# Noisy Independent Factor Analysis Model for Density Estimation and Classification

2 SMS - Statistique et Modélisation Stochatisque
LJK - Laboratoire Jean Kuntzmann
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.
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Article dans une revue
Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2010, 4, pp.707-736. <10.1214/09-EJS498>
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https://hal.archives-ouvertes.fr/hal-00853950
Contributeur : Brigitte Bidégaray-Fesquet <>
Soumis le : dimanche 25 août 2013 - 20:33:08
Dernière modification le : jeudi 9 février 2017 - 15:02:55

### Citation

Umberto Amato, Anestis Antoniadis, Alexander Samarov, Alexandre Tsybakov. Noisy Independent Factor Analysis Model for Density Estimation and Classification. Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2010, 4, pp.707-736. <10.1214/09-EJS498>. <hal-00853950>

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