A Review of Inference Algorithms for Hybrid Bayesian Networks

Hybrid Bayesian networks have received an increasing attention during the last years. The difference with respect to standard Bayesian networks is that they can host discrete and continuous variables simultaneously, which extends the applicability of the Bayesian network framework in general. However, this extra feature also comes at a cost: inference in these types of models is computationally more challenging and the underlying models and updating procedures may not even support closed-form solutions. In this paper we provide an overview of the main trends and principled approaches for performing inference in hybrid Bayesian networks. The methods covered in the paper are organized and discussed according to their methodological basis. We consider how the methods have been extended and adapted to also include (hybrid) dynamic Bayesian networks, and we end with an overview of established software systems supporting inference in these types of models

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

MAP inference in dynamic hybrid Bayesian networks

In this paper, we study the maximum a posteriori (MAP) problem in dynamic hybrid Bayesian networks. We are interested in finding the sequence of values of a class variable that maximizes the posterior probability given evidence. We propose an approximate solution based on transforming the MAP problem into a simpler belief update problem. The proposed solution constructs a set of auxiliary networks by grouping consecutive instantiations of the variable of interest, thus capturing some of the potential temporal dependences between these variables while ignoring others. Belief update is carried out independently in the auxiliary models, after which the results are combined, producing a configuration of values for the class variable along the entire time sequence. Experiments have been carried out to analyze the behavior of the approach. The algorithm has been implemented using Java 8 streams, and its scalability has been evaluated