In this paper, we consider a generalization of the state-of-art discriminative method for optimizing the conditional likelihood in Hidden Markov Models (HMMs), called the Extended Baum-Welch (EBW) algorithm, that has had significant impact on the speech recognition community. We propose a generalized form of EBW update rules that can be associated with a weighted sum of updated and initial mode...

Baum-Katz theorem asserts that the Cesàro means of i.i.d. increments distributed like X r-converge if and only if |X| is integrable. We generalize this, and we unify other results, by proving that the following equivalence holds, if and only if G is moderate: the Cesàro means G-converge if and only if G(La) is integrable for every a if and only if |X| G(|X|) is integrable. Here, La is the last ...

We describe the maximum-likelihood parameter estimation problem and how the ExpectationMaximization (EM) algorithm can be used for its solution. We first describe the abstract form of the EM algorithm as it is often given in the literature. We then develop the EM parameter estimation procedure for two applications: 1) finding the parameters of a mixture of Gaussian densities, and 2) finding the...

This paper presents new application of Particle Swarm Optimization (PSO) algorithm for training Hidden Markov Models (HMMs). The problem of finding an optimal set of model parameters is numerical optimization problem constrained by stochastic character of HMM parameters. Constraint handling is carried out using three different ways and the results are compared to Baum-Welch algorithm (BW), comm...

In this paper, we derive an algorithm similar to the well-known Baum–Welch algorithm for estimating the parameters of a hidden Markov model (HMM). The new algorithm allows the observation PDF of each state to be defined and estimated using a different feature set. We show that estimating parameters in this manner is equivalent to maximizing the likelihood function for the standard parameterizat...

In this paper several results concerning static hand gesture recognition using an algorithm based on left-right Hidden Markov Models (HMM) are presented. The features used as observables in the training as well as in the recognition phases are based either on the 2D Discrete Cosine Transform (DCT) or on the Principal Component Analysis (PCA). The left-right topology of the HMM together with the...

This paper presents an algorithm for learning the underlying models which generate streams of observations, found in video data, which encode activities performed by a person who appears in the video. With these learned models, we then aim to carry out recognition in new video streams which display the same activities as the ones that were learned. Our algorithm represents the underlying models...

Recently a generalized hidden Markov model (GHMM) was proposed for solving the information fusion problems under aleatory and epistemic uncertainties in engineering application. In GHMM, aleatory uncertainty is captured by the probability measure whereas epistemic uncertainty is modeled by generalized interval. In this paper, the problem of how to train the GHMM with a small amount of observati...

We demonstrate the generalizability of the Extended BaumWelch (EBW) algorithm not only for HMM parameter estimation but for decoding as well. We show that there can exist a general function associated with the objective function under EBW that reduces to the well-known auxiliary function used in the Baum-Welch algorithm for maximum likelihood estimates. We generalize representation for the upda...