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We present a transductive learning algorithm that takes as input training examples from a distribution P and arbitrary (unlabeled) test examples, possibly chosen by an adversary. This is unlike prior work that assumes that test examples are small perturbations of P. Our algorithm outputs a selective classifier, which abstains from predicting on some examples. By considering selective transductive learning, we give the first nontrivial guarantees for learning classes of bounded VC dimension with arbitrary train and test distributions—no prior guarantees were known even for simple classes of functions such as intervals on the line. In particular, for any function in a class C of bounded VC dimension, we guarantee a low test error rate and a low rejection rate with respect to P. Our algorithm is efficient given an Empirical Risk Minimizer (ERM) for C. Our guarantees hold even for test examples chosen by an unbounded whitebox adversary. We also give guarantees for generalization, agnostic, and unsupervised settings.
Author Information
Shafi Goldwasser (The Simons Institute for the Theory of Computing)
Shafi Goldwasser is Director of the Simons Institute for the Theory of Computing, and Professor of Electrical Engineering and Computer Science at the University of California Berkeley. Goldwasser is also Professor of Electrical Engineering and Computer Science at MIT and Professor of Computer Science and Applied Mathematics at the Weizmann Institute of Science, Israel. Goldwasser holds a B.S. Applied Mathematics from Carnegie Mellon University (1979), and M.S. and Ph.D. in Computer Science from the University of California Berkeley (1984). Goldwasser's pioneering contributions include the introduction of probabilistic encryption, interactive zero knowledge protocols, elliptic curve primality testings, hardness of approximation proofs for combinatorial problems, and combinatorial property testing. Goldwasser was the recipient of the ACM Turing Award in 2012, the Gödel Prize in 1993 and in 2001, the ACM Grace Murray Hopper Award in 1996, the RSA Award in Mathematics in 1998, the ACM Athena Award for Women in Computer Science in 2008, the Benjamin Franklin Medal in 2010, the IEEE Emanuel R. Piore Award in 2011, the Simons Foundation Investigator Award in 2012, and the BBVA Foundation Frontiers of Knowledge Award in 2018. Goldwasser is a member of the NAS, NAE, AAAS, the Russian Academy of Science, the Israeli Academy of Science, and the London Royal Mathematical Society. Goldwasser holds honorary degrees from Ben Gurion University, Bar Ilan University, Carnegie Mellon University, Haifa University, University of Oxford, and the University of Waterloo, and has received the UC Berkeley Distinguished Alumnus Award and the Barnard College Medal of Distinction.
Adam Tauman Kalai (Microsoft Research)
Yael Kalai (Micr)
Omar Montasser (Toyota Technological Institute at Chicago)
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