Matrix Estimation with Latent Permutations

Job Candidate Talk
Thursday, January 17, 2019 - 11:00am for 1 hour (actually 50 minutes)
Skiles 006
Cheng Mao – Yale University –
Mayya Zhilova
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.