Quantum Enhanced Inference in Markov Logic Networks
Abstract
Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and firstorder logic, which allows for formal deduction. An MLN is essentially a firstorder logic template to generate Markov networks. Inference in MLNs is probabilistic and it is often performed by approximate methods such as Markov chain Monte Carlo (MCMC) Gibbs sampling. An MLN has many regular, symmetric structures that can be exploited at both firstorder level and in the generated Markov network. We analyze the graph structures that are produced by various lifting methods and investigate the extent to which quantum protocols can be used to speed up Gibbs sampling with state preparation and measurement schemes. We review different such approaches, discuss their advantages, theoretical limitations, and their appeal to implementations. We find that a straightforward application of a recent result yields exponential speedup compared to classical heuristics in approximate probabilistic inference, thereby demonstrating another example where advanced quantum resources can potentially prove useful in machine learning.
 Publication:

Scientific Reports
 Pub Date:
 April 2017
 DOI:
 10.1038/srep45672
 arXiv:
 arXiv:1611.08104
 Bibcode:
 2017NatSR...745672W
 Keywords:

 Statistics  Machine Learning;
 Computer Science  Artificial Intelligence;
 Quantum Physics
 EPrint:
 8 pages, 1 figure