Given a target vector and a feature vector, how to computer the weightHow to calculate inverse of square...
Is there any danger of my neighbor having my wife's signature?
Protagonist constantly has to have long words explained to her. Will this get tedious?
What is an explicit bijection in combinatorics?
How do I narratively explain how in-game circumstances do not mechanically allow a PC to instantly kill an NPC?
Would water spill from a bowl in a Bag of Holding?
Connecting to SMTP server from AWS Lambda
Expression for "unconsciously using words (or accents) used by a person you often talk with or listen to"?
Boss asked me to sign a resignation paper without a date on it along with my new contract
Limits of Rolle theorem
How can I prevent an oracle who can see into the past from knowing everything that has happened?
Minimum Viable Product for RTS game?
Given a target vector and a feature vector, how to computer the weight
Running away from a conflict
Is "accuse people to be racist" grammatical?
In a post-apocalypse world, with no power and few survivors, would Satnav still work?
When does a person lose diplomatic status?
What if I miss a connection and don't have money to book next flight?
Dealing with an internal ScriptKiddie
Color of alien seas
Why can all solutions to the simple harmonic motion equation be written in terms of sines and cosines?
How can I handle players killing my NPC outside of combat?
What happened to Hermione’s clothing and other possessions after she wiped her parents’ memories of her?
Process substitution inside a subshell to set a variable
How can I give a Ranger advantage on a check due to Favored Enemy without spoiling the story for the player?
Given a target vector and a feature vector, how to computer the weight
How to calculate inverse of square matrix for streaming or online data as all data are not available at once?An unbiased simulator for policy simulation in reinforcement learningHow does “linear algebraic” weight training function work?default kernels in cnn in keras?Locally Weighted Regression (Loess) - Robustifying iterationsBackpropagationMapping between original feature space and an interpretable feature spaceHow to derive the sum-of squares error function formula?How to compute the maximum likelihood hypothesis?not quite sure about the difference between RNN and feed forward neural net
$begingroup$
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
New contributor
$endgroup$
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
New contributor
$endgroup$
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
New contributor
$endgroup$
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
New contributor
New contributor
edited 3 hours ago
Siong Thye Goh
1,177418
1,177418
New contributor
asked 5 hours ago
user8314628user8314628
1083
1083
New contributor
New contributor
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 $$X^TXw=X^Tt$$
$$w=(X^TX)^{-1}X^Tt$$
$endgroup$
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');
});
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 $$X^TXw=X^Tt$$
$$w=(X^TX)^{-1}X^Tt$$
$endgroup$
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 $$X^TXw=X^Tt$$
$$w=(X^TX)^{-1}X^Tt$$
$endgroup$
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 $$X^TXw=X^Tt$$
$$w=(X^TX)^{-1}X^Tt$$
$endgroup$
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
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');
});
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');
});
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