Learning in threshold networks
COLT '88 Proceedings of the first annual workshop on Computational learning theory
Redundant noisy attributes, attribute errors, and linear-threshold learning using winnow
COLT '91 Proceedings of the fourth annual workshop on Computational learning theory
Threshold circuits of bounded depth
Journal of Computer and System Sciences
On the Size of Weights for Threshold Gates
SIAM Journal on Discrete Mathematics
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
Boosting a weak learning algorithm by majority
Information and Computation
The Markov chain Monte Carlo method: an approach to approximate counting and integration
Approximation algorithms for NP-hard problems
A decision-theoretic generalization of on-line learning and an application to boosting
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
Simulating Threshold Circuits by Majority Circuits
SIAM Journal on Computing
On Restricted-Focus-of-Attention Learnability of Boolean Functions
Machine Learning - Special issue on the ninth annual conference on computational theory (COLT '96)
Learning with restricted focus of attention
Journal of Computer and System Sciences
Chow Parameters in Threshold Logic
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
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Neural Networks and Complexity Theory
MFCS '92 Proceedings of the 17th International Symposium on Mathematical Foundations of Computer Science
On Small Depth Threshold Circuits
SWAT '92 Proceedings of the Third Scandinavian Workshop on Algorithm Theory
On Small Depth Threshold Circuits
SWAT '92 Proceedings of the Third Scandinavian Workshop on Algorithm Theory
A Note on the Simulation of Exponential Threshold Weights
COCOON '96 Proceedings of the Second Annual International Conference on Computing and Combinatorics
Learnability with Restricted Focus of Attention guarantees Noise-Tolerance
AII '94 Proceedings of the 4th International Workshop on Analogical and Inductive Inference: Algorithmic Learning Theory
Approximate counting by dynamic programming
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Random Walks on Truncated Cubes and Sampling 0-1 Knapsack Solutions
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
On connectionist models
Learning intersections and thresholds of halfspaces
Journal of Computer and System Sciences - Special issue on FOCS 2002
Markov chains and polynomial time algorithms
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Bounding the average sensitivity and noise sensitivity of polynomial threshold functions
Proceedings of the forty-second ACM symposium on Theory of computing
SIAM Journal on Computing
Testing (subclasses of) halfspaces
Property testing
Testing (subclasses of) halfspaces
Property testing
Bounded Independence Fools Halfspaces
SIAM Journal on Computing
SIAM Journal on Computing
Hardness results for agnostically learning low-degree polynomial threshold functions
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Nearly optimal solutions for the chow parameters problem and low-weight approximation of halfspaces
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Low-weight halfspaces for sparse boolean vectors
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Improved Approximation of Linear Threshold Functions
Computational Complexity
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Given any linear threshold function f on n Boolean variables, we construct a linear threshold function g which disagrees with f on at most an 驴 fraction of inputs and has integer weights each of magnitude at most $${\sqrt{n}\cdot}2^{{\tilde{O}}(1/ \epsilon^{2})}$$ We show that the construction is optimal in terms of its dependence on n by proving a lower bound of $$\Omega(\sqrt{n})$$ on the weights required to approximate a particular linear threshold function. We give two applications. The first is a deterministic algorithm for approximately counting the fraction of satisfying assignments to an instance of the zero-one knapsack problem to within an additive 卤 驴. The algorithm runs in time polynomial in n (but exponential in $${1}/{\epsilon^{2}}$$ ). In our second application, we show that any linear threshold function f is specified to within error 驴 by estimates of its Chow parameters (degree 0 and 1 Fourier coefficients) which are accurate to within an additive $$\pm{1}/({n}\cdot 2^{{\tilde{O}}(1/ \epsilon^{2})})$$ . This is the first such accuracy bound which is inverse polynomial in n, and gives the first polynomial bound (in terms of n) on the number of examples required for learning linear threshold functions in the "restricted focus of attention" framework.