利用部分加权信息确定并概率的界
On Bounding the Union Probability Using Partial Weighted Information
摘要：
联合概率的有效界在概率论、信息论、统计通信、计算和运筹学等许多领域的随机问题分析中是非常有用的。在这项工作中，我们提出了新的结果上绑定的概率有限工会的事件，${P\left(\bigcup_{i=1}^N A_i\right)}$，为一个固定的正整数${N}$，使用部分信息的事件方面的${\{P(A_i)\}}$和${\{\sum_j c_j P(A_i\cap A_j)\}}$其中${c_1}$，${\dots}$，${c_N}$给定的权重。我们推导出两类新的下界至多伪多项式的计算复杂性。这些类的下界推广现有的界限在\cite{Kuai2000}和最近的界限在\cite{Yang2014,Yang2014ISIT}和数字显示，在某些情况下，更严格的Gallot-Kounias界\cite{Gallot1966,Kounias1968}和Pr{é}kopa-Gao界\cite{Prekopa2005}，需要更多的信息的事件概率。
英文摘要：
Effective bounds on the union probability are well known to be beneficial in the analysis of stochastic problems in many areas, including probability theory, information theory, statistical communications, computing and operations research. In this work we present new results on bounding the probability of a finite union of events, ${P\left(\bigcup_{i=1}^N A_i\right)}$, for a fixed positive integer ${N}$, using partial information on the events in terms of ${\{P(A_i)\}}$ and ${\{\sum_j c_j P(A_i\cap A_j)\}}$ where ${c_1}$, ${\dots}$, ${c_N}$ are given weights. We derive two new classes of lower bounds of at most pseudo-polynomial computational complexity. These classes of lower bounds generalize the existing bound in \cite{Kuai2000} and recent bounds in \cite{Yang2014,Yang2014ISIT} and are numerically shown to be tighter in some cases than the Gallot-Kounias bound \cite{Gallot1966,Kounias1968} and the Pr{é}kopa-Gao bound \cite{Prekopa2005} which require more information on the events probabilities.
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