Hybrid joint PDF estimation and classification for sparse systems

We developed methods for estimating joint probability density functions (PDFs) of statistically dependent features from sparse data with the main focus on computing likelihood functions for classification. We limited methods to those that use marginal probabilities as building blocks. The estimators studied are (1) semiparametric models, i.e., combinations of nonparametric and parametric components of the form /spl Pi//sub i/p/sub i/(f/sub i/)[M/sub n/(f)//spl Pi//sub i/m/sub i/(f/sub i/)], where f represents a set of n features p/sub i/(f/sub i/) are the marginal probabilities and M/sub n/(f) is a model for the n-dimensional multivariate PDF with model marginals m/sub i/(f/sub i/); and (2) nonparametric expansion models: the PDF is expanded in terms of its excess probabilities, /spl Pi//sub l/p/sub l/(f/sub l/)[1+/spl Sigma//sub i\n\n\t\t