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13 votes
1 answer
10k views

KL divergence and mixture of Gaussians

Do we have an exact formula to compute the KL divergence between 2 mixtures of Gaussians (i.e convex combinations of a finite number of Gaussian distributions)? If not exactly known, are there good ...
gradstudent's user avatar
  • 2,246
9 votes
1 answer
2k views

Uniform sampling from general simplex with a twist

This is part of a question I had asked elsewhere, and then some of the links redirected me to CS stack exchange. Given $0\leq a_1\leq\dots\leq a_D\leq1$ (all strictly positive), I want to draw points ...
Juanito's user avatar
  • 221
7 votes
1 answer
509 views

An order statistics problem with some interesting geometry

Let $a_n$ be a given sequence of positive numbers, and $X_n$ a sequence of independent random variables with each $X_n$ uniformly distributed on $[0, a_n]$. Question: Let $N \geq 2$ be an arbitrary ...
Nate River's user avatar
  • 6,223
0 votes
0 answers
113 views

How much a probability distribution is non-uniform in a convex subspace of $\mathbb{R}^d$?

I know a number of (standard and well known) ways to measure the distance between two probability distributions and, more in general, to quantify how much one is far from another. Could you please ...
Penelope Benenati's user avatar