- On Gibbs sampling architecture for multi-object tracking of labeled random finite sets.
Author: Anthony Trezza, Donald J. Bucci Jr., Pramod K. Varshney
Abstract: Gibbs sampling is one of the most popular Markov chain Monte Carlo algorithms due to its simplicity, scalability, and wide applicability in many areas of statistics, science, and engineering. In the labeled random finite set literature, Gibbs sampling procedures have recently been applied to efficiently truncate single-sensor and multi-sensor δ-generalized labeled multi-Bernoulli posterior densities, as well as multi-sensor adaptive labeled multi-Bernoulli birth distributions. It's done. However, only limited discussion is provided regarding important Gibbs sampler architectural details, such as the Markov chain Monte Carlo sample generation technique and early termination criteria. This paper begins with a brief background on Markov chain Monte Carlo methods and a review of the proposed Gibbs sampler implementation for labeled random finite set filters. We then propose a short-chain multi-simulation sample generation technique that is suitable for these applications and allows the implementation of parallelism. Furthermore, we present two heuristic early termination criteria that achieve similar sampling performance with significantly fewer Markov chain observations. Finally, we demonstrate the advantages of the proposed Gibbs sampler through two Monte Carlo simulations.
2. About classes of Gibbs sampling on networks
Author: Bo Yuan, Jiaojiao Fan, Jiaming Liang, Andre Wibisono, Yongxin Chen
Summary: Consider the problem of sampling from a composite distribution whose potential (negative logarithmic density) is ∑ni=1fi(xi)+∑mj=1gj(yj)+∑ni=1∑mj=1σij2η∥xi−yj∥22 To do. xi and yj are each in Rd, f1,f2,…,fn,g1,g2,…,gm are strongly convex functions, and {σij} encodes the network structure. % Motivated by the task of sampling over a network in a distributed manner. Based on the Gibbs sampling method, we develop an efficient sampling framework for this problem when the network is a bipartite graph. More importantly, it establishes its non-asymptotic linear convergence rate. This work extends previous work that only includes graphs with two nodes \cite{lee2021structurd}. To our knowledge, this result represents the first non-asymptotic analysis of the Gibbs sampler for structured log-concave distributions on networks. Our framework could be used to sample from the distribution ∝exp(−∑ni=1fi(x)−∑mj=1gj(x)) in a distributed manner.
