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Cognitive Radio: BrainEmpowered Wireless Communications
, 2005
"... Cognitive radio is viewed as a novel approach for improving the utilization of a precious natural resource: the radio electromagnetic spectrum. The cognitive radio, built on a softwaredefined radio, is defined as an intelligent wireless communication system that is aware of its environment and use ..."
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Cited by 1479 (4 self)
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Cognitive radio is viewed as a novel approach for improving the utilization of a precious natural resource: the radio electromagnetic spectrum. The cognitive radio, built on a softwaredefined radio, is defined as an intelligent wireless communication system that is aware of its environment and uses the methodology of understandingbybuilding to learn from the environment and adapt to statistical variations in the input stimuli, with two primary objectives in mind: • highly reliable communication whenever and wherever needed; • efficient utilization of the radio spectrum. Following the discussion of interference temperature as a new metric for the quantification and management of interference, the paper addresses three fundamental cognitive tasks. 1) Radioscene analysis. 2) Channelstate estimation and predictive modeling. 3) Transmitpower control and dynamic spectrum management. This paper also discusses the emergent behavior of cognitive radio.
Learning in graphical models
 STATISTICAL SCIENCE
, 2004
"... Statistical applications in fields such as bioinformatics, information retrieval, speech processing, image processing and communications often involve largescale models in which thousands or millions of random variables are linked in complex ways. Graphical models provide a general methodology for ..."
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Cited by 800 (10 self)
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Statistical applications in fields such as bioinformatics, information retrieval, speech processing, image processing and communications often involve largescale models in which thousands or millions of random variables are linked in complex ways. Graphical models provide a general methodology for approaching these problems, and indeed many of the models developed by researchers in these applied fields are instances of the general graphical model formalism. We review some of the basic ideas underlying graphical models, including the algorithmic ideas that allow graphical models to be deployed in largescale data analysis problems. We also present examples of graphical models in bioinformatics, errorcontrol coding and language processing.
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 311 (48 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.
Implementing approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations: A manual for the inlaprogram
, 2008
"... Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalised) linear models, (generalised) additive models, smoothingspline models, statespace models, semiparametric regression, spatial and spatiotemp ..."
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Cited by 293 (20 self)
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Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalised) linear models, (generalised) additive models, smoothingspline models, statespace models, semiparametric regression, spatial and spatiotemporal models, logGaussian Coxprocesses, geostatistical and geoadditive models. In this paper we consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with nonGaussian response variables. The posterior marginals are not available in closed form due to the nonGaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, both in terms of convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations
Variational inference for Dirichlet process mixtures
 Bayesian Analysis
, 2005
"... Abstract. Dirichlet process (DP) mixture models are the cornerstone of nonparametric Bayesian statistics, and the development of MonteCarlo Markov chain (MCMC) sampling methods for DP mixtures has enabled the application of nonparametric Bayesian methods to a variety of practical data analysis prob ..."
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Cited by 241 (26 self)
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Abstract. Dirichlet process (DP) mixture models are the cornerstone of nonparametric Bayesian statistics, and the development of MonteCarlo Markov chain (MCMC) sampling methods for DP mixtures has enabled the application of nonparametric Bayesian methods to a variety of practical data analysis problems. However, MCMC sampling can be prohibitively slow, and it is important to explore alternatives. One class of alternatives is provided by variational methods, a class of deterministic algorithms that convert inference problems into optimization problems (Opper and Saad 2001; Wainwright and Jordan 2003). Thus far, variational methods have mainly been explored in the parametric setting, in particular within the formalism of the exponential family (Attias 2000; Ghahramani and Beal 2001; Blei et al. 2003). In this paper, we present a variational inference algorithm for DP mixtures. We present experiments that compare the algorithm to Gibbs sampling algorithms for DP mixtures of Gaussians and present an application to a largescale image analysis problem.
Convergence of Sequential Monte Carlo Methods
 SEQUENTIAL MONTE CARLO METHODS IN PRACTICE
, 2000
"... Bayesian estimation problems where the posterior distribution evolves over time through the accumulation of data arise in many applications in statistics and related fields. Recently, a large number of algorithms and applications based on sequential Monte Carlo methods (also known as particle filter ..."
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Cited by 240 (15 self)
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Bayesian estimation problems where the posterior distribution evolves over time through the accumulation of data arise in many applications in statistics and related fields. Recently, a large number of algorithms and applications based on sequential Monte Carlo methods (also known as particle filtering methods) have appeared in the literature to solve this class of problems; see (Doucet, de Freitas & Gordon, 2001) for a survey. However, few of these methods have been proved to converge rigorously. The purpose of this paper is to address this issue. We present a general sequential Monte Carlo (SMC) method which includes most of the important features present in current SMC methods. This method generalizes and encompasses many recent algorithms. Under mild regularity conditions, we obtain rigorous convergence results for this general SMC method and therefore give theoretical backing for the validity of all the algorithms that can be obtained as particular cases of it.
A Survey of Convergence Results on Particle Filtering Methods for Practitioners
, 2002
"... Optimal filtering problems are ubiquitous in signal processing and related fields. Except for a restricted class of models, the optimal filter does not admit a closedform expression. Particle filtering methods are a set of flexible and powerful sequential Monte Carlo methods designed to solve the o ..."
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Cited by 239 (9 self)
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Optimal filtering problems are ubiquitous in signal processing and related fields. Except for a restricted class of models, the optimal filter does not admit a closedform expression. Particle filtering methods are a set of flexible and powerful sequential Monte Carlo methods designed to solve the optimal filtering problem numerically. The posterior distribution of the state is approximated by a large set of Diracdelta masses (samples/particles) that evolve randomly in time according to the dynamics of the model and the observations. The particles are interacting; thus, classical limit theorems relying on statistically independent samples do not apply. In this paper, our aim is to present a survey of recent convergence results on this class of methods to make them accessible to practitioners.
Particle Filters for State Estimation of Jump Markov Linear Systems
, 2001
"... Jump Markov linear systems (JMLS) are linear systems whose parameters evolve with time according to a finite state Markov chain. In this paper, our aim is to recursively compute optimal state estimates for this class of systems. We present efficient simulationbased algorithms called particle filter ..."
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Cited by 174 (15 self)
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Jump Markov linear systems (JMLS) are linear systems whose parameters evolve with time according to a finite state Markov chain. In this paper, our aim is to recursively compute optimal state estimates for this class of systems. We present efficient simulationbased algorithms called particle filters to solve the optimal filtering problem as well as the optimal fixedlag smoothing problem. Our algorithms combine sequential importance sampling, a selection scheme, and Markov chain Monte Carlo methods. They use several variance reduction methods to make the most of the statistical structure of JMLS. Computer
Computational and Inferential Difficulties With Mixture Posterior Distributions
 Journal of the American Statistical Association
, 1999
"... This paper deals with both exploration and interpretation problems related to posterior distributions for mixture models. The specification of mixture posterior distributions means that the presence of k! modes is known immediately. Standard Markov chain Monte Carlo techniques usually have difficult ..."
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Cited by 167 (14 self)
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This paper deals with both exploration and interpretation problems related to posterior distributions for mixture models. The specification of mixture posterior distributions means that the presence of k! modes is known immediately. Standard Markov chain Monte Carlo techniques usually have difficulties with wellseparated modes such as occur here; the Markov chain Monte Carlo sampler stays within a neighbourhood of a local mode and fails to visit other equally important modes. We show that exploration of these modes can be imposed on the Markov chain Monte Carlo sampler using tempered transitions based on Langevin algorithms. However, as the prior distribution does not distinguish between the different components, the posterior mixture distribution is symmetric and thus standard estimators such as posterior means cannot be used. Since this is also true for most nonsymmetric priors, we propose alternatives for Bayesian inference for permutation invariant posteriors, including a cluster...