Results 1  10
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2,514
Stochastic Perturbation Theory
, 1988
"... . In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variatio ..."
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Cited by 907 (36 self)
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. In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating
Clustering by LeftStochastic Matrix Factorization
, 2011
"... We propose clustering samples given their pairwise similarities by factorizing the similarity matrix into the product of a cluster probability matrix and its transpose. We propose a rotationbased algorithm to compute this leftstochastic decomposition (LSD). Theoretical results link the LSD cluster ..."
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Cited by 7 (1 self)
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We propose clustering samples given their pairwise similarities by factorizing the similarity matrix into the product of a cluster probability matrix and its transpose. We propose a rotationbased algorithm to compute this leftstochastic decomposition (LSD). Theoretical results link the LSD
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 532 (5 self)
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stochastic matrix characterizing the algorithm. Designing the fastest gossip algorithm corresponds to minimizing this eigenvalue, which is a semidefinite program (SDP). In general, SDPs cannot be solved in a distributed fashion; however, exploiting problem structure, we propose a distributed subgradient
New results in linear filtering and prediction theory
 TRANS. ASME, SER. D, J. BASIC ENG
, 1961
"... A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary sta ..."
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Cited by 607 (0 self)
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A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary
Computing the Nearest Doubly Stochastic Matrix with A Prescribed Entry ∗
, 2006
"... In this paper a nearest doubly stochastic matrix problem is studied. This problem is to find the closest doubly stochastic matrix with the prescribed (1, 1) entry to a given matrix. According to the wellestablished dual theory in optimization, the dual of the underlying problem is an unconstrained ..."
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Cited by 4 (0 self)
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In this paper a nearest doubly stochastic matrix problem is studied. This problem is to find the closest doubly stochastic matrix with the prescribed (1, 1) entry to a given matrix. According to the wellestablished dual theory in optimization, the dual of the underlying problem is an unconstrained
The Nonstochastic Multiarmed Bandit Problem
 SIAM JOURNAL OF COMPUTING
, 2002
"... In the multiarmed bandit problem, a gambler must decide which arm of K nonidentical slot machines to play in a sequence of trials so as to maximize his reward. This classical problem has received much attention because of the simple model it provides of the tradeoff between exploration (trying out ..."
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Cited by 491 (34 self)
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of the process generating the payoffs of the slot machines. We give a solution to the bandit problem in which an adversary, rather than a wellbehaved stochastic process, has complete control over the payoffs. In a sequence of T plays, we prove that the perround payoff of our algorithm approaches
Testing for Common Trends
 Journal of the American Statistical Association
, 1988
"... Cointegrated multiple time series share at least one common trend. Two tests are developed for the number of common stochastic trends (i.e., for the order of cointegration) in a multiple time series with and without drift. Both tests involve the roots of the ordinary least squares coefficient matrix ..."
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Cited by 464 (7 self)
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matrix obtained by regressing the series onto its first lag. Critical values for the tests are tabulated, and their power is examined in a Monte Carlo study. Economic time series are often modeled as having a unit root in their autoregressive representation, or (equivalently) as containing a stochastic
Similaritybased Clustering by LeftStochastic Matrix Factorization
"... For similaritybased clustering, we propose modeling the entries of a given similarity matrix as the inner products of the unknown cluster probabilities. To estimate the cluster probabilities from the given similarity matrix, we introduce a leftstochastic nonnegative matrix factorization problem. ..."
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Cited by 1 (0 self)
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For similaritybased clustering, we propose modeling the entries of a given similarity matrix as the inner products of the unknown cluster probabilities. To estimate the cluster probabilities from the given similarity matrix, we introduce a leftstochastic nonnegative matrix factorization problem
Column Sums and the Conditioning of the Stationary Distribution for a Stochastic Matrix
, 2010
"... For an irreducible stochastic matrix T, we consider a certain condition number κ(T), which measures the sensitivity of the stationary distribution vector to perturbations in T, and study the extent to which the column sum vector for T provides information on κ(T). Specifically, if c T is the column ..."
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For an irreducible stochastic matrix T, we consider a certain condition number κ(T), which measures the sensitivity of the stationary distribution vector to perturbations in T, and study the extent to which the column sum vector for T provides information on κ(T). Specifically, if c T is the column
Markov chain Stochastic matrix Spectrum Phase locking
, 2014
"... ie 4h i g h l i g h t s • We study the Markov chain of consecutive spikes of periodically driven noisy neurons. • We relate the dynamics of the Markov chain to the spectrum of its transition operator. • Spectral spirals and zipping reveal quasiperiodicity and transition to phaselocking. • Stochasti ..."
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locking. • Stochastic bifurcation regions are observed, rather than bifurcation points. • Our method allows to predict dynamic regimes of noisy maps without direct simulation. a r t i c l e i n f o Article history:
Results 1  10
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