Pull Message Passing for Nonparametric Belief Propagation

TL;DR

This paper introduces a 'pull' message passing approach for nonparametric belief propagation that improves computational efficiency and scalability in high-dimensional, multi-modal distributions, enhancing inference accuracy.

Contribution

The paper proposes the PMPNBP algorithm, a novel 'pull' method for message updates in NBP, addressing computational challenges of traditional 'push' approaches.

Findings

PMPNBP scales better with the number of mixture components.

PMPNBP improves inference accuracy over existing methods.

The approach is demonstrated on pose inference in cluttered environments.

Abstract

We present a "pull" approach to approximate products of Gaussian mixtures within message updates for Nonparametric Belief Propagation (NBP) inference. Existing NBP methods often represent messages between continuous-valued latent variables as Gaussian mixture models. To avoid computational intractability in loopy graphs, NBP necessitates an approximation of the product of such mixtures. Sampling-based product approximations have shown effectiveness for NBP inference. However, such approximations used within the traditional "push" message update procedures quickly become computationally prohibitive for multi-modal distributions over high-dimensional variables. In contrast, we propose a "pull" method, as the Pull Message Passing for Nonparametric Belief propagation (PMPNBP) algorithm, and demonstrate its viability for efficient inference. We report results using an experiment from an existing NBP method, PAMPAS, for inferring the pose of an articulated structure in clutter. Results from this illustrative problem found PMPNBP has a greater ability to efficiently scale the number of components in its mixtures and, consequently, improve inference accuracy.