The supplemental material for this article available online includes an appendix with the proofs of Theorem 1 and Corollary 1 stated in Section 4 as well as the MATLAB/OCTAVE code used to implement the algorithm in the case of a noisily observed Markov chain considered in Section 5. In this case, the algorithm reaches estimation results that are comparable to those of the maximum likelihood estimator for large sample sizes. The performance of the proposed algorithm is numerically evaluated through simulations in the case of a noisily observed Markov chain. Imagine: You were locked in a room for several days and you were asked about the weather outside. Each state can emit an output which is observed. We thus provide limited results which identify the potential limiting points of the recursion as well as the large-sample behavior of the quantities involved in the algorithm. Hidden Markov Model Example Matlab Hidden Markov Model Matlab Code Introduction to Hidden Markov Models (HMM) A Hidden Markov Model, is a stochastic model where the states of the model are hidden. Although the proposed online EM algorithm resembles a classical stochastic approximation (or Robbins-Monro) algorithm, it is sufficiently different to resist conventional analysis of convergence.
The second ingredient consists in exploiting a purely recursive form of smoothing in HMMs based on an auxiliary recursion. The first one, which is deeply rooted in the Expectation-Maximization (EM) methodology, consists in reparameterizing the problem using complete-data sufficient statistics. In this work, we propose an online parameter estimation algorithm that combines two key ideas. Online (also called "recursive" or "adaptive") estimation of fixed model parameters in hidden Markov models is a topic of much interest in times series modeling.