A Convex Formulation for Mixed Regression with Two Components: Minimax Optimal Rates
This provides the first tractable algorithm with information-theoretically optimal guarantees for mixed regression, addressing a fundamental problem in statistical learning and signal processing.
The paper tackles the mixed regression problem with two components under adversarial and stochastic noise by proposing a convex optimization formulation that provably recovers the true solution with tight bounds on recovery errors and sample complexity, achieving minimax optimal rates up to log factors.
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.