期望值约束下的联合概率,运输问题,最大平均熵

IF 1.4 3区 数学 Q2 STATISTICS & PROBABILITY
H. Gzyl, Silvia Mayoral
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引用次数: 0

摘要

确定已知边际的联合概率问题有一些有趣的扩展。一方面,可以对联合概率施加大小约束。另一方面,可能会施加额外的约束,如已知随机变量的期望值。如果我们把边际概率看作需求或供给,联合概率看作供给从生产地点运到需求地点的比例,我们可以考虑运输政策而不是联合概率。显然,确定运输策略的成本相当于对联合概率的积分约束。我们将展示如何用均值最大熵的方法来解决成本受限的运输问题。我们还将展示这种方法如何导致求解相关线性规划问题的类内点方法。我们还将研究一些几何结构的交通政策的空间,或联合概率或像素空间,使用黎曼结构与熵的对偶相关联,用于确定概率之间或交通政策之间的界限。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Joint probabilities under expected value constraints, transportation problems, maximum entropy in the mean
There are interesting extensions of the problem of determining a joint probability with known marginals. On the one hand, one may impose size constraints on the joint probabilities. On the other, one may impose additional constraints like the expected values of known random variables. If we think of the marginal probabilities as demands or supplies, and of the joint probability as the fraction of the supplies to be shipped from the production sites to the demand sites, instead of joint probabilities we can think of transportation policies. Clearly, fixing the cost of a transportation policy is equivalent to an integral constraints upon the joint probability. We will show how to solve the cost constrained transportation problem by means of the method of maximum entropy in the mean. We shall also show how this approach leads to an interior point like method to solve the associated linear programming problem. We shall also investigate some geometric structure the space of transportation policies, or joint probabilities or pixel space, using a Riemannian structure associated with the dual of the entropy used to determine bounds between probabilities or between transportation policies.
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来源期刊
Statistica Neerlandica
Statistica Neerlandica 数学-统计学与概率论
CiteScore
2.60
自引率
6.70%
发文量
26
审稿时长
>12 weeks
期刊介绍: Statistica Neerlandica has been the journal of the Netherlands Society for Statistics and Operations Research since 1946. It covers all areas of statistics, from theoretical to applied, with a special emphasis on mathematical statistics, statistics for the behavioural sciences and biostatistics. This wide scope is reflected by the expertise of the journal’s editors representing these areas. The diverse editorial board is committed to a fast and fair reviewing process, and will judge submissions on quality, correctness, relevance and originality. Statistica Neerlandica encourages transparency and reproducibility, and offers online resources to make data, code, simulation results and other additional materials publicly available.
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