Description of current research

This document describes the research I have done since October 1995 for my PhD thesis at the Dept. of Computer Science, University of Sheffield, U.K., which I expect to complete by October/November 1999. My thesis research has involved two generic fields of machine learning: dimensionality reduction and sequential data reconstruction, which I have approached from the common point of view of latent variable models. I consider dimensionality reduction as the search for a parsimonious representation of high dimensional data— such as a scanned image or the output of an auditory model. This representation or coordinate change can be seen as a (nonlinear) projection from the pattern space onto another space of much lower dimension. Clearly, for dimensionality reduction to be useful, the reduced-dimension patterns must contain all, or most of, the information contained in the original patterns, so that subsequent processing (recognition, regression, classification, etc.) is not deteriorated. Besides that, dimensionality reduction can reveal structure contained in the original patterns which may not be apparent due to their high dimensionality. Missing data reconstruction is a very general problem which involves recovering part of a data set which, for different reasons, has been lost. It includes as particular cases multivariate regression, mapping approximation, inverse problems, missing data imputation and prediction—each of which are broad areas of machine learning. To implement dimensionality reduction and data reconstruction we need models. After having completed a literature review (Carreira-Perpiñán, 1996) during my first year, I chose to concentrate for my thesis into a class of probabilistic models: latent variable models. This is a very broad class, as nearly any variable from a model which is not one of the observed variables can be considered as a latent variable. Thus, Hidden Markov Models or mixture models can be considered as latent variable models. However, I have restricted myself to latent variable models where both the observed variables and the latent ones are continuous (except for Monte Carlo sampled latent variable models).