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Divya Padmanabhan(divya_padmanabhansutd.edu.sg) Abstract: We study the problem of computing the tightest upper and lower bounds on the probability that the sum of n dependent Bernoulli random variables exceeds an integer k. Under knowledge of all pairs of bivariate distributions denoted by a complete graph, the bounds are NPhard to compute. When the bivariate distributions are specified on a tree graph, we show that tight bounds are computable in polynomial time using linear optimization. These bounds provide robust probability estimates when the assumption of conditional independence in a tree structured graphical model is violated. Generalization of the result to finding probability bounds of order statistic for more general random variables and instances where the bounds provide the most significant improvements over univariate bounds is also discussed in the paper. Keywords: probability bounds, trees, linear optimization Category 1: Robust Optimization Category 2: Linear, Cone and Semidefinite Programming Category 3: Combinatorial Optimization Citation: Download: [PDF] Entry Submitted: 10/12/2019 Modify/Update this entry  
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