Our work is motivated by the goal of learning probabilistic graphical models that are both accurate and efficient for inference. In this paper, we investigate the "degree of approximability" of joint probability distributions by introducing the parameter k(), called the effective treewidth. This parameter captures the tradeoff between the accuracy of approximation Æ, measured as the information divergence from the true distribution, and model's inference complexity, which is exponential in its treewidth k. We show that both treewidth and information divergence exhibit a threshold behavior. The relative location of such thresholds is an inherent property of the underlying distribution. Finally, we propose an efficent sampling algorithm for estimating these thresholds from data, thereby predicting the effective treewidth (the approximability) of the underlying distribution. This provides a principled approach to model selection when learning bounded-treewidth models.
By: Alina Beygelzimer, Irina Rish
Published in: RC22558 in 2002
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