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The degree-$d$ Chow parameters of a Boolean function $f: \{-1,1\}^n \to \mathbb{R}$ are its degree at most $d$ Fourier coefficients.
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The elementary statistics of majority voting
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The Perceptron: a probabilistic model for information storage and organization in the brain
F. Rosenblatt · 1958
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Truth functions realizable by single threshold organs
C.C. Elgot · 1960
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On the characterization of threshold functions
C.K. Chow · 1961
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Theory of majority switching elements
S. Muroga, I. Toda, and S. Takasu · 1961
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Majority decision functions of up to six variables
S. Muroga, I. Toda, and M. Kondo · 1962
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A geometric test-synthesis procedure for a threshold device
P. Kaszerman · 1963
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Threshold logic in artificial intelligence
R.O. Winder · 1963
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Threshold functions through n = 7 n=7
R.O. Winder · 1964
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Weighted voting doesn’t work: A mathematical analysis
J. Banzhaf · 1965
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Threshold Logic: A Synthesis Approach
M. Dertouzos · 1965
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Chebyshev approximation and threshold functions
K.R. Kaplan and R.O. Winder · 1965
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Enumeration of threshold functions of eight variables
S. Muroga, T. Tsuboi, and C.R. Baugh · 1967
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Perceptrons: an introduction to computational geometry
M. Minsky and S. Papert · 1968
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Threshold gate approximations based on chow parameters
R.O. Winder · 1969
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The counting vector of a simple game
E. Lapidot · 1972
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Chow parameters in pseudothreshold logic
C. R. Baugh · 1973
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The application of Chow Parameters and Rademacher-Walsh matrices in the synthesis of binary functions
S.L. Hurst · 1973
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Mathematical properties of the Banzhaf power index
P. Dubey and L.S. Shapley · 1979
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Learning disjunctions of conjunctions
L. Valiant · 1985
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Regular simple games
E. Einy and E. Lehrer · 1989
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Harmonic analysis of polynomial threshold functions
J. Bruck · 1990
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Decision theoretic generalizations of the PAC model for neural net and other learning applications
D. Haussler · 1992
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A Characterization of Weighted Voting
A. Taylor and W. Zwicker · 1992
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Learning in the presence of malicious errors
M. Kearns and M. Li · 1993
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On the size of weights for threshold gates
J. Håstad · 1994
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Toward Efficient Agnostic Learning
M. Kearns, R. Schapire, and L. Sellie · 1994
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Discrete Neural Computation: A Theoretical Foundation
K.-Y. Siu, V.P. Roychowdhury, and T. Kailath · 1995
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Different ways to represent weighted majority games
J. Freixas · 1997
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Learning with restricted focus of attention
S. Ben-David and E. Dichterman · 1998
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On restricted-focus-of-attention learnability of Boolean functions
A. Birkendorf, E. Dichterman, J. Jackson, N. Klasner, and H.U. Simon · 1998
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Hardness results for agnostically learning low-degree polynomial threshold functions
I. Diakonikolas, R. O’Donnell, R. A. Servedio, and Y. Wu · 2011
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The Chow Parameters Problem
R. O’Donnell and R. Servedio · 2011
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Agnostic learning of monomials by halfspaces is hard
V. Feldman, V. Guruswami, P. Raghavendra, and Y. Wu · 2012
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Heuristic and exact solutions to the inverse power index problem for small voting bodies
S. Kurz and S. Napel · 2012
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On the inverse power index problem
S. Kurz · 2012
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Improved approximation of linear threshold functions
I. Diakonikolas and R. A. Servedio · 2013
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A. Laruelle and M. Widgren · 1998
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Distributional and L q L^{q} norm inequalities for polynomials over convex bodies in R n R^{n}
A. Carbery and J. Wright · 2001
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PAC Learning with Nasty Noise
N. Bshouty, N. Eiron, and E. Kushilevitz · 2002
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Designing the voting system for the eu council of ministers
D. Leech · 2002
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Voting power in the governance of the international monetary fund
D. Leech · 2002
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Power indices as an aid to institutional design: the generalised apportionment problem
D. Leech · 2003
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Pseudorandom generators for polynomial threshold functions
R. Meka and D. Zuckerman · 2013
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Real advantage
A. A. Razborov and E. Viola · 2013
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Nearly optimal solutions for the chow parameters problem and low-weight approximation of halfspaces
A. De, I. Diakonikolas, V. Feldman, and R. A. Servedio · 2014
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Deterministic approximate counting for juntas of degree-2 polynomial threshold functions
A. De, I. Diakonikolas, and R. A. Servedio · 2014
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Average sensitivity and noise sensitivity of polynomial threshold functions
I. Diakonikolas, P. Raghavendra, R. A. Servedio, and L. Y. Tan · 2014
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Efficient deterministic approximate counting for low-degree polynomial threshold functions
A. De and R. A. Servedio · 2014
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A regularity lemma and low-weight approximators for low-degree polynomial threshold functions
I. Diakonikolas, R. A. Servedio, L. Y. Tan, and A. Wan · 2014
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Bounding the sensitivity of polynomial threshold functions
P. Harsha, A. R. Klivans, and R. Meka · 2014
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The correct exponent for the gotsman-linial conjecture
D. M. Kane · 2014
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Analysis of Boolean Functions
R. O’Donnell · 2014
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A PTAS for agnostically learning halfspaces
A. Daniely · 2015
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Pseudorandomness via the discrete fourier transform
P. Gopalan, D. M. Kane, and R. Meka · 2015
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Complexity theoretic limitations on learning halfspaces
A. Daniely · 2016
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Robust estimators in high dimensions without the computational intractability
I. Diakonikolas, G. Kamath, D. M. Kane, J. Li, A. Moitra, and A. Stewart · 2016
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Super-linear gate and super-quadratic wire lower bounds for depth-two and depth-three threshold circuits
D. M. Kane and R. Williams · 2016
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Anti-concentration for polynomials of independent random variables
R. Meka, O. Nguyen, and V. Vu · 2016
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The power of localization for efficiently learning linear separators with noise
P. Awasthi, M. F. Balcan, and P. M. Long · 2017
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The inverse shapley value problem
A. De, I. Diakonikolas, and R. A. Servedio · 2017
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A structure theorem for poorly anticoncentrated polynomials of gaussians and applications to the study of polynomial threshold functions
D. M. Kane · 2017
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Hardness of learning noisy halfspaces using polynomial thresholds
A. Bhattacharyya, S. Ghoshal, and R. Saket · 2018
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Learning geometric concepts with nasty noise
I. Diakonikolas, D. M. Kane, and A. Stewart · 2018
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