Scaling Probabilistic Inference Through Message Contraction Optimization

Within the realm of probabilistic graphical models, message-passing algorithms offer a powerful framework for efficient inference. When dealing with discrete variables, these algorithms essentially amount to the addition and multiplication of multidimensional arrays with labeled dimensions, known as factors. The complexity of these algorithms is dictated by the highest-dimensional factor appearing across all computations, a metric known as the induced tree width. Although state-of-the-art methods aimed at minimizing this metric have expanded the feasi-bility of exact inference, many real-world problems continue to be intractable. In this paper, we introduce a novel method for adding and multiplying factors that results in a substantial improvement in the inference performance, especially for increasingly complex models. Our approach aligns well with existing state-of-the-art methods designed to minimize the induced tree width, thereby further expanding the tractability spectrum of exact inference for more complex models. To demonstrate the efficacy of our method, we conduct a comparative evaluation against two other open-source libraries for probabilistic inference. Our approach exhibits an average speedup of 23 times for the UAI 2014 benchmark set. For the 10 most complex problems, the average speedup increases to 64 times, demonstrating its scalability.