MACHINE LEARNING SEMINAR

Thời gian: 15:00 đến 16:30 Ngày 08/08/2024

Địa điểm: Viện Nghiên cứu cao cấp về Toán (VIASM), 157 Phố Chùa Láng, Đống Đa, Hà Nội.

Tittle: Dendrogram of mixing measures: Hierarchical clustering and mixture models

Báo cáo viên: Prof. Xuan-Long Nguyen, University of Michigan, USA

Abstract: We present a new way to summarize and select mixture models via the hierarchical clustering tree (dendrogram) constructed from an overfitted latent mixing measure. Our proposed method bridges agglomerative hierarchical clustering and mixture modeling. The dendrogram's construction is derived from the theory of convergence of the mixing measures, and as a result, we can both consistently select the true number of mixing components and obtain the pointwise optimal convergence rate for parameter estimation from the tree, even when the model parameters are only weakly identifiable.

In theory, it explicates the choice of the optimal number of clusters in hierarchical clustering. In practice, the dendrogram reveals more information on the hierarchy of subpopulations compared to traditional ways of summarizing mixture models. Several simulation studies are carried out to support our theory. We also illustrate the methodology with an application to single-cell RNA sequence analysis. This work is joint with Dat Do, Linh Do, Scott McKinley and Jonathan Terhorst.

Bio: Long Nguyen is Professor of Statistics, and by courtesy, of Electrical Engineering and Computer Science at the University of Michigan, Ann Arbor. His research interests include nonparametric Bayesian statistics, optimal transport and statistical inference, and machine learning with complex spatiotemporal models. Nguyen has served as associate editor of the Annals of Statistics, the Annals of Institute of Statistical Mathematics, Bayesian Analysis, Journal of Machine Learning Research, SIAM Journal on Mathematics of Data Science, and Journal of American Statistical Association. He has received the Leon O. Chua award from UC Berkeley, the IEEE Signal Processing society's Young Author best paper award, twice best paper awards from the International Conference on Machine Learning (ICML), and the CAREER award from the NSF's Division of Mathematical Sciences. He has given keynote lectures at the Vietnam Congress on Statistics and Probability, the Pacific-Asia Knowledge Discovery and Data Mining conference, the International Conference on Bayesian Nonparametrics, and the BAYSM conference. He is elected fellow of the IMS, the ASA, and a distinguished associate member of Vietnam Institute for Advanced Study in Mathematics.

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