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» Learning Intersections and Thresholds of Halfspaces
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STOC
2003
ACM
110views Algorithms» more  STOC 2003»
14 years 7 months ago
New degree bounds for polynomial threshold functions
A real multivariate polynomial p(x1, . . . , xn) is said to sign-represent a Boolean function f : {0, 1}n {-1, 1} if the sign of p(x) equals f(x) for all inputs x {0, 1}n. We gi...
Ryan O'Donnell, Rocco A. Servedio
APPROX
2009
Springer
129views Algorithms» more  APPROX 2009»
14 years 2 months ago
Baum's Algorithm Learns Intersections of Halfspaces with Respect to Log-Concave Distributions
In 1990, E. Baum gave an elegant polynomial-time algorithm for learning the intersection of two origin-centered halfspaces with respect to any symmetric distribution (i.e., any D s...
Adam R. Klivans, Philip M. Long, Alex K. Tang
STOC
2012
ACM
209views Algorithms» more  STOC 2012»
11 years 10 months ago
Nearly optimal solutions for the chow parameters problem and low-weight approximation of halfspaces
The Chow parameters of a Boolean function f : {−1, 1}n → {−1, 1} are its n + 1 degree-0 and degree-1 Fourier coefficients. It has been known since 1961 [Cho61, Tan61] that ...
Anindya De, Ilias Diakonikolas, Vitaly Feldman, Ro...
COLT
1995
Springer
13 years 11 months ago
Learning with Unreliable Boundary Queries
We introduce a new model for learning with membership queries in which queries near the boundary of a target concept may receive incorrect or “don’t care” responses. In part...
Avrim Blum, Prasad Chalasani, Sally A. Goldman, Do...
FOCS
2010
IEEE
13 years 5 months ago
Learning Convex Concepts from Gaussian Distributions with PCA
We present a new algorithm for learning a convex set in n-dimensional space given labeled examples drawn from any Gaussian distribution. The complexity of the algorithm is bounded ...
Santosh Vempala