Learnability and the Vapnik-Chervonenkis dimension
Journal of the ACM (JACM)
Redundant noisy attributes, attribute errors, and linear-threshold learning using winnow
COLT '91 Proceedings of the fourth annual workshop on Computational learning theory
Equivalence of models for polynomial learnability
Information and Computation
Learning in the presence of malicious errors
SIAM Journal on Computing
How fast can a threshold gate learn?
Proceedings of a workshop on Computational learning theory and natural learning systems (vol. 1) : constraints and prospects: constraints and prospects
Toward Efficient Agnostic Learning
Machine Learning - Special issue on computational learning theory, COLT'92
Learning conjuctions with noise under product distributions
Information Processing Letters
Large Margin Classification Using the Perceptron Algorithm
Machine Learning - The Eleventh Annual Conference on computational Learning Theory
Improved Boosting Algorithms Using Confidence-rated Predictions
Machine Learning - The Eleventh Annual Conference on computational Learning Theory
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
PAC Analogues of Perceptron and Winnow Via Boosting the Margin
Machine Learning
Efficient algorithms in computational learning theory
Efficient algorithms in computational learning theory
Optimally-smooth adaptive boosting and application to agnostic learning
The Journal of Machine Learning Research
Smooth boosting and learning with malicious noise
The Journal of Machine Learning Research
Optimal outlier removal in high-dimensional spaces
Journal of Computer and System Sciences - STOC 2001
Hardness of Learning Halfspaces with Noise
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Cryptographic Hardness for Learning Intersections of Halfspaces
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
New Results for Learning Noisy Parities and Halfspaces
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
The geometry of logconcave functions and sampling algorithms
Random Structures & Algorithms
Agnostically Learning Halfspaces
SIAM Journal on Computing
The hardness of approximate optima in lattices, codes, and systems of linear equations
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Using the doubling dimension to analyze the generalization of learning algorithms
Journal of Computer and System Sciences
Learning disjunction of conjunctions
IJCAI'85 Proceedings of the 9th international joint conference on Artificial intelligence - Volume 1
Extensions of principal components analysis
Extensions of principal components analysis
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We give new algorithms for learning halfspaces in the challenging malicious noise model, where an adversary may corrupt both the labels and the underlying distribution of examples. Our algorithms can tolerate malicious noise rates exponentially larger than previous work in terms of the dependence on the dimension n, and succeed for the fairly broad class of all isotropic log-concave distributions. We give poly(n, 1/ε)-time algorithms for solving the following problems to accuracy ε: Learning origin-centered halfspaces in Rn with respect to the uniform distribution on the unit ball with malicious noise rate η = Ω(ε2 / log(n/ε)). (The best previous result was Ω(ε / (n log(n/ε))1/4).) Learning origin-centered halfspaces with respect to any isotropic log-concave distribution on Rn with malicious noise rate η = Ω(ε3 / log2(n/ε)). This is the first efficient algorithm for learning under isotropic log-concave distributions in the presence of malicious noise. We also give a poly(n,1/ε)-time algorithm for learning origin-centered halfspaces under any isotropic log-concave distribution on Rn in the presence of adversarial label noise at rate η = Ω(ε3 / log(1/ε)). In the adversarial label noise setting (or agnostic model), labels can be noisy, but not example points themselves. Previous results could handle η = Ω(ε) but had running time exponential in an unspecified function of 1/ε. Our analysis crucially exploits both concentration and anti-concentration properties of isotropic log-concave distributions. Our algorithms combine an iterative outlier removal procedure using Principal Component Analysis together with "smooth" boosting.