Data processing inequality for mutual information

If

X \to Y \to Z

is a Markov chain, then

I (X; Z) \leq I (X; Y), I (X; Z) \leq I (Y; Z) .

Thus deterministic or randomized processing cannot increase the information shared with an unprocessed variable.

 Ancestors (6)

 Incoming links (5)

Entropy submodularity for three independent sums
Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 164 / 1 / iii / Solution
Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 224 / 1 / a / Solution
Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 224 / 1 / b / Solution
Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 224 / 1 / c / Solution

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