Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Monday, April 23, 2012, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Hemant Tyagi (EPFL)

Learning multi ridge functions in high dimensions via low rank matrix recovery

We consider the problem of learning multi ridge functions of the form f(x) = g(Ax) from point evaluations of f. We assume that the function f is defined on an l₂-ball in R^d, g is twice continuously differentiable, and A is a k x d, rank k matrix, k « d. We leverage recent techniques from low rank matrix recovery and propose a randomized, polynomial-complexity sampling scheme for uniform approximation of such functions. As a consequence we remove the commonly made compressibility assumption on the rows of A in the existing literature. Furthermore we establish the tractability of our scheme when f is a sum of k ridge functions provided f satisfies additional smoothness properties in a neighborhood of the origin.

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