Communications of the ACM
Learning decision trees from random examples needed for learning
Information and Computation
A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
C4.5: programs for machine learning
C4.5: programs for machine learning
Learning decision trees using the Fourier spectrum
SIAM Journal on Computing
Constant depth circuits, Fourier transform, and learnability
Journal of the ACM (JACM)
Toward Efficient Agnostic Learning
Machine Learning - Special issue on computational learning theory, COLT'92
The harmonic sieve: a novel application of Fourier analysis to machine learning theory and practice
The harmonic sieve: a novel application of Fourier analysis to machine learning theory and practice
Learning functions represented as multiplicity automata
Journal of the ACM (JACM)
Near-optimal sparse fourier representations via sampling
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
The monotone theory for the PAC-model
Information and Computation
Online convex optimization in the bandit setting: gradient descent without a gradient
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Agnostically Learning Halfspaces
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
An empirical comparison of supervised learning algorithms
ICML '06 Proceedings of the 23rd international conference on Machine learning
New Results for Learning Noisy Parities and Halfspaces
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
One sketch for all: fast algorithms for compressed sensing
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
COLT'06 Proceedings of the 19th annual conference on Learning Theory
Bounding the average sensitivity and noise sensitivity of polynomial threshold functions
Proceedings of the forty-second ACM symposium on Theory of computing
The Fourier entropy-influence conjecture for certain classes of Boolean functions
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Journal of Computer and System Sciences
A composition theorem for the fourier entropy-influence conjecture
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Decision trees, protocols and the entropy-influence conjecture
Proceedings of the 5th conference on Innovations in theoretical computer science
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We give a query algorithm for agnostically learning decision trees with respect to the uniform distribution on inputs. Given black-box access to an *arbitrary* binary function f on the n-dimensional hypercube, our algorithm finds a function that agrees with f on almost (within an epsilon fraction) as many inputs as the best size-t decision tree, in time poly(n,t,1ε). This is the first polynomial-time algorithm for learning decision trees in a harsh noise model. We also give a *proper* agnostic learning algorithm for juntas, a sub-class of decision trees, again using membership queries. Conceptually, the present paper parallels recent work towards agnostic learning of halfspaces (Kalai et al, 2005); algorithmically, it is more challenging. The core of our learning algorithm is a procedure to implicitly solve a convex optimization problem over the L1 ball in 2n dimensions using an approximate gradient projection method.