Mixing
tighter bound for the expectation of max of sets of functions
$begingroup$
Let $Xinmathbb{R}^{ntimes d}$ be a random matrix, and ${f_k}_{k=1}^K, m_k in mathbb{R}^{d}$ be a fixed set of matrices. I was wondering, what is the expectation (or upper bound of the expectation) of
$mathbb{E}max_{k}{f_k(X)}$
I asked a similar question before
https://math.stackexchange.com/posts/3076407/edit, but I was wondering if there is some inequality for this more general case. The only one I know is
$mathbb{E}max_{k}{f_k(X)} le sum_{k=1}^K mathbb{E}f_k(X)$,
which seems too loose.
Any comment or hint will be appreciated!
probability probability-theory inequality expected-value
asked Jan 18 at 19:09
user3138073user3138073
1758
$endgroup$
add a comment |
$begingroup$
Let $Xinmathbb{R}^{ntimes d}$ be a random matrix, and ${f_k}_{k=1}^K, m_k in mathbb{R}^{d}$ be a fixed set of matrices. I was wondering, what is the expectation (or upper bound of the expectation) of
$mathbb{E}max_{k}{f_k(X)}$
I asked a similar question before
https://math.stackexchange.com/posts/3076407/edit, but I was wondering if there is some inequality for this more general case. The only one I know is
$mathbb{E}max_{k}{f_k(X)} le sum_{k=1}^K mathbb{E}f_k(X)$,
which seems too loose.
Any comment or hint will be appreciated!
probability probability-theory inequality expected-value
asked Jan 18 at 19:09
user3138073user3138073
1758
$endgroup$
add a comment |
$begingroup$
Let $Xinmathbb{R}^{ntimes d}$ be a random matrix, and ${f_k}_{k=1}^K, m_k in mathbb{R}^{d}$ be a fixed set of matrices. I was wondering, what is the expectation (or upper bound of the expectation) of
$mathbb{E}max_{k}{f_k(X)}$
I asked a similar question before
https://math.stackexchange.com/posts/3076407/edit, but I was wondering if there is some inequality for this more general case. The only one I know is
$mathbb{E}max_{k}{f_k(X)} le sum_{k=1}^K mathbb{E}f_k(X)$,
which seems too loose.
Any comment or hint will be appreciated!
probability probability-theory inequality expected-value
asked Jan 18 at 19:09
user3138073user3138073
1758
$endgroup$
Let $Xinmathbb{R}^{ntimes d}$ be a random matrix, and ${f_k}_{k=1}^K, m_k in mathbb{R}^{d}$ be a fixed set of matrices. I was wondering, what is the expectation (or upper bound of the expectation) of
$mathbb{E}max_{k}{f_k(X)}$
I asked a similar question before
https://math.stackexchange.com/posts/3076407/edit, but I was wondering if there is some inequality for this more general case. The only one I know is
$mathbb{E}max_{k}{f_k(X)} le sum_{k=1}^K mathbb{E}f_k(X)$,
which seems too loose.
Any comment or hint will be appreciated!
probability probability-theory inequality expected-value
probability probability-theory inequality expected-value
asked Jan 18 at 19:09
user3138073user3138073
1758
asked Jan 18 at 19:09
user3138073user3138073
1758
asked Jan 18 at 19:09
user3138073user3138073
1758
asked Jan 18 at 19:09
user3138073user3138073
1758
asked Jan 18 at 19:09
user3138073user3138073
1758
1758
add a comment |
add a comment |
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