Void Probabilities and Cauchy-Schwarz Divergence for Generalized Labeled\n Multi-Bernoulli Models

2015/10/19 by Michael Beard, Beard, Michael, Ba-Tuong Vo +5 · 2 citations
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Bayesian Modeling and Causal Inference #Computation (stat.CO) #FOS: Computer and information sciences #Statistical Methods and Bayesian Inference

paper · pdf · doi:10.48550/arxiv.1510.05532

openalex publication_date 2015/10/19 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

The generalized labeled multi-Bernoulli (GLMB) is a family of tractable\nmodels that alleviates the limitations of the Poisson family in dynamic\nBayesian inference of point processes. In this paper, we derive closed form\nexpressions for the void probability functional and the Cauchy-Schwarz\ndivergence for GLMBs. The proposed analytic void probability functional is a\nnecessary and sufficient statistic that uniquely characterizes a GLMB, while\nthe proposed analytic Cauchy-Schwarz divergence provides a tractable measure of\nsimilarity between GLMBs. We demonstrate the use of both results on a partially\nobserved Markov decision process for GLMBs, with Cauchy-Schwarz divergence\nbased reward, and void probability constraint.\n

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