Quantum algorithm for structure learning of Markov Random Fields

• URL: http://arxiv.org/abs/2109.01014v1
• Date: Thu, 2 Sep 2021 15:22:38 GMT
• Title: Quantum algorithm for structure learning of Markov Random Fields
• Authors: Liming Zhao, Siyi Yang, and Patrick Rebentrost
• Abstract summary: 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.
• Score: 6.174721516017139
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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.

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