Probabilistic Inference in the Era of Tensor Networks and Differential Programming

TL;DR

This paper explores tensor network methods for probabilistic inference in graphical models, introducing new tensor-based algorithms for key inference tasks and demonstrating their effectiveness through experiments inspired by quantum physics advances.

Contribution

It advances the integration of tensor networks with probabilistic graphical models, providing novel tensor-based algorithms for inference tasks and sampling methods.

Findings

Tensor network algorithms improve inference accuracy

Enhanced methods for computing partition functions and marginals

Effective sampling from learned distributions

Abstract

Probabilistic inference is a fundamental task in modern machine learning. Recent advances in tensor network (TN) contraction algorithms have enabled the development of better exact inference methods. However, many common inference tasks in probabilistic graphical models (PGMs) still lack corresponding TN-based adaptations. In this work, we advance the connection between PGMs and TNs by formulating and implementing tensor-based solutions for the following inference tasks: (i) computing the partition function, (ii) computing the marginal probability of sets of variables in the model, (iii) determining the most likely assignment to a set of variables, and (iv) the same as (iii) but after having marginalized a different set of variables. We also present a generalized method for generating samples from a learned probability distribution. Our work is motivated by recent technical advances in the fields of quantum circuit simulation, quantum many-body physics, and statistical physics. Through an experimental evaluation, we demonstrate that the integration of these quantum technologies with a series of algorithms introduced in this study significantly improves the effectiveness of existing methods for solving probabilistic inference tasks.