Rényi entropies uniquely determine probability distributions
abeirami · x · 2026-08-19
A tweet explains an information theory fact: for a well-behaved probability distribution, the collection of all Rényi entropies of all orders uniquely determines the entire distribution. This is why studying the moments of the information random variable $\iota(X) = -\log p(X)$ defines the core of information theory. Relaxing the chain rule leads to a family of solutions parameterized by a single hyperparameter: Rényi entropy.
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