Abstract

Probabilistic graphical models are a key tool in machine learning applications. Computing the partition function, i.e., normalizing constant, is fundamental task of statistical inference but it i generally computationally intractable, leading to extensive study of approximation methods. Iterative variational methods are a popular and success ful family of approaches. However, even state of the art variational methods can return poor result or fail to converge on difficult instances. In thi paper, we instead consider computing the partition function via sequential summation over variables. We develop robust approximate algorithms by combining ideas from mini-bucket elimination with tensor network and renormalization group methods from statistical physics. The resulting “convergence-free” methods show good empirical performance on both synthetic and real-world benchmark models, even for difficult instances.