Multi-Object Posterior Computation via Gibbs Sampling

2026-04-14

AI Summary

This work addresses the challenges of multi-object posterior inference under non-standard observations, where conventional filtering approaches suffer from poor smoothness and loss of historical information. To overcome these limitations, the paper proposes a multi-scan multi-object smoothing algorithm based on Gibbs sampling. By constructing conditionally conjugate Bernoulli random field distributions that admit efficient computation and sampling, the method achieves, for the first time, Bayesian multi-object smoothing suitable for superpositional measurements, thereby breaking through the inference bottleneck imposed by non-standard sensing modalities. The approach jointly models object existence probabilities and attribute densities, significantly outperforming existing detection-based smoothing techniques in low signal-to-noise ratio scenarios while providing a complete statistical characterization of key variables and parameters.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Multi-instance/Multi-view Learning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

This work presents a tractable approach to multi-object posterior computation under a generic measurement likelihood function. While filtering is a popular solution, valuable historical information is discarded. Posterior inference, which captures the full history of the multi-object states, provides a more comprehensive solution but is notoriously difficult and has received limited attention. Our proposed approach uses Gibbs Sampling (GS) to generate samples from the multi-object posterior. In particular, we establish that the conditional distributions of the multi-object posterior are Bernoulli random finite sets with explicit existence probabilities and attribute densities. These conditionals are straightforward to evaluate and sample from, enabling the construction of an efficient Gibbs sampler with standard convergence guarantees. To demonstrate its versatility, we develop the first multi-scan multi-object smoothing algorithm for superpositional measurements. Numerical experiments show that the proposed method delivers robust performance in challenging low-SNR scenarios where detection based smoothing deteriorates. Moreover, posterior samples obtained from our approach provide statistical characterizations of key variables and parameters, highlighting the advantages of posterior inference. This approach enriches multi-object estimation techniques, which historically lacked smoothing capabilities for non-standard measurements.

Problem

• multi-object posterior
• posterior inference
• Gibbs sampling
• smoothing
• random finite sets

Innovation

• Gibbs Sampling
• multi-object posterior
• Bernoulli random finite set
• multi-scan smoothing
• superpositional measurements