Quantum algorithm for Markov Random Fields structure learning by information theoretic properties

TL;DR

This paper introduces a quantum algorithm for learning the structure of Markov random fields, achieving a polynomial speed-up over classical methods and highlighting quantum computing's potential in machine learning tasks.

Contribution

It presents a novel quantum algorithm for structure learning of Markov random fields, based on a classical greedy approach, with improved efficiency.

Findings

Quantum algorithm offers polynomial speed-up over classical methods.

Demonstrates potential of quantum computing in machine learning.

Applicable to r-wise Markov Random Fields with bounded degree.

Abstract

Probabilistic graphical models play a crucial role in machine learning and have wide applications in various fields. One pivotal subset is undirected graphical models, also known as Markov random fields. In this work, we investigate the structure learning methods of Markov random fields on quantum computers. We propose a quantum algorithm for structure learning of an $r$-wise Markov Random Field with a bounded degree underlying graph, based on a nearly optimal classical greedy algorithm. The quantum algorithm provides a polynomial speed-up over the classical counterpart in terms of the number of variables. Our work demonstrates the potential merits of quantum computation over classical computation in solving some problems in machine learning.