Hidden Markov models are mixture models in which the populations from one observation to the next are selected according to an unobserved finite state-space Markov chain. Given a realization of the observation process, our aim is to estimate both the parameters of the Markov chain and of the mixture model in a Bayesian framework. In this paper, we present an original simulated annealing algorit...

| We address the problem of probability density function estimation using a Gaussian mixture model updated with the EM algorithm. To deal with the case of an unknown number of mixing kernels, we deene a new measure for Gaussian mixtures, called total kurtosis, which is based on the weighted sample kurtoses of the kernels. This measure provides an indication of how well the Gaussian mixture ts t...

For a direct-sequence spread-spectrum (DS-SS) system we pose and solve the problem of maximum-likelihood (ML) sequence estimation in the presence of narrowband interference, using the expectation-maximization (EM) algorithm. It is seen that the iterative EM algorithm obtains at each iteration an estimate of the interference which is then subtracted from the data before a new sequence estimate i...

We investigate the rigid registration of a set of points onto a surface for computer-guided oral implants surgery. We first formulate the Iterative Closest Point (ICP) algorithm as a Maximum Likelihood (ML) estimation of the transformation and the matches. Then, considering matches as a hidden random variable, we show that the ML estimation of the transformation alone leads to a criterion effic...

We present a maximum likelihood ( M l ) solution to the problem of obtaining high-resolution images from sequences of noisy, blurred, and low-resolution images. In our formulation, the registration parameters of the low-resolution images, the degrading blur, and noise variance are unknown. Our algorithm has the advantage that all unknown parameters are obtained simultaneously using all of the a...

Hidden semi-Markov models (HSMMs) are latent variable models which allow latent state persistence and can be viewed as a generalization of the popular hidden Markov models (HMMs). In this paper, we introduce a novel spectral algorithm to perform inference in HSMMs. Unlike expectation maximization (EM), our approach correctly estimates the probability of given observation sequence based on a set...

We discuss a framework for modeling the switching dynamics of a time series based on hidden Markov models (HMM) of prediction experts, here neural networks. Learning is treated as a maximum likelihood problem. In particular, we present an Expectation-Maximization (EM) algorithm for adjusting the expert parameters as well as the HMM transition probabilities. Based on this algorithm, we develop a...

This paper reviews the Maximum Likelihood estimation problem and its solution via the Expectation-Maximization algorithm. Emphasis is made on the description of finite mixtures of multi-variate Bernoulli distributions for modeling 0-1 data. General ideas about convergence and non-identifiability are presented. We discuss improvements to the algorithm and describe thoroughly what we believe are ...