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# A Quantum-Inspired Hamiltonian Monte Carlo Method for Missing Data Imputation

*Proceedings of Mathematical and Scientific Machine Learning*, PMLR 190:17-32, 2022.

#### Abstract

We propose a hybrid technique combining Bayesian inference and quantum-inspired Hamiltonian Monte Carlo (QHMC) method for imputation of missing datasets. QHMC is an efficient way to sample from a broad class of distributions. Unlike the standard Hamiltonian Monte Carlo algorithm in which a particle has a fixed mass, QHMC allows a particle to have a random mass matrix with a probability distribution. Our data imputation method uses stochastic gradient optimization in QHMC to avoid calculating the full gradient on the entire dataset when evolving the Hamiltonian system. We combine the stochastic gradient QHMC and first order Langevin dynamics to obtain samples whose distribution converges to the posterior one. Comparing the performance of our method with existing imputation methods on several datasets, we found out that our proposed algorithm improves the efficiency of data imputation.