Probabilistic Inference in the Era of Tensor Networks and Differential Programming

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.

arXiv comment12 pages, 4 figures

References in corpus (16)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Entanglement renormalization
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Classical simulation of quantum many-body systems with a tree tensor network
• Simulating quantum computation by contracting tensor networks
• Unsupervised Generative Modeling Using Matrix Product States
• Differentiable Programming Tensor Networks
• Hyper-optimized tensor network contraction
• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• Tree Tensor Networks for Generative Modeling
• Tensor Networks and Quantum Error Correction
• Scaling Exact Inference for Discrete Probabilistic Programs
• Tropical Tensor Network for Ground States of Spin Glasses
• Limitations of Linear Cross-Entropy as a Measure for Quantum Advantage
• Computing solution space properties of combinatorial optimization problems via generic tensor networks