Bucket Renormalization for Approximate Inference
This addresses the challenge of approximate inference in machine learning, offering a convergence-free method that improves reliability for difficult cases, though it appears incremental as it builds on existing mini-bucket elimination and renormalization group techniques.
The paper tackled the computationally intractable problem of computing partition functions in probabilistic graphical models by developing robust approximate algorithms based on sequential summation over variables, achieving good empirical performance on synthetic and real-world benchmarks, including difficult instances.
Probabilistic graphical models are a key tool in machine learning applications. Computing the partition function, i.e., normalizing constant, is a fundamental task of statistical inference but it is generally computationally intractable, leading to extensive study of approximation methods. Iterative variational methods are a popular and successful family of approaches. However, even state of the art variational methods can return poor results or fail to converge on difficult instances. In this 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.