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A PolynomialTime Approximation Algorithm for the Permanent of a Matrix with NonNegative Entries
 Journal of the ACM
, 2004
"... Abstract. We present a polynomialtime randomized algorithm for estimating the permanent of an arbitrary n ×n matrix with nonnegative entries. This algorithm—technically a “fullypolynomial randomized approximation scheme”—computes an approximation that is, with high probability, within arbitrarily ..."
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Cited by 324 (25 self)
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Abstract. We present a polynomialtime randomized algorithm for estimating the permanent of an arbitrary n ×n matrix with nonnegative entries. This algorithm—technically a “fullypolynomial randomized approximation scheme”—computes an approximation that is, with high probability, within arbitrarily small specified relative error of the true value of the permanent. Categories and Subject Descriptors: F.2.2 [Analysis of algorithms and problem complexity]: Nonnumerical
An Introduction to MCMC for Machine Learning
, 2003
"... This purpose of this introductory paper is threefold. First, it introduces the Monte Carlo method with emphasis on probabilistic machine learning. Second, it reviews the main building blocks of modern Markov chain Monte Carlo simulation, thereby providing and introduction to the remaining papers of ..."
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Cited by 222 (2 self)
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This purpose of this introductory paper is threefold. First, it introduces the Monte Carlo method with emphasis on probabilistic machine learning. Second, it reviews the main building blocks of modern Markov chain Monte Carlo simulation, thereby providing and introduction to the remaining papers of this special issue. Lastly, it discusses new interesting research horizons.
Expander Graphs and their Applications
, 2003
"... Contents 1 The Magical Mystery Tour 7 1.1 Some Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.1 Hardness results for linear transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.2 Error Correcting Codes . . . . . . . ..."
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Cited by 188 (5 self)
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Contents 1 The Magical Mystery Tour 7 1.1 Some Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.1 Hardness results for linear transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.2 Error Correcting Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.1.3 Derandomizing Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Magical Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2.1 A Super Concentrator with O(n) edges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2.2 Error Correcting Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2.3 Derandomizing Random Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Path coupling: A technique for proving rapid mixing in markov chains
 In FOCS ’97: Proceedings of the 38th Annual Symposium on Foundations of Computer Science (FOCS
, 1997
"... The main technique used in algorithm design for approximating #Phard counting problems is the Markov chain Monte Carlo method. At the heart of the method is the study of the convergence (mixing) rates of particular Markov chains of interest. In this paper we illustrate a new approach to the couplin ..."
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Cited by 150 (20 self)
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The main technique used in algorithm design for approximating #Phard counting problems is the Markov chain Monte Carlo method. At the heart of the method is the study of the convergence (mixing) rates of particular Markov chains of interest. In this paper we illustrate a new approach to the coupling technique, which we call path coupling, for bounding mixing rates. Previous appliccitions of coupling have required detailed insights into the combinatorics of the problem at hand, and this complexity can make the technique extremely difficult to apply successfully. Path coupling helps to minimize the combinatorial difficulty and in all cases provides simpler convergence proofs than does the standard coupling method. Howevel; the true power of the method i>i that the simpl$cation obtained may allow coupling proofs which were previously unknown, or provide significantly better bounds than those obtained using the standard method. We apply the path coupling method to several hard combinatorial problems, obtaining new or improved results. We examine combinatorial probr'ems such as graph colouring and TWICESAT, and problems fn?m statistical physics, such as the antiferromagnetic Potts model and the hardcore lattice gas model. In each case we provide either a proof of rapid mixing where none was known previously, or substantial simpl$cation of existing proofs with conseqent gains in the pegormance of the resulting algorithms. 1
Sequential Monte Carlo Samplers
, 2002
"... In this paper, we propose a general algorithm to sample sequentially from a sequence of probability distributions known up to a normalizing constant and de ned on a common space. A sequence of increasingly large arti cial joint distributions is built; each of these distributions admits a marginal ..."
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Cited by 141 (24 self)
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In this paper, we propose a general algorithm to sample sequentially from a sequence of probability distributions known up to a normalizing constant and de ned on a common space. A sequence of increasingly large arti cial joint distributions is built; each of these distributions admits a marginal which is a distribution of interest. To sample from these distributions, we use sequential Monte Carlo methods. We show that these methods can be interpreted as interacting particle approximations of a nonlinear FeynmanKac ow in distribution space. One interpretation of the FeynmanKac ow corresponds to a nonlinear Markov kernel admitting a speci ed invariant distribution and is a natural nonlinear extension of the standard MetropolisHastings algorithm. Many theoretical results have already been established for such ows and their particle approximations. We demonstrate the use of these algorithms through simulation.
A random polynomialtime algorithm for approximating the volume of convex bodies
 Journal of the ACM
, 1991
"... We consider the problem of counting the number of contingency tables with given row and column sums. This problem is known to be #Pcomplete, even when there are only two rows [7]. In this paper we present the first fullypolynomial randomized approximation scheme for counting contingency tables whe ..."
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Cited by 115 (9 self)
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We consider the problem of counting the number of contingency tables with given row and column sums. This problem is known to be #Pcomplete, even when there are only two rows [7]. In this paper we present the first fullypolynomial randomized approximation scheme for counting contingency tables when the number of rows is constant. A novel feature of our algorithm is that it is a hybrid of an exact counting technique with an approximation algorithm, giving two distinct phases. In the first, the columns are partitioned into “small ” and “large”. We show that the number of contingency tables can be expressed as the weighted sum of a polynomial number of new instances of the problem, where each instance consists of some new row sums and the original large column sums. In the second phase, we show how to approximately count contingency tables when all the column sums are large. In this case, we show that the solution lies in approximating the volume of a single convex body, a problem which is known to be solvable in polynomial time [5]. 1.
OneDimensional Quantum Walks
 STOC'01
, 2001
"... We define and analyze quantum computational variants of random walks on onedimensional lattices. In particular, we analyze a quantum analog of the symmetric random walk, which we call the Hadamard walk. Several striking differences between the quantum and classical cases are observed. For example, ..."
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Cited by 90 (11 self)
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We define and analyze quantum computational variants of random walks on onedimensional lattices. In particular, we analyze a quantum analog of the symmetric random walk, which we call the Hadamard walk. Several striking differences between the quantum and classical cases are observed. For example, when unrestricted in either direction, the Hadamard walk has position that is nearly uniformly distributed in the range [\Gamma t= p
Markov Chain Monte Carlo Data Association for General MultipleTarget Tracking Problems
, 2004
"... In this paper, we consider the general multipletarget tracking problem in which an unknown number of targets appears and disappears at random times and the goal is to find the tracks of targets from noisy observations. We propose an efficient realtime algorithm that solves the data association prob ..."
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Cited by 86 (20 self)
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In this paper, we consider the general multipletarget tracking problem in which an unknown number of targets appears and disappears at random times and the goal is to find the tracks of targets from noisy observations. We propose an efficient realtime algorithm that solves the data association problem and is capable of initiating and terminating a varying number of tracks. We take the dataoriented, combinatorial optimization approach to the data association problem but avoid the enumeration of tracks by applying a sampling method called Markov chain Monte Carlo (MCMC). The MCMC data association algorithm can be viewed as a "deferred logic" method since its decision about forming a track is based on both current and past observations. At the same time, it can be viewed as an approximation to the optimal Bayesian filter. The algorithm shows remarkable performance compared to the greedy algorithm and the multiple hypothesis tracker (MHT) under extreme conditions, such as a large number of targets in a dense environment, low detection probabilities, and high false alarm rates.
Distributed Construction of Random Expander Networks
 In IEEE Infocom
, 2003
"... We present a novel distributed algorithm for constructing random overlay networks that are composed of d Hamilton cycles. The protocol is completely decentralized as no globallyknown server is required. The constructed topologies are expanders with O(log d n) diameter with high probability. ..."
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Cited by 77 (0 self)
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We present a novel distributed algorithm for constructing random overlay networks that are composed of d Hamilton cycles. The protocol is completely decentralized as no globallyknown server is required. The constructed topologies are expanders with O(log d n) diameter with high probability.
On Markov chains for independent sets
 Journal of Algorithms
, 1997
"... Random independent sets in graphs arise, for example, in statistical physics, in the hardcore model of a gas. A new rapidly mixing Markov chain for independent sets is defined in this paper. We show that it is rapidly mixing for a wider range of values of the parameter than the LubyVigoda chain, ..."
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Cited by 72 (20 self)
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Random independent sets in graphs arise, for example, in statistical physics, in the hardcore model of a gas. A new rapidly mixing Markov chain for independent sets is defined in this paper. We show that it is rapidly mixing for a wider range of values of the parameter than the LubyVigoda chain, the best previously known. Moreover the new chain is apparently more rapidly mixing than the LubyVigoda chain for larger values of (unless the maximum degree of the graph is 4). An extension of the chain to independent sets in hypergraphs is described. This chain gives an efficient method for approximately counting the number of independent sets of hypergraphs with maximum degree two, or with maximum degree three and maximum edge size three. Finally, we describe a method which allows one, under certain circumstances, to deduce the rapid mixing of one Markov chain from the rapid mixing of another, with the same state space and stationary distribution. This method is applied to two Markov ch...