Description 
Speaker: Bryon Aragam
Title: Identifiability of nonparametric mixture models, clustering, and semisupervised learning
Abstract: Motivated by problems in data clustering and semisupervised 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 modelbased clustering to nonparametric settings and develop a practical algorithm for learning nonparametric mixtures. Second, we analyze the sample complexity of semisupervised 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 nearoptimal 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. https://arxiv.org/abs/1802.04397 [2] Dan, C., Leqi, L., Aragam, B., Ravikumar, P., and Xing, E. P. The Sample Complexity of SemiSupervised Learning with Nonparametric Mixture Models. NeurIPS 2018. http://papers.nips.cc/paper/8144thesamplecomplexityofsemisupervisedlearningwithnonparametricmixturemodels
Biography:
Bryon Aragam is a Project Scientist in the Machine Learning Department at Carnegie Mellon University. He received his PhD from UCLA in 2015. His research is at the intersection of machine learning and highdimensional statistics, with a focus on problems with noniid, nonconvex, and heterogeneous structure. His previous work includes work on theoretical foundations and algorithms for graphical models, mixture models, and semisupervised learning.
