Results 1  10
of
276
A PolynomialTime Approximation Algorithm for the Permanent of a Matrix with NonNegative Entries
 JOURNAL OF THE ACM
, 2004
"... 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 spec ..."
Abstract

Cited by 427 (27 self)
 Add to MetaCart
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.
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 defined on a common space. A sequence of increasingly large artificial joint distributions is built; each of these distributions admits a marginal ..."
Abstract

Cited by 303 (44 self)
 Add to MetaCart
In this paper, we propose a general algorithm to sample sequentially from a sequence of probability distributions known up to a normalizing constant and defined on a common space. A sequence of increasingly large artificial 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 flow in distribution space. One interpretation of the FeynmanKac flow corresponds to a nonlinear Markov kernel admitting a specified invariant distribution and is a natural nonlinear extension of the standard MetropolisHastings algorithm. Many theoretical results have already been established for such flows and their particle approximations. We demonstrate the use of these algorithms through simulation.
Clustering categorical data: An approach based on dynamical systems
, 1998
"... We describe a novel approach for clustering collections of sets, and its application to the analysis and mining of categorical data. By “categorical data, ” we mean tables with fields that cannot be naturally ordered by a metric e.g., the names of producers of automobiles, or the names of product ..."
Abstract

Cited by 180 (1 self)
 Add to MetaCart
We describe a novel approach for clustering collections of sets, and its application to the analysis and mining of categorical data. By “categorical data, ” we mean tables with fields that cannot be naturally ordered by a metric e.g., the names of producers of automobiles, or the names of products offered by a manufacturer. Our approach is based on an iterative method for assigning and propagating weights on the categorical values in a table; this facilitates a type of similarity measure arising from the cooccurrence of values in the dataset. Our techniques can be studied analytically in terms of certain types of nonlinear dynamical systems. We discuss experiments on a variety of tables of synthetic and real data; we find that our iterative methods converge quickly to prominently correlated values of various categorical fields.
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 ..."
Abstract

Cited by 175 (20 self)
 Add to MetaCart
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$cation obtained may allow coupling proofs which were previously unknown, or provide significantly better bounds than those obtained using the standard method. We apply the path coupling method to several hard combinatorial problems, obtaining new or improved results. We examine combinatorial problems such as graph colouring and TWICESAT, and problems fn?m statistical physics, such as the antiferromagnetic Potts model and the hardcore lattice gas model. In each case we provide either a proof of rapid mixing where none was known previously, or substantial simpl$cation of existing proofs with conseqent gains in the pegormance of the resulting algorithms.
Markov Chain Monte Carlo Data Association for MultiTarget Tracking Univ
, 2008
"... data association (MCMCDA) for solving data association problems arising in multitarget tracking in a cluttered environment. When the number of targets is fixed, the singlescan version of MCMCDA approximates joint probabilistic data association (JPDA). Although the exact computation of association ..."
Abstract

Cited by 151 (25 self)
 Add to MetaCart
(Show Context)
data association (MCMCDA) for solving data association problems arising in multitarget tracking in a cluttered environment. When the number of targets is fixed, the singlescan version of MCMCDA approximates joint probabilistic data association (JPDA). Although the exact computation of association probabilities in JPDA is NPhard, we prove that the singlescan MCMCDA algorithm provides a fully polynomial randomized approximation scheme for JPDA. For general multitarget tracking problems, in which unknown numbers of targets appear and disappear at random times, we present a multiscan MCMCDA algorithm that approximates the optimal Bayesian filter. We also present extensive simulation studies supporting theoretical results in this paper. Our simulation results also show that MCMCDA outperforms multiple hypothesis tracking (MHT) by a significant margin in terms of accuracy and efficiency under extreme conditions, such as a large number of targets in a dense environment, low detection probabilities, and high false alarm rates. Index Terms—Joint probabilistic data association (JPDA), Markov chain Monte Carlo data association (MCMCDA), multiple hypothesis tracking (MHT). I.
A polynomialtime algorithm to approximately count contingency tables when the number of rows is constant
, 2003
"... ..."
(Show Context)
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, ..."
Abstract

Cited by 134 (10 self)
 Add to MetaCart
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