Abstract
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.
Highlights
Data acquisition is nowadays ubiquitous in any technological environment, and large amounts of data are being produced, often to an extent where it becomes a major challenge to make use of it
We focus on Bayesian networks (BNs) [15], which constitute a particular type of Probabilistic graphical models (PGMs)
We have proposed a technique for solving the maximum a posteriori (MAP) problem in hybrid dynamic hybrid BNs (DBNs)
Summary
Data acquisition is nowadays ubiquitous in any technological environment, and large amounts of data are being produced, often to an extent where it becomes a major challenge to make use of it. Due to the computational complexity of the MAP calculations [14] and their inability to benefit from the regularities of the network structure of the unrolled dynamic model, this approach would, only be feasible for very short sequences Another immediate idea is to use the well-known Viterbi algorithm [5]. By making operations on the structure of the original model, we approximately solve a MAP inference problem by performing a set of (simpler) probabilistic inference tasks. In this general formulation, any exact or approximate algorithm for belief update can be employed for the inference process in i).
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