Suppose I have a Markov chain $X \to Y \to Z$ of continuous r.vs. Is it true that: $I(X;Y) \geq I(X;Z)$?
2026-03-26 19:23:44.1774553024
Does the data processing inequality hold for continuous variables?
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Yes, because conditioning still reduces entropy. (which is true because mutual information is still positive which is true because the KL divergence is still non-negative) In particular, $H(X|Y) = H(X | Y, Z) \leq H(X|Z)$, which is equivalent to the inequality you have above.