一个精确的裸模拟方法来最小化一些距离。基础
A precise bare simulation approach to the minimization of some distances. Foundations
摘要：
在信息论中--以及在统计学、机器学习、人工智能、信号处理和模式识别等邻近领域中--无所不在的Kullback-Leibler信息距离（相对熵）和密切相关的Shannon熵的许多灵活化已经成为频繁使用的工具。本文的主要目的是通过一种新的无量纲裸（纯）模拟方法来处理相应的约束最小化（分别为最大化）问题。在我们的任意维度的离散设置内，几乎不需要对约束集的假设（如凸性），并且我们的方法是精确的（即，收敛于极限）。作为一个副作用，我们还得到了一个创新的方式来构建新的有用的距离/分歧。为了说明我们的方法的核心，我们提出了许多解决的情况。的广泛适用性的潜力，也表示，特别是，我们提供了许多最近的参考使用所涉及的距离/分歧和熵在各种不同的研究领域（这也可以作为一个跨学科的接口）。
英文摘要：
In information theory -- as well as in the adjacent fields of statistics, machine learning, artificial intelligence, signal processing and pattern recognition -- many flexibilizations of the omnipresent Kullback-Leibler information distance (relative entropy) and of the closely related Shannon entropy have become frequently used tools. To tackle corresponding constrained minimization (respectively maximization) problems by a newly developed dimension-free bare (pure) simulation method, is the main goal of this paper. Almost no assumptions (like convexity) on the set of constraints are needed, within our discrete setup of arbitrary dimension, and our method is precise (i.e., converges in the limit). As a side effect, we also derive an innovative way of constructing new useful distances/divergences. To illustrate the core of our approach, we present numerous solved cases. The potential for widespread applicability is indicated, too; in particular, we deliver many recent references for uses of the involved distances/divergences and entropies in various different research fields (which may also serve as an interdisciplinary interface).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
