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

TL;DR

This paper derives closed-form expressions for void probability and Cauchy-Schwarz divergence in generalized labeled multi-Bernoulli models, enabling improved Bayesian inference and model comparison in point process applications.

Contribution

It introduces analytic formulas for void probability and divergence measures specific to GLMBs, enhancing their tractability and utility in dynamic Bayesian inference.

Findings

Derived closed-form void probability functional for GLMBs

Established Cauchy-Schwarz divergence as a similarity measure for GLMBs

Demonstrated applications in partially observed Markov decision processes

Abstract

The generalized labeled multi-Bernoulli (GLMB) is a family of tractable models that alleviates the limitations of the Poisson family in dynamic Bayesian inference of point processes. In this paper, we derive closed form expressions for the void probability functional and the Cauchy-Schwarz divergence for GLMBs. The proposed analytic void probability functional is a necessary and sufficient statistic that uniquely characterizes a GLMB, while the proposed analytic Cauchy-Schwarz divergence provides a tractable measure of similarity between GLMBs. We demonstrate the use of both results on a partially observed Markov decision process for GLMBs, with Cauchy-Schwarz divergence based reward, and void probability constraint.