Noisy Independent Factor Analysis Model for Density Estimation and Classification

TL;DR

This paper introduces a fast, adaptive density estimation method for noisy independent factor analysis models, enabling effective classification in high-dimensional settings with unknown parameters.

Contribution

It develops a nearly parametric rate density estimator that adapts to unknown components and mixing matrix, improving density estimation and classification in noisy IFA models.

Findings

Estimator achieves nearly parametric rate log^(1/4)n/sqrt(n).

Classifier attains optimal excess Bayes risk rate.

Method performs well on simulated and real remote sensing data.

Abstract

We consider the problem of multivariate density estimation when the unknown density is assumed to follow a particular form of dimensionality reduction, a noisy independent factor analysis (IFA) model. In this model the data are generated by a number of latent independent components having unknown distributions and are observed in Gaussian noise. We do not assume that either the number of components or the matrix mixing the components are known. We show that the densities of this form can be estimated with a fast rate. Using the mirror averaging aggregation algorithm, we construct a density estimator which achieves a nearly parametric rate log^(1/4)n/sqrt(n), independent of the dimensionality of the data, as the sample size $n$ tends to infinity. This estimator is adaptive to the number of components, their distributions and the mixing matrix. We then apply this density estimator to construct nonparametric plug-in classifiers and show that they achieve the best obtainable rate of the excess Bayes risk, to within a logarithmic factor independent of the dimension of the data. Applications of this classifier to simulated data sets and to real data from a remote sensing experiment show promising results.