Mixed Regression: Minimax Optimal Rates

author: Constantine Caramanis, Department of Electrical and Computer Engineering, University of Texas at Austin
published: July 15, 2014,   recorded: June 2014,   views: 2187


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We consider the mixed regression problem with two components, under adversarial and stochastic noise. We give a convex optimization formulation that provably recovers the true solution, and provide upper bounds on the recovery errors for both arbitrary noise and stochastic noise settings. We also give matching minimax lower bounds (up to log factors), showing that under certain assumptions, our algorithm is information-theoretically optimal. Our results represent the first (and currently only known) tractable algorithm guaranteeing successful recovery with tight bounds on recovery errors and sample complexity.

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