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Title: L1-Penalization in Functional Linear Regression with Gaussian Design

  • Speaker: Jin Yan (Department of Mathematics, UMCP)
  • Date/Time: Thursday, February 6, 2014, 3:30pm
  • Location: Room 1313, Math Building, University of Maryland College Park (directions).
  • Sponsor: University of Maryland, Statistics Program (seminar updates).


The goal of this talk is to discuss the functional regression model with random Gaussian design and real-valued response. The main focus is on the problems in which the regression function can be well-approximated by a functional linear model with the slope function being "sparse" in the sense that it can be represented as a sum of a small number of well-separated "spikes".

This can be viewed as an extension of now classical sparse estimation problems to the infinite-dimensional case. We study an estimator of the regression function which is based on penalized empirical risk minimization with quadratic loss and the complexity penalty defined in terms of L1-norm (a continuous version of LASSO). We will introduce several important parameters characterizing sparsity in this class of models and present sharp oracle inequalities showing how the L2-error of the continuous LASSO estimator depends on the underlying sparse structure of the problem. As a corollary of our general results, we obtain new bounds for performance of the usual LASSO estimator applied to the problems with highly correlated design.

This talk is based on a joint work with Vladimir Koltchinskii.