do people just plug the test data in directly when testing, in place of $W*H$, and just rely on those learned weights $B$?
regression linear-regression matrix-factorisation matrix
edited 3 hours ago
Stephen Rauch
1,52551330
asked 4 hours ago
JibrilJibril
1111
$endgroup$
add a comment |
$begingroup$
I've recently been reading a lot of papers and watching a lot of videos on both subspace learning, and matrix factorization. One thing is particularly eluding me though - how does any of this get tested?
Let's take, straight from Wikipedia, Matrix Factorization Non-Negative.
$$V = WH$$
So, you have a data matrix $V$. Your goal is to learn components $W$ and $H$, which when multiplied together, give a good approximation of $V$. This can be done by minimizing over $W$, $H$
$$| V - WH |$$
That seems fine so far. My problem, theoretically, is understanding when we want to apply this to a problem, like say Regression.
If you wanted to minimize:
$$Y - WH*B$$
How do you do this with a test point? I get confused here, because if we had, say a 100-user test set with 10 features. Then we do a 90/10 split, we get a size of $W*H$ that is different than the size of our test data.
Do people just plug the test data in directly when testing, in place of $W*H$, and just rely on those learned weights $B$?
regression linear-regression matrix-factorisation matrix
edited 3 hours ago
Stephen Rauch
1,52551330
asked 4 hours ago
JibrilJibril
1111
$endgroup$
I've recently been reading a lot of papers and watching a lot of videos on both subspace learning, and matrix factorization. One thing is particularly eluding me though - how does any of this get tested?
Let's take, straight from Wikipedia, Matrix Factorization Non-Negative.
$$V = WH$$
So, you have a data matrix $V$. Your goal is to learn components $W$ and $H$, which when multiplied together, give a good approximation of $V$. This can be done by minimizing over $W$, $H$
$$| V - WH |$$
That seems fine so far. My problem, theoretically, is understanding when we want to apply this to a problem, like say Regression.
If you wanted to minimize:
$$Y - WH*B$$
How do you do this with a test point? I get confused here, because if we had, say a 100-user test set with 10 features. Then we do a 90/10 split, we get a size of $W*H$ that is different than the size of our test data.
Do people just plug the test data in directly when testing, in place of $W*H$, and just rely on those learned weights $B$?
regression linear-regression matrix-factorisation matrix
regression linear-regression matrix-factorisation matrix
edited 3 hours ago
Stephen Rauch
1,52551330
asked 4 hours ago
JibrilJibril
1111
edited 3 hours ago
Stephen Rauch
1,52551330
asked 4 hours ago
JibrilJibril
1111
edited 3 hours ago
Stephen Rauch
1,52551330
edited 3 hours ago
Stephen Rauch
1,52551330
edited 3 hours ago
Stephen Rauch
1,52551330
1,52551330
asked 4 hours ago
JibrilJibril
1111
asked 4 hours ago
JibrilJibril
1111
asked 4 hours ago
JibrilJibril
1111
1111
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: "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%2f48838%2fhow-does-on-test-regression-for-a-subspace-or-matrix-factorization%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%2f48838%2fhow-does-on-test-regression-for-a-subspace-or-matrix-factorization%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
