We present a learning algorithm for hidden Markov models with continuous state and observation spaces. All necessary probability density functions are approximated using samples, along with density trees generated from such samples. A Monte Carlo version of Baum-Welch (EM) is employed to learn models from data, just as in regular HMM learning. Regularization during learning is obtained using an...

Consider a stationary precise hidden Markov model (HMM) with n hidden states Xk, taking values xk in a set {1, . . . ,m} and n observations Ok, taking values ok. Both the marginal model pX1(x1), the emission models pOk|Xk(ok|xk) and the transition models pXk|Xk−1(xk|xk−1) are unknown. We can then use the Baum–Welch algorithm [see, e.g., 4] to get a maximum-likelihood estimate of these models. T...

In this paper we study ergodic properties of hidden Markov models with a generalized observation structure. In particular sufficient conditions for the existence of a unique invariant measure for the pair filter-observation are given. Furthermore, necessary and sufficient conditions for the existence of a unique invariant measure of the triple state-observation-filter are provided in terms of a...

In the following, we will outline how to obtain invariants for hidden Markov and related models, based on an approach which, in its most prevalent application, served to solve the identifiability problem for hidden Markov processes (HMPs) in 1992 [13]. Some of its foundations had been layed in the late 50’s and early 60’s in order to get a grasp of problems related to that of identifying HMPs [...

A hidden Markov model for labeled observations, called a CHMM, is introduced and a maximum likelihood method is developed for estimating the parameters of the model. Instead of training it to model the statistics of the training sequences it is trained to optimize recognition. It resembles MMI training, but is more general, and has MMI as a special case. The standard forward-backward procedure ...

Since their formulation by Andrei Markov in 1906 [7], Markov chains (MC) and hidden Markov models (HMM) have found a place in diverse fields of science and engineering, from speech recognition to weather prediction to protein sequence alignment. Wherever a data set can be expressed as a string of discrete symbols, and when the data has a common source or common underlying principle, then for th...

We present products of hidden Markov models (PoHMM's), a way of combining HMM's to form a distributed state time series model. Inference in a PoHMM is tractable and eÆcient. Learning of the parameters, although intractable, can be e ectively done using the Product of Experts learning rule. The distributed state helps the model to explain data which has multiple causes, and the fact that each mo...

In this paper we present the Infinite Hierarchical Hidden Markov Model (IHHMM), a nonparametric generalization of Hierarchical Hidden Markov Models (HHMMs). HHMMs have been used for modeling sequential data in applications such as speech recognition, detecting topic transitions in video and extracting information from text. The IHHMM provides more flexible modeling of sequential data by allowin...

In previous work [4], we extended the hidden Markov model (HMM) framework to incorporate a global parametric variation in the output probabilities of the states of the HMM. Development of the parametric HMM was motivated by the task of simultaneoiusly recognizing and interpreting gestures that exhibit meaningful variation. With standard HMMs, such global variation confounds the recognition proc...