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
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$endgroup$
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.
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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.
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add a comment |
add a comment |
1 Answer
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$begingroup$
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 |
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1 Answer
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1 Answer
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$begingroup$
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 |
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