Notation: What does the tilde below of the expectation mean?What is the meaning of superscript in $p_theta(x)$ and $mathbb E_thetaleft[S(theta)right]$?What does the notation $(textbfX perp textbfY , textbfWmid textbfZ)$ mean?Bounding the expectation of the difference between empirical vs generalization errorNotation is confusing me (sufficiency principle)Is value of ELBO a scalar or a distribution?Concentration of maximum of subexponential random variablesExpected value of Log Gamma function transformed Poisson random variableNotation and Transformation Rules of the Normal DistributionExpectation of Sufficient StatisticExpected value notation in GAN loss
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Notation: What does the tilde below of the expectation mean?
What is the meaning of superscript in $p_theta(x)$ and $mathbb E_thetaleft[S(theta)right]$?What does the notation $(textbfX perp textbfY , textbfWmid textbfZ)$ mean?Bounding the expectation of the difference between empirical vs generalization errorNotation is confusing me (sufficiency principle)Is value of ELBO a scalar or a distribution?Concentration of maximum of subexponential random variablesExpected value of Log Gamma function transformed Poisson random variableNotation and Transformation Rules of the Normal DistributionExpectation of Sufficient StatisticExpected value notation in GAN loss
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I am reading about variational auto encoders, and there is the below loss function:
$l_i(Theta,phi) = - mathbbE_zsim q [log p_phi(x_i|z)] + KL(q_phi(z_i|x)||p(z))$
What does the notation $zsim q$ under $mathbbE$ mean? I just have
seen notations like $E(X)$ or $ langle Xrangle $ for expected value, $mathbbE$.
What does this notation generally mean when using $mathbbE_xsim y$ for some $x$ and some $y$?
expected-value notation
edited 23 mins ago
Peter Mortensen
20728
asked 10 hours ago
Code PopeCode Pope
1336
$endgroup$
add a comment |
$begingroup$
I am reading about variational auto encoders, and there is the below loss function:
$l_i(Theta,phi) = - mathbbE_zsim q [log p_phi(x_i|z)] + KL(q_phi(z_i|x)||p(z))$
What does the notation $zsim q$ under $mathbbE$ mean? I just have
seen notations like $E(X)$ or $ langle Xrangle $ for expected value, $mathbbE$.
What does this notation generally mean when using $mathbbE_xsim y$ for some $x$ and some $y$?
expected-value notation
edited 23 mins ago
Peter Mortensen
20728
asked 10 hours ago
Code PopeCode Pope
1336
$endgroup$
add a comment |
$begingroup$
I am reading about variational auto encoders, and there is the below loss function:
$l_i(Theta,phi) = - mathbbE_zsim q [log p_phi(x_i|z)] + KL(q_phi(z_i|x)||p(z))$
What does the notation $zsim q$ under $mathbbE$ mean? I just have
seen notations like $E(X)$ or $ langle Xrangle $ for expected value, $mathbbE$.
What does this notation generally mean when using $mathbbE_xsim y$ for some $x$ and some $y$?
expected-value notation
edited 23 mins ago
Peter Mortensen
20728
asked 10 hours ago
Code PopeCode Pope
1336
$endgroup$
I am reading about variational auto encoders, and there is the below loss function:
$l_i(Theta,phi) = - mathbbE_zsim q [log p_phi(x_i|z)] + KL(q_phi(z_i|x)||p(z))$
What does the notation $zsim q$ under $mathbbE$ mean? I just have
seen notations like $E(X)$ or $ langle Xrangle $ for expected value, $mathbbE$.
What does this notation generally mean when using $mathbbE_xsim y$ for some $x$ and some $y$?
expected-value notation
expected-value notation
edited 23 mins ago
Peter Mortensen
20728
asked 10 hours ago
Code PopeCode Pope
1336
edited 23 mins ago
Peter Mortensen
20728
asked 10 hours ago
Code PopeCode Pope
1336
edited 23 mins ago
Peter Mortensen
20728
edited 23 mins ago
Peter Mortensen
20728
edited 23 mins ago
Peter Mortensen
20728
20728
asked 10 hours ago
Code PopeCode Pope
1336
asked 10 hours ago
Code PopeCode Pope
1336
asked 10 hours ago
Code PopeCode Pope
1336
1336
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
$zsim q$ means that RV $Z$ is distributed with respect to $q$ function, i.e. $q(z)$, where $q(z)$ is a valid PDF/PMF. So, the expectation can be unfold as (assuming $z$ being continuous)
$$E_zsim q[log_phi(x_i|z)]=int_-infty^infty log_phi (x_i|z) q(z) dz$$
answered 10 hours ago
gunesgunes
8,7091418
$endgroup$
$begingroup$
Ok. Thank you. I think now it is clear to me.
$endgroup$
– Code Pope
9 hours ago
add a comment |
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1 Answer
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oldest
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oldest
votes
$begingroup$
$zsim q$ means that RV $Z$ is distributed with respect to $q$ function, i.e. $q(z)$, where $q(z)$ is a valid PDF/PMF. So, the expectation can be unfold as (assuming $z$ being continuous)
$$E_zsim q[log_phi(x_i|z)]=int_-infty^infty log_phi (x_i|z) q(z) dz$$
answered 10 hours ago
gunesgunes
8,7091418
$endgroup$
$begingroup$
Ok. Thank you. I think now it is clear to me.
$endgroup$
– Code Pope
9 hours ago
add a comment |
$begingroup$
$zsim q$ means that RV $Z$ is distributed with respect to $q$ function, i.e. $q(z)$, where $q(z)$ is a valid PDF/PMF. So, the expectation can be unfold as (assuming $z$ being continuous)
$$E_zsim q[log_phi(x_i|z)]=int_-infty^infty log_phi (x_i|z) q(z) dz$$
answered 10 hours ago
gunesgunes
8,7091418
$endgroup$
$begingroup$
Ok. Thank you. I think now it is clear to me.
$endgroup$
– Code Pope
9 hours ago
add a comment |
$begingroup$
$zsim q$ means that RV $Z$ is distributed with respect to $q$ function, i.e. $q(z)$, where $q(z)$ is a valid PDF/PMF. So, the expectation can be unfold as (assuming $z$ being continuous)
$$E_zsim q[log_phi(x_i|z)]=int_-infty^infty log_phi (x_i|z) q(z) dz$$
answered 10 hours ago
gunesgunes
8,7091418
$endgroup$
$zsim q$ means that RV $Z$ is distributed with respect to $q$ function, i.e. $q(z)$, where $q(z)$ is a valid PDF/PMF. So, the expectation can be unfold as (assuming $z$ being continuous)
$$E_zsim q[log_phi(x_i|z)]=int_-infty^infty log_phi (x_i|z) q(z) dz$$
answered 10 hours ago
gunesgunes
8,7091418
edited 10 hours ago
answered 10 hours ago
gunesgunes
8,7091418
answered 10 hours ago
gunesgunes
8,7091418
answered 10 hours ago
gunesgunes
8,7091418
8,7091418
$begingroup$
Ok. Thank you. I think now it is clear to me.
$endgroup$
– Code Pope
9 hours ago
add a comment |
$begingroup$
Ok. Thank you. I think now it is clear to me.
$endgroup$
– Code Pope
9 hours ago
$begingroup$
Ok. Thank you. I think now it is clear to me.
$endgroup$
– Code Pope
9 hours ago
$begingroup$
Ok. Thank you. I think now it is clear to me.
$endgroup$
– Code Pope
9 hours ago
add a comment |
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