Robust Learning under Strong Noise via SQs

Abstract

This work provides several new insights on the robustness of Kearns' statistical query framework against challenging label-noise models. First, we build on a recent result by \cite{DBLP:journals/corr/abs-2006-04787} that showed noise tolerance of distribution-independently evolvable concept classes under Massart noise. Specifically, we extend their characterization to more general noise models, including the Tsybakov model which considerably generalizes the Massart condition by allowing the flipping probability to be arbitrarily close to $\frac{1}{2}$ for a subset of the domain. As a corollary, we employ an evolutionary algorithm by \cite{DBLP:conf/colt/KanadeVV10} to obtain the first polynomial time algorithm with arbitrarily small excess error for learning linear threshold functions over any spherically symmetric distribution in the presence of spherically symmetric Tsybakov noise. Moreover, we posit access to a stronger oracle, in which for every labeled example we additionally obtain its flipping probability. In this model, we show that every SQ learnable class admits an efficient learning algorithm with OPT + $\epsilon$ misclassification error for a broad class of noise models. This setting substantially generalizes the widely-studied problem of classification under RCN with known noise rate, and corresponds to a non-convex optimization problem even when the noise function -- i.e. the flipping probabilities of all points -- is known in advance.

References in corpus (11)

• 2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization
• Noise Tolerance under Risk Minimization
• Risk bounds for statistical learning
• Distribution-Independent PAC Learning of Halfspaces with Massart Noise
• Revisiting Perceptron: Efficient and Label-Optimal Learning of Halfspaces
• Efficient active learning of sparse halfspaces with arbitrary bounded noise
• Evolution with Drifting Targets
• Classification Under Misspecification: Halfspaces, Generalized Linear Models, and Connections to Evolvability
• A Polynomial Time Algorithm for Learning Halfspaces with Tsybakov Noise
• Learning Halfspaces with Tsybakov Noise
• Efficient Learning of Linear Separators under Bounded Noise