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# Decontamination of Mutually Contaminated Models

*Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics*, PMLR 33:1-9, 2014.

#### Abstract

A variety of machine learning problems are characterized by data sets that are drawn from multiple different convex combinations of a fixed set of base distributions. We call this a mutual contamination model. In such problems, it is often of interest to recover these base distributions, or otherwise discern their properties. This work focuses on the problem of classification with multiclass label noise, in a general setting where the noise proportions are unknown and the true class distributions are nonseparable and potentially quite complex. We develop a procedure for decontamination of the contaminated models from data, which then facilitates the design of a consistent discrimination rule. Our approach relies on a novel method for estimating the error when projecting one distribution onto a convex combination of others, where the projection is with respect to an information divergence known as the separation distance. Under sufficient conditions on the amount of noise and purity of the base distributions, this projection procedure successfully recovers the underlying class distributions. Connections to novelty detection, topic modeling, and other learning problems are also discussed.