Estimating the Accuracy of Spectral Learning for HMMs

Hidden Markov models (HMMs) are usually learned using the expectation maximisation algorithm which is, unfortunately, subject to local optima. Spectral learning for HMMs provides a unique, optimal solution subject to availability of a sufficient amount of data. However, with access to limited data, there is no means of estimating the accuracy of the solution of a given model. In this paper, a new spectral evaluation method has been proposed which can be used to assess whether the algorithm is converging to a stable solution on a given dataset. The proposed method is designed for real-life datasets where the true model is not available. A number of empirical experiments on synthetic as well as real datasets indicate that our criterion is an accurate proxy to measure quality of models learned using spectral learning

Hidden Quantum Markov Models and Open Quantum Systems with Instantaneous Feedback

Hidden Markov Models are widely used in classical computer science to model stochastic processes with a wide range of applications. This paper concerns the quantum analogues of these machines --- so-called Hidden Quantum Markov Models (HQMMs). Using the properties of Quantum Physics, HQMMs are able to generate more complex random output sequences than their classical counterparts, even when using the same number of internal states. They are therefore expected to find applications as quantum simulators of stochastic processes. Here, we emphasise that open quantum systems with instantaneous feedback are examples of HQMMs, thereby identifying a novel application of quantum feedback control.Comment: 10 Pages, proceedings for the Interdisciplinary Symposium on Complex Systems in Florence, September 2014, minor correction