Quantum algorithm for structure learning of Markov Random Fields

TL;DR

This paper introduces a quantum-enhanced algorithm for learning the structure of Markov Random Fields, achieving a polynomial speedup over classical methods for bounded-degree MRFs.

Contribution

It develops a modified classical algorithm that incorporates quantum subroutines, enabling faster structure learning of MRFs with bounded degree.

Findings

Achieves polynomial quantum speedup in learning MRF structure

Retains classical algorithm's runtime and guarantees

Applicable to MRFs with bounded degree

Abstract

Markov random fields (MRFs) appear in many problems in machine learning and statistics. From a computational learning theory point of view, a natural problem of learning MRFs arises: given samples from an MRF from a restricted class, learn the structure of the MRF, that is the neighbors of each node of the underlying graph. In this work, we start at a known near-optimal classical algorithm for this learning problem and develop a modified classical algorithm. This classical algorithm retains the run time and guarantee of the previous algorithm and enables the use of quantum subroutines. Adapting a previous quantum algorithm, the Quantum Sparsitron, we provide a polynomial quantum speedup in terms of the number of variables for learning the structure of an MRF, if the MRF has bounded degree.