Gaussian Mixture Reduction for Time-Constrained Approximate Inference in Hybrid Bayesian Networks

TL;DR

This paper introduces a Gaussian mixture reduction technique and an optimization algorithm for time-constrained approximate inference in hybrid Bayesian networks, specifically targeting the computational challenges in conditional Gaussian networks.

Contribution

It extends the Hybrid Message Passing algorithm with Gaussian mixture reduction and develops a pre-processing method to optimize accuracy within time bounds.

Findings

The extended algorithm outperforms existing methods in accuracy and speed.

Optimal runtime settings significantly improve inference efficiency.

Experimental results validate the effectiveness of the proposed approach.

Abstract

Hybrid Bayesian Networks (HBNs), which contain both discrete and continuous variables, arise naturally in many application areas (e.g., image understanding, data fusion, medical diagnosis, fraud detection). This paper concerns inference in an important subclass of HBNs, the conditional Gaussian (CG) networks, in which all continuous random variables have Gaussian distributions and all children of continuous random variables must be continuous. Inference in CG networks can be NP-hard even for special-case structures, such as poly-trees, where inference in discrete Bayesian networks can be performed in polynomial time. Therefore, approximate inference is required. In approximate inference, it is often necessary to trade off accuracy against solution time. This paper presents an extension to the Hybrid Message Passing inference algorithm for general CG networks and an algorithm for optimizing its accuracy given a bound on computation time. The extended algorithm uses Gaussian mixture reduction to prevent an exponential increase in the number of Gaussian mixture components. The trade-off algorithm performs pre-processing to find optimal run-time settings for the extended algorithm. Experimental results for four CG networks compare performance of the extended algorithm with existing algorithms and show the optimal settings for these CG networks.