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.

Maximum Entropy Interval Aggregations

Cicalese, Ferdinando
;
2018-01-01

Abstract

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.
2018
978-1-5386-4781-3
Entropy, Information theory, Probability distributions
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/990326
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