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619
Efficient Learning Algorithms Yield Circuit Lower Bounds
"... For C equal to polynomialsize, depthtwo threshold circuits (i.e., neural networks with a polynomial number of hidden nodes), our result shows that efficient learning algorithms for this class would solve one of the most challenging open problems in computational complexity theory: proving the exis ..."
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Cited by 9 (0 self)
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that derandomizing BPP yields nontrivial circuit lower bounds. 1 Introduction Discovering the limits of efficient learnability remains an important challenge incomputational learning theory. Traditionally, computational learning theorists have reduced problems from computational complexity theory or cryptographyto
DavenportSchinzel Sequences and Their Geometric Applications
, 1998
"... An (n; s) DavenportSchinzel sequence, for positive integers n and s, is a sequence composed of n distinct symbols with the properties that no two adjacent elements are equal, and that it does not contain, as a (possibly noncontiguous) subsequence, any alternation a \Delta \Delta \Delta b \Delta \ ..."
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Cited by 439 (105 self)
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of geometric problems can be formulated in terms of lower envelopes. A nearlinear bound on the maximum length of DavenportSchinzel sequences enable us to derive sharp bounds on the combinatorial structure underlying various geometric problems, which in turn yields efficient algorithms for these problems.
How to Use Expert Advice
 JOURNAL OF THE ASSOCIATION FOR COMPUTING MACHINERY
, 1997
"... We analyze algorithms that predict a binary value by combining the predictions of several prediction strategies, called experts. Our analysis is for worstcase situations, i.e., we make no assumptions about the way the sequence of bits to be predicted is generated. We measure the performance of the ..."
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Cited by 377 (79 self)
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is on the order of the square root of the number of mistakes of the best expert, and we give efficient algorithms that achieve this. Our upper and lower bounds have matching leading constants in most cases. We then show howthis leads to certain kinds of pattern recognition/learning algorithms with performance
Hardness vs. randomness
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 1994
"... We present a simple new construction of a pseudorandom bit generator, based on the constant depth generators of [N]. It stretches a short string of truly random bits into a long string that looks random to any algorithm from a complexity class C (eg P, NC, PSPACE,...) using an arbitrary function tha ..."
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Cited by 298 (27 self)
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that is hard for C. This construction reveals an equivalence between the problem of proving lower bounds and the problem of generating good pseudorandom sequences. Our construction has many consequences. The most direct one is that efficient deterministic simulation of randomized algorithms is possible under
ExternalMemory Graph Algorithms
, 1995
"... We present a collection of new techniques for designing and analyzing efficient externalmemory algorithms for graph problems and illustrate how these techniques can be applied to a wide variety of specific problems. Our results include: ffl Proximateneighboring. We present a simple method for der ..."
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Cited by 186 (22 self)
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for efficiently simulating PRAM computations in external memory, even for some cases in which the PRAM algorithm is not workoptimal. We apply this to derive a number of optimal (and simple) externalmemory graph algorithms. ffl Timeforward processing. We present a general technique for evaluating circuits (or
Mining circuit lower bound proofs for metaalgorithms
, 2013
"... We show that circuit lower bound proofs based on the method of random restrictions yield nontrivial compression algorithms for “easy ” Boolean functions from the corresponding circuit classes. The compression problem is defined as follows: given the truth table of an nvariate Boolean function f co ..."
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Cited by 6 (0 self)
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We show that circuit lower bound proofs based on the method of random restrictions yield nontrivial compression algorithms for “easy ” Boolean functions from the corresponding circuit classes. The compression problem is defined as follows: given the truth table of an nvariate Boolean function f
The pyramid match kernel: Efficient learning with sets of features
 Journal of Machine Learning Research
, 2007
"... In numerous domains it is useful to represent a single example by the set of the local features or parts that comprise it. However, this representation poses a challenge to many conventional machine learning techniques, since sets may vary in cardinality and elements lack a meaningful ordering. Kern ..."
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Cited by 136 (10 self)
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the pyramid match yields a Mercer kernel, and we prove bounds on its error relative to the optimal partial matching cost. We demonstrate our algorithm on both classification and regression tasks, including object recognition, 3D human pose inference, and time of publication estimation for documents, and we
On Basing LowerBounds for Learning on WorstCase Assumptions
"... We consider the question of whether P != NP implies that there exists some concept class that is efficiently representable but is still hard to learn in the PAC model of Valiant (CACM ’84), where the learner is allowed to output any efficient hypothesis approximating the concept, including an “impro ..."
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Cited by 15 (4 self)
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by showing that lower bounds for improper learning are intimately related to the complexity of zeroknowledge arguments and to the existence of weak cryptographic primitives. In particular, we prove that if a language L reduces to the task of improper learning of circuits, then, depending on the type
Exact Learning Algorithms, Betting Games, and Circuit
"... This paper extends and improves work of Fortnow and Klivans [6], who showed that if a circuit class C has an efficient learning algorithm in Angluin’s model of exact learning via equivalence and membership queries [2], then we have the lower bound EXP NP ⊆ C. We use entirely different techniques in ..."
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Cited by 1 (0 self)
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This paper extends and improves work of Fortnow and Klivans [6], who showed that if a circuit class C has an efficient learning algorithm in Angluin’s model of exact learning via equivalence and membership queries [2], then we have the lower bound EXP NP ⊆ C. We use entirely different techniques
On Basing LowerBounds for Learning on WorstCase Assumptions
"... We consider the question of whether P � = NP implies that there exists some concept class that is efficiently representable but is still hard to learn in the PAC model of Valiant (CACM ’84), where the learner is allowed to output any efficient hypothesis approximating the concept, including an “impr ..."
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by showing that lower bounds for improper learning are intimately related to the complexity of zeroknowledge arguments and to the existence of weak cryptographic primitives. In particular, we prove that if a language L reduces to the task of improper learning of circuits, then, depending on the type
Results 1  10
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619