Threshold circuits of bounded depth
Journal of Computer and System Sciences
Active Learning Using Arbitrary Binary Valued Queries
Machine Learning
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Testing Boolean function isomorphism
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Testing (subclasses of) halfspaces
Property testing
Testing (subclasses of) halfspaces
Property testing
Approximating the influence of monotone boolean functions in O(√n) query complexity
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Approximating the Influence of Monotone Boolean Functions in O(√n) Query Complexity
ACM Transactions on Computation Theory (TOCT)
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We consider the problem of testing whether a Boolean function f :{ - 1,1} n --{ - 1,1} is a ±1-weight halfspace , i.e. a function of the form f (x ) = sgn(w 1 x 1 + w 2 x 2 + ... + w n x n ) where the weights w i take values in { - 1,1}. We show that the complexity of this problem is markedly different from the problem of testing whether f is a general halfspace with arbitrary weights. While the latter can be done with a number of queries that is independent of n [7], to distinguish whether f is a ±-weight halfspace versus ε -far from all such halfspaces we prove that nonadaptive algorithms must make Ω(logn ) queries. We complement this lower bound with a sublinear upper bound showing that $O(\sqrt{n}\cdot $poly$(\frac{1}{\epsilon}))$ queries suffice.