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

Didem Kochan, Zheng Zhang, Xiu Yang
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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v190-kochan22a, title = {A Quantum-Inspired Hamiltonian Monte Carlo Method for Missing Data Imputation}, author = {Kochan, Didem and Zhang, Zheng and Yang, Xiu}, booktitle = {Proceedings of Mathematical and Scientific Machine Learning}, pages = {17--32}, year = {2022}, editor = {Dong, Bin and Li, Qianxiao and Wang, Lei and Xu, Zhi-Qin John}, volume = {190}, series = {Proceedings of Machine Learning Research}, month = {15--17 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v190/kochan22a/kochan22a.pdf}, url = {https://proceedings.mlr.press/v190/kochan22a.html}, 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.} }
Endnote
%0 Conference Paper %T A Quantum-Inspired Hamiltonian Monte Carlo Method for Missing Data Imputation %A Didem Kochan %A Zheng Zhang %A Xiu Yang %B Proceedings of Mathematical and Scientific Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Bin Dong %E Qianxiao Li %E Lei Wang %E Zhi-Qin John Xu %F pmlr-v190-kochan22a %I PMLR %P 17--32 %U https://proceedings.mlr.press/v190/kochan22a.html %V 190 %X 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.
APA
Kochan, D., Zhang, Z. & Yang, X.. (2022). A Quantum-Inspired Hamiltonian Monte Carlo Method for Missing Data Imputation. Proceedings of Mathematical and Scientific Machine Learning, in Proceedings of Machine Learning Research 190:17-32 Available from https://proceedings.mlr.press/v190/kochan22a.html.

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