Given a target vector and a feature vector, how to computer the weight
$begingroup$
In page 13 of the slide, given $t$ and $X$ as following. I don't understand how we get $w$.
$$t=[t^{(1)},t^{(2)}, ldots, t^{(N)} ]^T$$
$$X=begin{bmatrix}1, x^{(1)} \ 1, x^{(2)} \ vdots\1, x^{(N)} end{bmatrix}$$
- Then:
$$w=(X^TX)^{-1}X^Tt$$
machine-learning
edited 3 hours ago
Siong Thye Goh
1,177418
asked 5 hours ago
user8314628user8314628
1083
New contributor
user8314628 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 |
$begingroup$
In page 13 of the slide, given $t$ and $X$ as following. I don't understand how we get $w$.
$$t=[t^{(1)},t^{(2)}, ldots, t^{(N)} ]^T$$
$$X=begin{bmatrix}1, x^{(1)} \ 1, x^{(2)} \ vdots\1, x^{(N)} end{bmatrix}$$
- Then:
$$w=(X^TX)^{-1}X^Tt$$
machine-learning
edited 3 hours ago
Siong Thye Goh
1,177418
asked 5 hours ago
user8314628user8314628
1083
New contributor
user8314628 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 |
$begingroup$
In page 13 of the slide, given $t$ and $X$ as following. I don't understand how we get $w$.
$$t=[t^{(1)},t^{(2)}, ldots, t^{(N)} ]^T$$
$$X=begin{bmatrix}1, x^{(1)} \ 1, x^{(2)} \ vdots\1, x^{(N)} end{bmatrix}$$
- Then:
$$w=(X^TX)^{-1}X^Tt$$
machine-learning
edited 3 hours ago
Siong Thye Goh
1,177418
asked 5 hours ago
user8314628user8314628
1083
New contributor
user8314628 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
In page 13 of the slide, given $t$ and $X$ as following. I don't understand how we get $w$.
$$t=[t^{(1)},t^{(2)}, ldots, t^{(N)} ]^T$$
$$X=begin{bmatrix}1, x^{(1)} \ 1, x^{(2)} \ vdots\1, x^{(N)} end{bmatrix}$$
- Then:
$$w=(X^TX)^{-1}X^Tt$$
machine-learning
machine-learning
edited 3 hours ago
Siong Thye Goh
1,177418
asked 5 hours ago
user8314628user8314628
1083
New contributor
user8314628 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 3 hours ago
Siong Thye Goh
1,177418
asked 5 hours ago
user8314628user8314628
1083
New contributor
user8314628 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 3 hours ago
Siong Thye Goh
1,177418
edited 3 hours ago
Siong Thye Goh
1,177418
edited 3 hours ago
Siong Thye Goh
1,177418
1,177418
asked 5 hours ago
user8314628user8314628
1083
New contributor
user8314628 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 5 hours ago
user8314628user8314628
1083
asked 5 hours ago
user8314628user8314628
1083
1083
New contributor
user8314628 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
user8314628 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
user8314628 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 |
1 Answer
1
active
oldest
votes
$begingroup$
The least square problem is to minimize $$|Xw-t|^2$$
Differentiating it with respect to $w$ and equating it to $0$, we have
$$2X^T(Xw-t)=0$$
Hence, we have
$$X^TXw-X^Tt=0$$
That is $$X^TXw=X^Tt$$
$$w=(X^TX)^{-1}X^Tt$$
answered 3 hours ago
Siong Thye GohSiong Thye Goh
1,177418
$endgroup$
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: "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
});
}
});
user8314628 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');
var $window = $(window),
onScroll = function(e) {
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom)) {
StackExchange.using('gps', function() { StackExchange.gps.track('embedded_signup_form.view', { location: 'question_page' }); });
$window.unbind('scroll', onScroll);
}
};
$window.on('scroll', onScroll);
});
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%2f46114%2fgiven-a-target-vector-and-a-feature-vector-how-to-computer-the-weight%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The least square problem is to minimize $$|Xw-t|^2$$
Differentiating it with respect to $w$ and equating it to $0$, we have
$$2X^T(Xw-t)=0$$
Hence, we have
$$X^TXw-X^Tt=0$$
That is $$X^TXw=X^Tt$$
$$w=(X^TX)^{-1}X^Tt$$
answered 3 hours ago
Siong Thye GohSiong Thye Goh
1,177418
$endgroup$
add a comment |
$begingroup$
The least square problem is to minimize $$|Xw-t|^2$$
Differentiating it with respect to $w$ and equating it to $0$, we have
$$2X^T(Xw-t)=0$$
Hence, we have
$$X^TXw-X^Tt=0$$
That is $$X^TXw=X^Tt$$
$$w=(X^TX)^{-1}X^Tt$$
answered 3 hours ago
Siong Thye GohSiong Thye Goh
1,177418
$endgroup$
add a comment |
$begingroup$
The least square problem is to minimize $$|Xw-t|^2$$
Differentiating it with respect to $w$ and equating it to $0$, we have
$$2X^T(Xw-t)=0$$
Hence, we have
$$X^TXw-X^Tt=0$$
That is $$X^TXw=X^Tt$$
$$w=(X^TX)^{-1}X^Tt$$
answered 3 hours ago
Siong Thye GohSiong Thye Goh
1,177418
$endgroup$
The least square problem is to minimize $$|Xw-t|^2$$
Differentiating it with respect to $w$ and equating it to $0$, we have
$$2X^T(Xw-t)=0$$
Hence, we have
$$X^TXw-X^Tt=0$$
That is $$X^TXw=X^Tt$$
$$w=(X^TX)^{-1}X^Tt$$
answered 3 hours ago
Siong Thye GohSiong Thye Goh
1,177418
answered 3 hours ago
Siong Thye GohSiong Thye Goh
1,177418
answered 3 hours ago
Siong Thye GohSiong Thye Goh
1,177418
answered 3 hours ago
Siong Thye GohSiong Thye Goh
1,177418
1,177418
add a comment |
add a comment |
user8314628 is a new contributor. Be nice, and check out our Code of Conduct.
user8314628 is a new contributor. Be nice, and check out our Code of Conduct.
user8314628 is a new contributor. Be nice, and check out our Code of Conduct.
user8314628 is a new contributor. Be nice, and check out our Code of Conduct.
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');
var $window = $(window),
onScroll = function(e) {
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom)) {
StackExchange.using('gps', function() { StackExchange.gps.track('embedded_signup_form.view', { location: 'question_page' }); });
$window.unbind('scroll', onScroll);
}
};
$window.on('scroll', onScroll);
});
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%2f46114%2fgiven-a-target-vector-and-a-feature-vector-how-to-computer-the-weight%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');
var $window = $(window),
onScroll = function(e) {
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom)) {
StackExchange.using('gps', function() { StackExchange.gps.track('embedded_signup_form.view', { location: 'question_page' }); });
$window.unbind('scroll', onScroll);
}
};
$window.on('scroll', onScroll);
});
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');
var $window = $(window),
onScroll = function(e) {
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom)) {
StackExchange.using('gps', function() { StackExchange.gps.track('embedded_signup_form.view', { location: 'question_page' }); });
$window.unbind('scroll', onScroll);
}
};
$window.on('scroll', onScroll);
});
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');
var $window = $(window),
onScroll = function(e) {
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom)) {
StackExchange.using('gps', function() { StackExchange.gps.track('embedded_signup_form.view', { location: 'question_page' }); });
$window.unbind('scroll', onScroll);
}
};
$window.on('scroll', onScroll);
});
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
