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Classification Under Misspecification: Halfspaces, Generalized Linear Models, and Evolvability
Sitan Chen · Frederic Koehler · Ankur Moitra · Morris Yau

Tue Dec 08 08:10 AM -- 08:20 AM (PST) @ Orals & Spotlights: Learning Theory
In this paper, we revisit the problem of distribution-independently learning halfspaces under Massart noise with rate $\eta$. Recent work resolved a long-standing problem in this model of efficiently learning to error $\eta + \epsilon$ for any $\epsilon > 0$, by giving an improper learner that partitions space into $\text{poly}(d,1/\epsilon)$ regions. Here we give a much simpler algorithm and settle a number of outstanding open questions: (1) We give the first \emph{proper} learner for Massart halfspaces that achieves $\eta + \epsilon$. (2) Based on (1), we develop a blackbox knowledge distillation procedure to convert an arbitrarily complex classifier to an equally good proper classifier. (3) By leveraging a simple but overlooked connection to \emph{evolvability}, we show any SQ algorithm requires super-polynomially many queries to achieve $\mathsf{OPT} + \epsilon$. We then zoom out to study generalized linear models and give an efficient algorithm for learning under a challenging new corruption model generalizing Massart noise. Finally we study our algorithm for learning halfspaces under Massart noise empirically and find that it exhibits some appealing fairness properties as a byproduct of its strong provable robustness guarantees.

Author Information

Sitan Chen (MIT)
Frederic Koehler (MIT)
Ankur Moitra (MIT)
Morris Yau (UC Berkeley)

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