The Statistics Seminar speaker for Thursday, December 6, 2018, is Cheng Mao, a postdoctoral researcher in the Department of Statistics and Data Science at Yale University. He recently obtained his Ph.D. in Mathematics and Statistics from MIT, under the supervision of Professor Philippe Rigollet. Cheng’s research interests include high-dimensional and nonparametric statistics, machine learning, and probability. His recent research focuses on matrix estimation problems with latent permutations and shape constraints. Cheng received his B.S. and M.A. degrees in Mathematics from UCLA.
Talk: Matrix Estimation with Latent Permutations
Abstract: A wide variety of applied tasks, such as ranking, clustering, graph matching and network reconstruction, can be formulated as a matrix estimation problem where the rows and columns of the matrix are shuffled by a latent permutation. The combinatorial nature of the unknown permutation and the non-convexity of the parameter space result in both statistical and algorithmic challenges. I will present recent developments of average-case models and efficient algorithms, primarily for the problems of ranking from comparisons and statistical seriation. On the statistical side, imposing shape constraints on the underlying matrix extends traditional parametric approaches, allowing for more robust and adaptive estimation. On the algorithmic front, I discuss efficient local algorithms with provable guarantees, one of which tightens a conjectured statistical-computational gap for a stochastically transitive ranking model.