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2 votes
0 answers
111 views

Generalization of the min-entropy that looks at the top $n$ probabilities

The min-entropy of a random variable $X$ can often be much easier to compute than the Shannon entropy. This is because the min-entropy is simply a function of the most probable value, and sometimes, ...
1 vote
2 answers
1k views

Approximation of the sum involving binary entropy function

Given the following sum: $S(n) = \sum_{i=1}^{n} \frac{1}{(1-\operatorname{H}(p))^i}$ where $H$ is the binary entropy function defined as: $\operatorname{H}(p) = -p\log p - (1-p)\log (1-p) $. Let $...
3 votes
0 answers
180 views

A.G. Vitushkin's "Easily representable families of functions" - can it be generalized?

Background In his monograph "Estimation of the complexity of the tabulation problem" (translated into English as "Theory of the Transmission and Processing of Information") Vitushkin studies ...