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Convexity of conditional relative entropy for Markov distributions

The conditional relative entropy between them is \begin{align} D(p\parallel q)& =\sum_a p(a)\sum_b p(b\mid a)\log\frac{p(b\mid a)}{q(b\mid a)}\\ & =\sum_{ab}p(ab)\log\frac{p(b\mid a)}{q(b\mid a)} \end …
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