A reservoir-driven non-stationary hidden Markov model

In this work, we propose a novel approach towards sequential data modeling that leverages the strengths of hidden Markov models and echo-state networks (ESNs) in the context of non-parametric Bayesian inference approaches. We introduce a non-stationary hidden Markov model, the time-dependent state transition probabilities of which are driven by a high-dimensional signal that encodes the whole history of the modeled observations, namely the state vector of a postulated observations-driven ESN reservoir. We derive an efficient inference algorithm for our model under the variational Bayesian paradigm, and we examine the efficacy of our approach considering a number of sequential data modeling applications.