Exponentiated Strongly Rayleigh Distributions
Exponentiated Strongly Rayleigh Distributions
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发表时间：
2018
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通讯作者：
Zelda E. Mariet;S. Sra;S. Jegelka
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作者：
Zelda E. Mariet;S. Sra;S. Jegelka
强瑞利测度是一个基集子集上的离散概率分布。它们具有很强的负相关性质，因此它们赋予不同元素的子集更高的概率。我们在本文中引入了指数强瑞利（ESR）测度，它通过单个参数（指数）锐化（或平滑）SR测度的负相关特性，该参数可以直观地理解为逆温度。我们开发了从esr近似采样的有效MCMC程序，并获得了两个具体实例的明确混合时间界限：确定性点过程的指数版本和双体积采样。我们通过将esr应用于一些机器学习任务来说明esr的一些潜力；实证结果证实，除了理论吸引力之外，基于esr的模型在这些任务中具有重要的前景。
Strongly Rayleigh (SR) measures are discrete probability distributions over the subsets of a ground set. They enjoy strong negative dependence properties, as a result of which they assign higher probability to subsets of diverse elements. We introduce in this paper Exponentiated Strongly Rayleigh (ESR) measures, which sharpen (or smoothen) the negative dependence property of SR measures via a single parameter (the exponent) that can intuitively understood as an inverse temperature. We develop efficient MCMC procedures for approximate sampling from ESRs, and obtain explicit mixing time bounds for two concrete instances: exponentiated versions of Determinantal Point Processes and Dual Volume Sampling. We illustrate some of the potential of ESRs, by applying them to a few machine learning tasks; empirical results confirm that beyond their theoretical appeal, ESR-based models hold significant promise for these tasks.