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» Learning Intersections and Thresholds of Halfspaces
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STOC
2003
ACM
110views Algorithms» more  STOC 2003»
15 years 12 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»
15 years 6 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»
13 years 2 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
15 years 3 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
14 years 9 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