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56
Cryptographic Hardness of Distributionspecific Learning
"... We investigate cryptographic lower bounds on the learnability of Boolean formulas and constant depth circuits on the {niform distribution and other specifi; distributions. We first show that weakly learning Boolean formulas and constant depth threshold circuits with membership queries on the unifor ..."
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We investigate cryptographic lower bounds on the learnability of Boolean formulas and constant depth circuits on the {niform distribution and other specifi; distributions. We first show that weakly learning Boolean formulas and constant depth threshold circuits with membership queries
DistributionFree Testing Lower Bounds for BasicBoolean Functions
"... Abstract. In the distributionfree property testing model, the distance betweenfunctions is measured with respect to an arbitrary and unknown probability distribution D over the input domain. We consider distributionfree testing of several basic Boolean function classes over { 0, 1}n, namely monot ..."
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Cited by 10 (1 self)
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Abstract. In the distributionfree property testing model, the distance betweenfunctions is measured with respect to an arbitrary and unknown probability distribution D over the input domain. We consider distributionfree testing of several basic Boolean function classes over { 0, 1}n, namely
On Learning Monotone Boolean Functions
, 1998
"... We consider the problem of learning monotone Boolean functions over f0; 1g n under the uniform distribution. Specifically, given a polynomial number of uniform random samples for an unknown monotone Boolean function f , and given polynomial computing time, we would like to approximate f as well a ..."
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Cited by 24 (0 self)
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We consider the problem of learning monotone Boolean functions over f0; 1g n under the uniform distribution. Specifically, given a polynomial number of uniform random samples for an unknown monotone Boolean function f , and given polynomial computing time, we would like to approximate f as well
AverageCase Lower Bounds for Noisy Boolean Decision Trees
 SIAM J. Comput
, 1998
"... : We present a new method for deriving lower bounds to the expected number of queries made by noisy decision trees computing Boolean functions. The new method has the feature that expectations are taken with respect to a uniformly distributed random input, as well as with respect to the random noise ..."
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Cited by 13 (1 self)
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: We present a new method for deriving lower bounds to the expected number of queries made by noisy decision trees computing Boolean functions. The new method has the feature that expectations are taken with respect to a uniformly distributed random input, as well as with respect to the random
Optimal Cryptographic Hardness of Learning Monotone Functions
"... Abstract. A wide range of positive and negative results have been established for learning different classes of Boolean functions from uniformly distributed random examples. However, polynomialtime algorithms have thus far been obtained almost exclusively for various classes of monotone functions, ..."
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Cited by 5 (4 self)
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Abstract. A wide range of positive and negative results have been established for learning different classes of Boolean functions from uniformly distributed random examples. However, polynomialtime algorithms have thus far been obtained almost exclusively for various classes of monotone functions
Lower Bounds for Noisy . . .
 SIAM J. COMPUT
, 1996
"... We present a new method for deriving lower bounds to the expected number of queries made by noisy decision trees computing Boolean functions. The new method has the feature that expectations are taken with respect to a uniformly distributed random input, as well as with respect to the random noise, ..."
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We present a new method for deriving lower bounds to the expected number of queries made by noisy decision trees computing Boolean functions. The new method has the feature that expectations are taken with respect to a uniformly distributed random input, as well as with respect to the random noise
Restriction, terms and nonlinearity of Boolean functions
, 1999
"... Nonlinear characteristics of (Boolean) functions is one of the important issues both in the design and cryptanalysis of (private key) ciphers or encryption algorithms. This paper studies nonlinear properties of functions from three di erent but closely related perspectives: maximal odd weighting sub ..."
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Cited by 4 (0 self)
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subspaces, restrictions to cosets, and hypergraphs, all associated with a function. Main contributions of this work include (1) by using a duality property of a function, we have obtained several results that are related to lower bounds on nonlinearity as well as on the number of terms, of the function, (2
Weakly Learning DNF and Characterizing Statistical Query Learning Using Fourier Analysis
 IN PROCEEDINGS OF THE TWENTYSIXTH ANNUAL SYMPOSIUM ON THEORY OF COMPUTING
, 1994
"... We present new results on the wellstudied problem of learning DNF expressions. We prove that an algorithm due to Kushilevitz and Mansour [13] can be used to weakly learn DNF formulas with membership queries with respect to the uniform distribution. This is the rst positive result known for learn ..."
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Cited by 130 (22 self)
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various restricted forms of DNF and decision trees will solve the general problem. These lower bounds are a corollary of a more general characterization of the complexity of statistical query learning in terms of the number of uncorrelated functions in the concept class. The underlying tool for all
Lower Bounds and Hardness Amplification for Learning Shallow Monotone Formulas
"... Much work has been done on learning various classes of “simple ” monotone functions under the uniform distribution. In this paper we give the first unconditional lower bounds for learning problems of this sort by showing that polynomialtime algorithms cannot learn shallow monotone Boolean formulas ..."
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Cited by 12 (7 self)
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Much work has been done on learning various classes of “simple ” monotone functions under the uniform distribution. In this paper we give the first unconditional lower bounds for learning problems of this sort by showing that polynomialtime algorithms cannot learn shallow monotone Boolean formulas
Unconditional lower bounds for learning intersections of halfspaces
 Machine Learning
, 2007
"... We prove new lower bounds for learning intersections of halfspaces, one of the most important concept classes in computational learning theory. Our main result is that any statisticalquery algorithm for learning the intersection of √ n halfspaces in n dimensions must make 2 Ω( √ n) queries. This is ..."
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Cited by 20 (11 self)
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weight halfspaces) cannot be computed by a polynomial threshold function (PTF) with fewer than n Ω(logn/loglogn) monomials. This is the first superpolynomial lower bound on the PTF length of this concept class, and is nearly optimal. For intersections of k = ω(logn) lowweight halfspaces, we improve our lower
Results 1  10
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