Probabilistic Independence Networks for Hidden Markov Probability Models

Graphical techniques for modeling the dependencies of randomvariables have been explored in a variety of different areas includingstatistics, statistical physics, artificial intelligence, speech recognition, image processing, and genetics.Formalisms for manipulating these models have been developedrelatively independently in these research communities. In this paper weexplore hidden Markov models (HMMs) and related structures within the general framework of probabilistic independencenetworks (PINs). The paper contains a self-contained review of the basic principles of PINs.It is shown that the well-known forward-backward (F-B) and Viterbialgorithms for HMMs are special cases of more general inference algorithms forarbitrary PINs. Furthermore, the existence of inference and estimationalgorithms for more general graphical models provides a set of analysistools for HMM practitioners who wish to explore a richer class of HMMstructures.Examples of relatively complex models to handle sensorfusion and coarticulationin speech recognitionare introduced and treated within the graphical model framework toillustrate the advantages of the general approach.

Active Learning with Statistical Models

For many types of learners one can compute the statistically 'optimal' way to select data. We review how these techniques have been used with feedforward neural networks. We then show how the same principles may be used to select data for two alternative, statistically-based learning architectures: mixtures of Gaussians and locally weighted regression. While the techniques for neural networks are expensive and approximate, the techniques for mixtures of Gaussians and locally weighted regression are both efficient and accurate.

Statistical Models for Co-occurrence Data

Modeling and predicting co-occurrences of events is a fundamental problem of unsupervised learning. In this contribution we develop a statistical framework for analyzing co-occurrence data in a general setting where elementary observations are joint occurrences of pairs of abstract objects from two finite sets. The main challenge for statistical models in this context is to overcome the inherent data sparseness and to estimate the probabilities for pairs which were rarely observed or even unobserved in a given sample set. Moreover, it is often of considerable interest to extract grouping structure or to find a hierarchical data organization. A novel family of mixture models is proposed which explain the observed data by a finite number of shared aspects or clusters. This provides a common framework for statistical inference and structure discovery and also includes several recently proposed models as special cases. Adopting the maximum likelihood principle, EM algorithms are derived to fit the model parameters. We develop improved versions of EM which largely avoid overfitting problems and overcome the inherent locality of EM--based optimization. Among the broad variety of possible applications, e.g., in information retrieval, natural language processing, data mining, and computer vision, we have chosen document retrieval, the statistical analysis of noun/adjective co-occurrence and the unsupervised segmentation of textured images to test and evaluate the proposed algorithms.