Gaussian Mixture Reduction for Time-Constrained Approximate Inference in Hybrid Bayesian Networks
This work addresses time-constrained inference for hybrid Bayesian networks, which is incremental as it builds on existing methods to enhance efficiency in applications like image understanding and medical diagnosis.
The paper tackles the problem of approximate inference in conditional Gaussian networks, which is NP-hard, by extending the Hybrid Message Passing algorithm with Gaussian mixture reduction to prevent exponential growth in components and optimizing settings for a given time bound, achieving improved performance in experiments on four networks.
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.