Dartmouth Events

Abstract:A practical problem of fundamental interest is to complete a large data matrix from relatively few observed entries. A well known example is the Netflix prize problem. Perturbation theory provides perturbation bounds on spectral parameters of a matrix under a small perturbation. In recent works, we discovered that many classical perturbation bounds (such as Weyl theorem) can be improved significantly when the perturbation is random. In this talk, I will going to give a brief survey on mathematical approaches to the matrix completion problems, and discuss a very simple new algorithm based on our results concerning random perturbation. The key of this study is a new Davis-Kahan bound in the infinity norm.

Bio:Van Vu is currently Percey F. Smith Professor of Mathematics and Professor of Statistics and Data Science at Yale. His research focuses on random matrices, random graphs, foundation of data science, and additive combinatorics. Prof. Vu got his PhD from Yale in 1998 under the direction of Laszlo Lovasz. Before coming back to Yale in 2011, he worked at IAS, Microsoft Research, UCSD, and Rutgers. Prof. Vu is a recipient of a Sloan Fellowship, a Polya prize (SIAM), and a Fulkerson prize (AMS). He was a Medallion speaker at the 8th World Congress in Probability (Istanbul) and an invited speaker at ICM (Seoul).