0
votes
1answer
155 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 ...
2
votes
0answers
110 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 ...
4
votes
1answer
408 views

Low degree polynomial approximation for the entropy function

Let $X$ be a discrete random variable with possible values $\{x_1,\ldots,x_n\}$, and let $p$ denote the probability mass function of $X$. In addition, denote $p_i=p(x_i)$. The entropy of $X$ is ...