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Probabilistic divide-and-conquer -- A new method for exact simulation -- and lower bound expansions for random Bernoulli matrices via novel integer partitions.

机译：概率分治法-一种精确模拟的新方法-以及通过新颖的整数分区对随机伯努利矩阵进行下界展开的方法。

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This thesis is divided into two areas of combinatorial probability: probabilistic divide-and-conquer, and random Bernoulli matrices via novel integer partitions.;Probabilistic divide-and-conquer is a new method of exact sampling that simulates from a set of objects by dividing each object into two disjoint parts, and pieces them together.;The study of random Bernoulli matrices is driven by the asymptotics of the probability that a random matrix whose entries are independent, identically distributed Bernoulli random variables with parameter 1/2 is singular. Our approach is an inclusion-exclusion expansion for this probability, defining a necessary and sufficient class of integer partitions as an index set to characterize all of the singularities.

机译：本文将组合概率分为两个区域：概率除数和概率，以及通过新型整数分区的随机伯努利矩阵。概率除数和概率是一种精确采样的新方法，该方法通过对一组对象进行除法来模拟每个对象分成两个不相交的部分，并将它们组合在一起。随机伯努利矩阵的研究是由渐近性驱动的，该随机矩阵的项是独立的，参数为1/2的均匀分布的伯努利随机变量是奇异的。我们的方法是对此可能性进行包含－排除扩展，定义一个必要和充分的整数分区类，作为表征所有奇点的索引集。

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作者
DeSalvo, Stephen Anthony.;
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作者单位

University of Southern California.;

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授予单位 University of Southern California.;
学科 Mathematics.
学位 Ph.D.
年度 2012
页码 106 p.
总页数 106
原文格式 PDF
正文语种 eng
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专利

1. On the Singularity of Random Bernoulli Matrices- Novel Integer Partitions and Lower Bound Expansions [J] . Arratia R., DeSalvo S. Annals of combinatorics . 2013,第2期

机译：关于随机伯努利矩阵的奇异性-新的整数分区和下界展开
2. Probabilistic Divide-and-Conquer: A New Exact Simulation Method, With Integer Partitions as an Example [J] . Arratia Richard, deSalvo Stephen Combinatorics, probability & computing: CPC . 2016,第3期

机译：概率分而治之：一种新的精确模拟方法，以整数分区为例
3. Exact Sampling Algorithms for Latin Squares and Sudoku Matrices via Probabilistic Divide-and-Conquer [J] . DeSalvo Stephen Algorithmica . 2017,第3期

机译：通过概率分治法对拉丁平方和数独矩阵进行精确采样的算法
4. Lower Bounds for Exact Model Counting and Applications in Probabilistic Databases [C] . Paul Beame, Jerry Li, Sudeepa Roy, Conference on uncertainty in artificial intelligence . 2013

机译：精确模型计数的下界及其在概率数据库中的应用
5. On High-Performance Benders-Decomposition-Based Exact Methods With Application to Mixed-Integer and Stochastic Problems [D] . Rahmaniani, Ragheb. 2018

机译：基于高性能Benders分解的精确方法及其在混合整数和随机问题中的应用
6. Cannons and sparrows II: the enhanced Bernoulli exact method for determining statistical significance and effect size in the meta-analysis of k 2 × 2 tables [O] . Lawrence M. Paul 2021

机译：大炮和麻雀II：增强的Bernoulli精确方法用于确定K 2×2表的META分析中的统计显着性和效果大小的精确方法
7. ON THE SINGULARITY OF RANDOM BERNOULLI MATRICES — NOVEL INTEGER PARTITIONS AND LOWER BOUND EXPANSIONS [O] . Richard Arratia, Stephen Desalvo 2016

机译：关于随机BERNOULLI矩阵的奇异性 - 新的整数分布和下限扩张
8. Computing Probabilistic Bounds for Extreme Eigenvalues of Symmetric Matrices with211 the Lanczos Method. Modelling, Analysis and Simulation (MAS) [R] . van Dorsselaer, J. L. M., Hochstenbach, M. E., van der Vorst, H. A. 1999

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Probabilistic divide-and-conquer -- A new method for exact simulation -- and lower bound expansions for random Bernoulli matrices via novel integer partitions.

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