770 research outputs found
A Convex Formulation for Mixed Regression with Two Components: Minimax Optimal Rates
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 tractable algorithm guaranteeing successful
recovery with tight bounds on recovery errors and sample complexity.Comment: Added results on minimax lower bounds, which match our upper bounds
on recovery errors up to log factors. Appeared in the Conference on Learning
Theory (COLT), 2014. (JMLR W&CP 35 :560-604, 2014
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