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The Nature of Statistical Learning Theory
, 1999
"... Statistical learning theory was introduced in the late 1960’s. Until the 1990’s it was a purely theoretical analysis of the problem of function estimation from a given collection of data. In the middle of the 1990’s new types of learning algorithms (called support vector machines) based on the deve ..."
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Cited by 12991 (31 self)
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Statistical learning theory was introduced in the late 1960’s. Until the 1990’s it was a purely theoretical analysis of the problem of function estimation from a given collection of data. In the middle of the 1990’s new types of learning algorithms (called support vector machines) based
Maximum likelihood from incomplete data via the EM algorithm
 JOURNAL OF THE ROYAL STATISTICAL SOCIETY, SERIES B
, 1977
"... A broadly applicable algorithm for computing maximum likelihood estimates from incomplete data is presented at various levels of generality. Theory showing the monotone behaviour of the likelihood and convergence of the algorithm is derived. Many examples are sketched, including missing value situat ..."
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Cited by 11827 (17 self)
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A broadly applicable algorithm for computing maximum likelihood estimates from incomplete data is presented at various levels of generality. Theory showing the monotone behaviour of the likelihood and convergence of the algorithm is derived. Many examples are sketched, including missing value
A better algorithm for random kSAT
 SIAM Journal on Computing
"... Let Φ be a uniformly distributed random kSAT formula with n variables and m clauses. We present a polynomial time algorithm that finds a satisfying assignment of Φ with high probability for constraint densities m/n < (1 − εk)2 k ln(k)/k, where εk → 0. Previously no efficient algorithm was known ..."
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Cited by 16 (4 self)
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Let Φ be a uniformly distributed random kSAT formula with n variables and m clauses. We present a polynomial time algorithm that finds a satisfying assignment of Φ with high probability for constraint densities m/n < (1 − εk)2 k ln(k)/k, where εk → 0. Previously no efficient algorithm was known
On the Complexity of kSAT
, 2001
"... The kSAT problem is to determine if a given kCNF has a satisfying assignment. It is a celebrated open question as to whether it requires exponential time to solve kSAT for k 3. Here exponential time means 2 $n for some $>0. In this paper, assuming that, for k 3, kSAT requires exponential time ..."
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Cited by 111 (8 self)
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The kSAT problem is to determine if a given kCNF has a satisfying assignment. It is a celebrated open question as to whether it requires exponential time to solve kSAT for k 3. Here exponential time means 2 $n for some $>0. In this paper, assuming that, for k 3, kSAT requires exponential
An Approximation Algorithm for #kSAT
"... We present a simple randomized algorithm that approximates the number of satisfying assignments of Boolean formulas in conjunctive normal form. To the best of our knowledge this is the first algorithm which approximates #kSAT for any k ≥ 3 within a running time that is not only nontrivial, but als ..."
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Cited by 1 (0 self)
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We present a simple randomized algorithm that approximates the number of satisfying assignments of Boolean formulas in conjunctive normal form. To the best of our knowledge this is the first algorithm which approximates #kSAT for any k ≥ 3 within a running time that is not only non
An Improved Exponentialtime Algorithm for kSAT
, 1998
"... We propose and analyze a simple new randomized algorithm, called ResolveSat, for finding satisfying assignments of Boolean formulas in conjunctive normal form. The algorithm consists of two stages: a preprocessing stage in which resolution is applied to enlarge the set of clauses of the formula, ..."
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Cited by 116 (7 self)
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, followed by a search stage that uses a simple randomized greedy procedure to look for a satisfying assignment. We show that, for each k, the running time of ResolveSat on a kCNF formula is significantly better than 2 n , even in the worst case. In particular, we show that the algorithm finds a
Approximating MIN kSAT
"... We obtain substantially improved approximation algorithms for the MIN lSAT problem, for k = 2, 3. More specifically, we obtain a 1.1037approximation algorithm for the MIN 2SAT problem, improving a previous 1.5approximation algorithm, and a 1.2136approximation algorithm for the MIN 3SAT problem, ..."
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Cited by 9 (0 self)
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, improving a previous 1.75approximation algorithm for the problem. These results are obtained by adapting techniques that were previously used to obtain approximation algorithms for the MAX kSAT problem. We also obtain some hardness of approximation results.
Randomized Gossip Algorithms
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2006
"... Motivated by applications to sensor, peertopeer, and ad hoc networks, we study distributed algorithms, also known as gossip algorithms, for exchanging information and for computing in an arbitrarily connected network of nodes. The topology of such networks changes continuously as new nodes join a ..."
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Cited by 524 (5 self)
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distribute the computational burden and in which a node communicates with a randomly chosen neighbor. We analyze the averaging problem under the gossip constraint for an arbitrary network graph, and find that the averaging time of a gossip algorithm depends on the second largest eigenvalue of a doubly
On an Online Random kSAT model
"... Given n Boolean variables x1,..., xn, a kclause is a disjunction of k literals, where a literal is a variable or its negation. Suppose random kclauses are generated one at a time and an online algorithm accepts or rejects each clause as it is generated. Our goal is to accept as many randomly gener ..."
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Given n Boolean variables x1,..., xn, a kclause is a disjunction of k literals, where a literal is a variable or its negation. Suppose random kclauses are generated one at a time and an online algorithm accepts or rejects each clause as it is generated. Our goal is to accept as many randomly
Randomized Algorithms
, 1995
"... Randomized algorithms, once viewed as a tool in computational number theory, have by now found widespread application. Growth has been fueled by the two major benefits of randomization: simplicity and speed. For many applications a randomized algorithm is the fastest algorithm available, or the simp ..."
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Cited by 2228 (37 self)
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Randomized algorithms, once viewed as a tool in computational number theory, have by now found widespread application. Growth has been fueled by the two major benefits of randomization: simplicity and speed. For many applications a randomized algorithm is the fastest algorithm available
Results 1  10
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2,545,851