Expressiveness and Learning of Hidden Quantum Markov Models

Sandesh Adhikary, Siddarth Srinivasan, Geoff Gordon, Byron Boots
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:4151-4161, 2020.

Abstract

Extending classical probabilistic reasoning using the quantum mechanical view of probability has been of recent interest, particularly in the development of hidden quantum Markov models (HQMMs) to model stochastic processes. However, there has been little progress in characterizing the expressiveness of such models and learning them from data. We tackle these problems by showing that HQMMs are a special subclass of the general class of observable operator models (OOMs) that do not suffer from the negative probability problem by design. We also provide a feasible retraction-based learning algorithm for HQMMs using constrained gradient descent on the Stiefel manifold of model parameters. We demonstrate that this approach is faster and scales to larger models than previous learning algorithms.

Cite this Paper

BibTeX
@InProceedings{pmlr-v108-adhikary20a, title = {Expressiveness and Learning of Hidden Quantum Markov Models}, author = {Adhikary, Sandesh and Srinivasan, Siddarth and Gordon, Geoff and Boots, Byron}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {4151--4161}, year = {2020}, editor = {Chiappa, Silvia and Calandra, Roberto}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/adhikary20a/adhikary20a.pdf}, url = {https://proceedings.mlr.press/v108/adhikary20a.html}, abstract = {Extending classical probabilistic reasoning using the quantum mechanical view of probability has been of recent interest, particularly in the development of hidden quantum Markov models (HQMMs) to model stochastic processes. However, there has been little progress in characterizing the expressiveness of such models and learning them from data. We tackle these problems by showing that HQMMs are a special subclass of the general class of observable operator models (OOMs) that do not suffer from the negative probability problem by design. We also provide a feasible retraction-based learning algorithm for HQMMs using constrained gradient descent on the Stiefel manifold of model parameters. We demonstrate that this approach is faster and scales to larger models than previous learning algorithms.} }
Endnote
%0 Conference Paper %T Expressiveness and Learning of Hidden Quantum Markov Models %A Sandesh Adhikary %A Siddarth Srinivasan %A Geoff Gordon %A Byron Boots %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-adhikary20a %I PMLR %P 4151--4161 %U https://proceedings.mlr.press/v108/adhikary20a.html %V 108 %X Extending classical probabilistic reasoning using the quantum mechanical view of probability has been of recent interest, particularly in the development of hidden quantum Markov models (HQMMs) to model stochastic processes. However, there has been little progress in characterizing the expressiveness of such models and learning them from data. We tackle these problems by showing that HQMMs are a special subclass of the general class of observable operator models (OOMs) that do not suffer from the negative probability problem by design. We also provide a feasible retraction-based learning algorithm for HQMMs using constrained gradient descent on the Stiefel manifold of model parameters. We demonstrate that this approach is faster and scales to larger models than previous learning algorithms.
APA
Adhikary, S., Srinivasan, S., Gordon, G. & Boots, B.. (2020). Expressiveness and Learning of Hidden Quantum Markov Models. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:4151-4161 Available from https://proceedings.mlr.press/v108/adhikary20a.html.

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