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Statistics Department Seminar Series: Bryon Aragam, Machine Learning Department, Carnegie Mellon University

"Identifiability of nonparametric mixture models, clustering, and semi-supervised learning"
Friday, January 18, 2019
11:30 AM-1:00 PM
411 West Hall Map
Motivated by problems in data clustering and semi-supervised learning, we establish general conditions under which families of nonparametric mixture models are identifiable by introducing a novel framework for clustering overfitted parametric (i.e. misspecified) mixture models. These conditions generalize existing conditions in the literature, allowing for general nonparametric mixture components. Notably, our results avoid imposing assumptions on the mixture components, and instead impose regularity assumptions on the underlying mixing measure. After a discussion of some statistical aspects of this problem, we will discuss two applications of this framework. First, we extend classical model-based clustering to nonparametric settings and develop a practical algorithm for learning nonparametric mixtures. Second, we analyze the sample complexity of semi-supervised learning (SSL) and introduce new assumptions based on the mismatch between a mixture model learned from unlabeled data and the true mixture model induced by the (unknown) class conditional distributions. Under these assumptions, we establish an \Omega(K\log K) labeled sample complexity bound without imposing parametric assumptions, where K is the number of classes. These results suggest that even in nonparametric settings it is possible to learn a near-optimal classifier using only a few labeled samples.

[1] Aragam, B., Dan, C., Ravikumar, P. and Xing, E. P. Identifiability of nonparametric mixture models and Bayes optimal clustering. Under review.
[2] Dan, C., Leqi, L., Aragam, B., Ravikumar, P., and Xing, E. P. The Sample Complexity of Semi-Supervised Learning with Nonparametric Mixture Models. NeurIPS 2018.
Building: West Hall
Event Type: Workshop / Seminar
Tags: seminar
Source: Happening @ Michigan from Department of Statistics, Department of Statistics Seminar Series