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What does this absolute value notation mean?
0
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In a regression model function, What does this absolute value notation mean?
linear-regression
asked Jan 14 at 21:24
Ibrahim AbouhashishIbrahim Abouhashish
367
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add a comment |
0
$begingroup$
In a regression model function, What does this absolute value notation mean?
linear-regression
asked Jan 14 at 21:24
Ibrahim AbouhashishIbrahim Abouhashish
367
$endgroup$
3
$begingroup$
For $n$-dimensional vectors $||cdot||_2$ typically represents the Euclidean, or standard, norm. $||v||_2 = sqrt{v_1^2+v_2^2+...+v_n^2}.$
$endgroup$
– D.B.
Jan 14 at 21:27
1
$begingroup$
$||x||_2 = sqrt{sum_{i=1}^{n}{x_i^2}}$
$endgroup$
– lightxbulb
Jan 14 at 21:27
1
$begingroup$
Even more generally, $|x|_p = left(sum_{i=1}^n |x_i|^pright)^{1/p}$ is the $p$-norm for $ell_p$ space which Euclidean norm/space is an example of. In your specific example, the super-script $2$ is there as a power so $|x|_2^2 = x_1^2+x_2^2+dots+x_n^2$
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– JMoravitz
Jan 14 at 21:31
$begingroup$
@D.B. considering x is also a matrix, what would $ x^{(n)} $ mean
$endgroup$
– Ibrahim Abouhashish
Jan 15 at 19:44
$begingroup$
I actually think that $x^{(n)}$ and $y^{(n)}$ are just vectors. The quantity you have shown looks like a measure of the error between your data $y^{(n)}$ and your regression model.
$endgroup$
– D.B.
Jan 17 at 5:30
add a comment |
0
0
0
$begingroup$
In a regression model function, What does this absolute value notation mean?
linear-regression
asked Jan 14 at 21:24
Ibrahim AbouhashishIbrahim Abouhashish
367
$endgroup$
In a regression model function, What does this absolute value notation mean?
linear-regression
linear-regression
asked Jan 14 at 21:24
Ibrahim AbouhashishIbrahim Abouhashish
367
asked Jan 14 at 21:24
Ibrahim AbouhashishIbrahim Abouhashish
367
asked Jan 14 at 21:24
Ibrahim AbouhashishIbrahim Abouhashish
367
asked Jan 14 at 21:24
Ibrahim AbouhashishIbrahim Abouhashish
367
asked Jan 14 at 21:24
Ibrahim AbouhashishIbrahim Abouhashish
367
367
3
$begingroup$
For $n$-dimensional vectors $||cdot||_2$ typically represents the Euclidean, or standard, norm. $||v||_2 = sqrt{v_1^2+v_2^2+...+v_n^2}.$
$endgroup$
– D.B.
Jan 14 at 21:27
1
$begingroup$
$||x||_2 = sqrt{sum_{i=1}^{n}{x_i^2}}$
$endgroup$
– lightxbulb
Jan 14 at 21:27
1
$begingroup$
Even more generally, $|x|_p = left(sum_{i=1}^n |x_i|^pright)^{1/p}$ is the $p$-norm for $ell_p$ space which Euclidean norm/space is an example of. In your specific example, the super-script $2$ is there as a power so $|x|_2^2 = x_1^2+x_2^2+dots+x_n^2$
$endgroup$
– JMoravitz
Jan 14 at 21:31
$begingroup$
@D.B. considering x is also a matrix, what would $ x^{(n)} $ mean
$endgroup$
– Ibrahim Abouhashish
Jan 15 at 19:44
$begingroup$
I actually think that $x^{(n)}$ and $y^{(n)}$ are just vectors. The quantity you have shown looks like a measure of the error between your data $y^{(n)}$ and your regression model.
$endgroup$
– D.B.
Jan 17 at 5:30
add a comment |
3
$begingroup$
For $n$-dimensional vectors $||cdot||_2$ typically represents the Euclidean, or standard, norm. $||v||_2 = sqrt{v_1^2+v_2^2+...+v_n^2}.$
$endgroup$
– D.B.
Jan 14 at 21:27
1
$begingroup$
$||x||_2 = sqrt{sum_{i=1}^{n}{x_i^2}}$
$endgroup$
– lightxbulb
Jan 14 at 21:27
1
$begingroup$
Even more generally, $|x|_p = left(sum_{i=1}^n |x_i|^pright)^{1/p}$ is the $p$-norm for $ell_p$ space which Euclidean norm/space is an example of. In your specific example, the super-script $2$ is there as a power so $|x|_2^2 = x_1^2+x_2^2+dots+x_n^2$
$endgroup$
– JMoravitz
Jan 14 at 21:31
$begingroup$
@D.B. considering x is also a matrix, what would $ x^{(n)} $ mean
$endgroup$
– Ibrahim Abouhashish
Jan 15 at 19:44
$begingroup$
I actually think that $x^{(n)}$ and $y^{(n)}$ are just vectors. The quantity you have shown looks like a measure of the error between your data $y^{(n)}$ and your regression model.
$endgroup$
– D.B.
Jan 17 at 5:30
3
3
$begingroup$
For $n$-dimensional vectors $||cdot||_2$ typically represents the Euclidean, or standard, norm. $||v||_2 = sqrt{v_1^2+v_2^2+...+v_n^2}.$
$endgroup$
– D.B.
Jan 14 at 21:27
$begingroup$
For $n$-dimensional vectors $||cdot||_2$ typically represents the Euclidean, or standard, norm. $||v||_2 = sqrt{v_1^2+v_2^2+...+v_n^2}.$
$endgroup$
– D.B.
Jan 14 at 21:27
1
1
$begingroup$
$||x||_2 = sqrt{sum_{i=1}^{n}{x_i^2}}$
$endgroup$
– lightxbulb
Jan 14 at 21:27
$begingroup$
$||x||_2 = sqrt{sum_{i=1}^{n}{x_i^2}}$
$endgroup$
– lightxbulb
Jan 14 at 21:27
1
1
$begingroup$
Even more generally, $|x|_p = left(sum_{i=1}^n |x_i|^pright)^{1/p}$ is the $p$-norm for $ell_p$ space which Euclidean norm/space is an example of. In your specific example, the super-script $2$ is there as a power so $|x|_2^2 = x_1^2+x_2^2+dots+x_n^2$
$endgroup$
– JMoravitz
Jan 14 at 21:31
$begingroup$
Even more generally, $|x|_p = left(sum_{i=1}^n |x_i|^pright)^{1/p}$ is the $p$-norm for $ell_p$ space which Euclidean norm/space is an example of. In your specific example, the super-script $2$ is there as a power so $|x|_2^2 = x_1^2+x_2^2+dots+x_n^2$
$endgroup$
– JMoravitz
Jan 14 at 21:31
$begingroup$
@D.B. considering x is also a matrix, what would $ x^{(n)} $ mean
$endgroup$
– Ibrahim Abouhashish
Jan 15 at 19:44
$begingroup$
@D.B. considering x is also a matrix, what would $ x^{(n)} $ mean
$endgroup$
– Ibrahim Abouhashish
Jan 15 at 19:44
$begingroup$
I actually think that $x^{(n)}$ and $y^{(n)}$ are just vectors. The quantity you have shown looks like a measure of the error between your data $y^{(n)}$ and your regression model.
$endgroup$
– D.B.
Jan 17 at 5:30
$begingroup$
I actually think that $x^{(n)}$ and $y^{(n)}$ are just vectors. The quantity you have shown looks like a measure of the error between your data $y^{(n)}$ and your regression model.
$endgroup$
– D.B.
Jan 17 at 5:30
add a comment |
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3
$begingroup$
For $n$-dimensional vectors $||cdot||_2$ typically represents the Euclidean, or standard, norm. $||v||_2 = sqrt{v_1^2+v_2^2+...+v_n^2}.$
$endgroup$
– D.B.
Jan 14 at 21:27
1
$begingroup$
$||x||_2 = sqrt{sum_{i=1}^{n}{x_i^2}}$
$endgroup$
– lightxbulb
Jan 14 at 21:27
1
$begingroup$
Even more generally, $|x|_p = left(sum_{i=1}^n |x_i|^pright)^{1/p}$ is the $p$-norm for $ell_p$ space which Euclidean norm/space is an example of. In your specific example, the super-script $2$ is there as a power so $|x|_2^2 = x_1^2+x_2^2+dots+x_n^2$
$endgroup$
– JMoravitz
Jan 14 at 21:31
$begingroup$
@D.B. considering x is also a matrix, what would $ x^{(n)} $ mean
$endgroup$
– Ibrahim Abouhashish
Jan 15 at 19:44
$begingroup$
I actually think that $x^{(n)}$ and $y^{(n)}$ are just vectors. The quantity you have shown looks like a measure of the error between your data $y^{(n)}$ and your regression model.
$endgroup$
– D.B.
Jan 17 at 5:30