SPEAKER: Oscar Madrid Padilla (Neyman Visiting Assistant Professor, Department of Statistics, UC Berkeley)
TITLE: “Fused lasso on network estimation problems.”
ABSTRACT: In this talk I will describe theory and methods for the fused lasso on network problems. Three classes of problems will be discussed: denoising on networks, nonparametric regression on general metric spaces, and graphon estimation. For the first of these tasks, we provide a general upper bound on the mean squared error of the fused lasso that depends on the sample size and the total variation of the underlying signal. We show that such upper bound is minimax when the graph is a tree of bounded degree, and we present a surrogate estimator that attains the same upper bound and can be found in linear time. The second part of the talk will focus on extending the fused lasso graphs to general nonparametric regression. The resulting approach, which we call the K-nearest neighbors (K-NN) fused lasso, involves (i) computing the K-NN graph of the design points; and (ii) performing the fused lasso over this K-NN graph. We show that this procedure has several theoretical advantages over competing approaches: specifically, it inherits local adaptivity from its connection to the fused lasso, and it inherits manifold adaptivity from its connection to the K-NN approach. Finally, I will talk about some recent developments of the fused lasso for graphon estimation.
DATE: Thursday, November 1st, 4:10pm
LOCATION: MSB 1147, Colloquium Room
REFRESHMENTS: 3:30pm MSB 4110 (4th floor lounge)
STA 290 Seminar List: https://statistics.ucdavis.edu/seminars