Find minimum distance projection of Gaussian distribution
Suppose $P$ is a $k$-dimensional Gaussian distribution $mathcal{N}(0, Sigma)$, and $Q$ is $mathcal{N}(0, A^T Sigma A)$ where $A$ is any $ktimes k$ matrix. Is there a closed form solution to the following optimization problem
$$min_A qquad KL(PVert Q) \ s.t. qquad a_i^TSigma a_i = 1 $$
where $a_i$ is the i-th column of A.
probability-distributions optimization
asked Nov 22 at 6:47
Shengjia Zhao
366114
add a comment |
Suppose $P$ is a $k$-dimensional Gaussian distribution $mathcal{N}(0, Sigma)$, and $Q$ is $mathcal{N}(0, A^T Sigma A)$ where $A$ is any $ktimes k$ matrix. Is there a closed form solution to the following optimization problem
$$min_A qquad KL(PVert Q) \ s.t. qquad a_i^TSigma a_i = 1 $$
where $a_i$ is the i-th column of A.
probability-distributions optimization
asked Nov 22 at 6:47
Shengjia Zhao
366114
add a comment |
Suppose $P$ is a $k$-dimensional Gaussian distribution $mathcal{N}(0, Sigma)$, and $Q$ is $mathcal{N}(0, A^T Sigma A)$ where $A$ is any $ktimes k$ matrix. Is there a closed form solution to the following optimization problem
$$min_A qquad KL(PVert Q) \ s.t. qquad a_i^TSigma a_i = 1 $$
where $a_i$ is the i-th column of A.
probability-distributions optimization
asked Nov 22 at 6:47
Shengjia Zhao
366114
Suppose $P$ is a $k$-dimensional Gaussian distribution $mathcal{N}(0, Sigma)$, and $Q$ is $mathcal{N}(0, A^T Sigma A)$ where $A$ is any $ktimes k$ matrix. Is there a closed form solution to the following optimization problem
$$min_A qquad KL(PVert Q) \ s.t. qquad a_i^TSigma a_i = 1 $$
where $a_i$ is the i-th column of A.
probability-distributions optimization
probability-distributions optimization
asked Nov 22 at 6:47
Shengjia Zhao
366114
asked Nov 22 at 6:47
Shengjia Zhao
366114
asked Nov 22 at 6:47
Shengjia Zhao
366114
asked Nov 22 at 6:47
Shengjia Zhao
366114
asked Nov 22 at 6:47
Shengjia Zhao
366114
366114
add a comment |
add a comment |
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