Expressiveness and Learning of Hidden Quantum Markov Models
This work addresses theoretical and practical challenges in quantum-inspired probabilistic modeling, offering incremental improvements for researchers in quantum machine learning and stochastic processes.
The paper tackles the problems of characterizing expressiveness and learning hidden quantum Markov models (HQMMs), showing that HQMMs are a special subclass of observable operator models without negative probability issues and providing a retraction-based learning algorithm that is faster and scales better than previous methods.
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 \emph{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.