Maximum Entropy Interval Aggregations

Given a probability distribution mathbf p=(p- 1, ⋖s,p- n) and an integer 1 leq m < n, we say that mathbf q=(q- 1, ldots, q- m) is a contiguous m-aggregation of p if there exist indices 0=i- 0 < i- 1 < cdots < i- m-1 < i- m=n such that for each j=1, ldots, m it holds that q- j= sum- k=i- i-1+1 x- jp- k. In this paper, we consider the problem of efficiently finding the contiguous m-aggregation of maximum entropy. We design a dynamic programming algorithm that solves the problem exactly, and two more time-efficient greedy algorithms that provide slightly sub-optimal solutions. We also discuss a few scenarios where our problem matters.