Mixing
Higher order lp regularization and lp least squares like regression with p>2
1
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Is $l_p$ norm with $2<p<infty$ used for regularization in any practical applications? Also least squares is usually used with $l_2$ norm squared. But are there any applications where $l_p$ norm is used with $2<p<infty$? Please give the references if so.
optimization convex-optimization regression machine-learning least-squares
asked Jan 10 at 16:42
user52705user52705
14810
$endgroup$
add a comment |
1
$begingroup$
Is $l_p$ norm with $2<p<infty$ used for regularization in any practical applications? Also least squares is usually used with $l_2$ norm squared. But are there any applications where $l_p$ norm is used with $2<p<infty$? Please give the references if so.
optimization convex-optimization regression machine-learning least-squares
asked Jan 10 at 16:42
user52705user52705
14810
$endgroup$
2
$begingroup$
The $ell_infty$ norm is sometimes used to control the largest component of a residual. For example, instead of finding a least squares solution to $Ax=b$ you could minimize $| Ax-b|_infty$, if you want the largest component of the residual to be as small as possible. I haven't encountered $ell_p$ regularization with $2 < p < infty$ in practical applications.
$endgroup$
– littleO
Jan 10 at 16:52
$begingroup$
Yes, you are right. I forgot to mention finiteness of p. Is $infty >p>2$ used anywhere else?
$endgroup$
– user52705
Jan 10 at 16:58
$begingroup$
A weighted Holder norm with $p=3/2$ appears in the market impact model in this MOSEK paper on portfolio optimization: docs.mosek.com/whitepapers/portfolio.pdf, section 2
$endgroup$
– Michael Grant
Jan 12 at 3:03
$begingroup$
Thanks for the reference. But it would be nice to see $2<p<infty$ example.
$endgroup$
– user52705
Jan 14 at 12:54
add a comment |
1
1
1
1
$begingroup$
Is $l_p$ norm with $2<p<infty$ used for regularization in any practical applications? Also least squares is usually used with $l_2$ norm squared. But are there any applications where $l_p$ norm is used with $2<p<infty$? Please give the references if so.
optimization convex-optimization regression machine-learning least-squares
asked Jan 10 at 16:42
user52705user52705
14810
$endgroup$
Is $l_p$ norm with $2<p<infty$ used for regularization in any practical applications? Also least squares is usually used with $l_2$ norm squared. But are there any applications where $l_p$ norm is used with $2<p<infty$? Please give the references if so.
optimization convex-optimization regression machine-learning least-squares
optimization convex-optimization regression machine-learning least-squares
asked Jan 10 at 16:42
user52705user52705
14810
asked Jan 10 at 16:42
user52705user52705
14810
edited Jan 11 at 10:08
user52705
asked Jan 10 at 16:42
user52705user52705
14810
asked Jan 10 at 16:42
user52705user52705
14810
asked Jan 10 at 16:42
user52705user52705
14810
14810
2
$begingroup$
The $ell_infty$ norm is sometimes used to control the largest component of a residual. For example, instead of finding a least squares solution to $Ax=b$ you could minimize $| Ax-b|_infty$, if you want the largest component of the residual to be as small as possible. I haven't encountered $ell_p$ regularization with $2 < p < infty$ in practical applications.
$endgroup$
– littleO
Jan 10 at 16:52
$begingroup$
Yes, you are right. I forgot to mention finiteness of p. Is $infty >p>2$ used anywhere else?
$endgroup$
– user52705
Jan 10 at 16:58
$begingroup$
A weighted Holder norm with $p=3/2$ appears in the market impact model in this MOSEK paper on portfolio optimization: docs.mosek.com/whitepapers/portfolio.pdf, section 2
$endgroup$
– Michael Grant
Jan 12 at 3:03
$begingroup$
Thanks for the reference. But it would be nice to see $2<p<infty$ example.
$endgroup$
– user52705
Jan 14 at 12:54
add a comment |
2
$begingroup$
The $ell_infty$ norm is sometimes used to control the largest component of a residual. For example, instead of finding a least squares solution to $Ax=b$ you could minimize $| Ax-b|_infty$, if you want the largest component of the residual to be as small as possible. I haven't encountered $ell_p$ regularization with $2 < p < infty$ in practical applications.
$endgroup$
– littleO
Jan 10 at 16:52
$begingroup$
Yes, you are right. I forgot to mention finiteness of p. Is $infty >p>2$ used anywhere else?
$endgroup$
– user52705
Jan 10 at 16:58
$begingroup$
A weighted Holder norm with $p=3/2$ appears in the market impact model in this MOSEK paper on portfolio optimization: docs.mosek.com/whitepapers/portfolio.pdf, section 2
$endgroup$
– Michael Grant
Jan 12 at 3:03
$begingroup$
Thanks for the reference. But it would be nice to see $2<p<infty$ example.
$endgroup$
– user52705
Jan 14 at 12:54
2
2
$begingroup$
The $ell_infty$ norm is sometimes used to control the largest component of a residual. For example, instead of finding a least squares solution to $Ax=b$ you could minimize $| Ax-b|_infty$, if you want the largest component of the residual to be as small as possible. I haven't encountered $ell_p$ regularization with $2 < p < infty$ in practical applications.
$endgroup$
– littleO
Jan 10 at 16:52
$begingroup$
The $ell_infty$ norm is sometimes used to control the largest component of a residual. For example, instead of finding a least squares solution to $Ax=b$ you could minimize $| Ax-b|_infty$, if you want the largest component of the residual to be as small as possible. I haven't encountered $ell_p$ regularization with $2 < p < infty$ in practical applications.
$endgroup$
– littleO
Jan 10 at 16:52
$begingroup$
Yes, you are right. I forgot to mention finiteness of p. Is $infty >p>2$ used anywhere else?
$endgroup$
– user52705
Jan 10 at 16:58
$begingroup$
Yes, you are right. I forgot to mention finiteness of p. Is $infty >p>2$ used anywhere else?
$endgroup$
– user52705
Jan 10 at 16:58
$begingroup$
A weighted Holder norm with $p=3/2$ appears in the market impact model in this MOSEK paper on portfolio optimization: docs.mosek.com/whitepapers/portfolio.pdf, section 2
$endgroup$
– Michael Grant
Jan 12 at 3:03
$begingroup$
A weighted Holder norm with $p=3/2$ appears in the market impact model in this MOSEK paper on portfolio optimization: docs.mosek.com/whitepapers/portfolio.pdf, section 2
$endgroup$
– Michael Grant
Jan 12 at 3:03
$begingroup$
Thanks for the reference. But it would be nice to see $2<p<infty$ example.
$endgroup$
– user52705
Jan 14 at 12:54
$begingroup$
Thanks for the reference. But it would be nice to see $2<p<infty$ example.
$endgroup$
– user52705
Jan 14 at 12:54
add a comment |
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2
$begingroup$
The $ell_infty$ norm is sometimes used to control the largest component of a residual. For example, instead of finding a least squares solution to $Ax=b$ you could minimize $| Ax-b|_infty$, if you want the largest component of the residual to be as small as possible. I haven't encountered $ell_p$ regularization with $2 < p < infty$ in practical applications.
$endgroup$
– littleO
Jan 10 at 16:52
$begingroup$
Yes, you are right. I forgot to mention finiteness of p. Is $infty >p>2$ used anywhere else?
$endgroup$
– user52705
Jan 10 at 16:58
$begingroup$
A weighted Holder norm with $p=3/2$ appears in the market impact model in this MOSEK paper on portfolio optimization: docs.mosek.com/whitepapers/portfolio.pdf, section 2
$endgroup$
– Michael Grant
Jan 12 at 3:03
$begingroup$
Thanks for the reference. But it would be nice to see $2<p<infty$ example.
$endgroup$
– user52705
Jan 14 at 12:54