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A mixture distribution is one that is written as a convex combination of other distributions. Use the "compound-distributions" tag for "concatenations" of distributions (where a parameter of a distribution is itself a random variable).
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Chain rule for KL divergence, conditional measures
The chain rule for KL divergence is widely seen in the theoretical machine learning literature and generally referenced to [1, Theorem 2.5.3]:
$$ \text{KL}[p(x, y) \mid q(x, y)]= \text{KL}[p(x) \mid q …