2 research outputs found
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