Search results for "Kullback–Leibler"

showing 7 items of 17 documents

Hierarchy and dynamics of trace distance correlations

2013

We define and analyze measures of correlations for bipartite states based on trace distance. For Bell diagonal states of two qubits, in addition to the known expression for quantum correlations using this metric, we provide analytic expressions for the classical and total correlations. The ensuing hierarchy of correlations based on trace distance is compared to the ones based on relative entropy and Hilbert-Schmidt norm. Although some common features can be found, the trace distance measure is shown to differentiate from the others in that the closest uncorrelated state to a given bipartite quantum state is not given by the product of the marginals, and further, the total correlations are s…

PhysicsQuantum PhysicsSettore FIS/02 - Fisica Teorica Modelli E Metodi MatematiciKullback–Leibler divergenceStatistical Mechanics (cond-mat.stat-mech)DiagonalGeneral Physics and AstronomyFOS: Physical sciencesProbability and statisticsMathematical Physics (math-ph)Entanglement measures witnesses and other characterizationQuantum stateQubitNorm (mathematics)Physics - Data Analysis Statistics and ProbabilityFoundations of quantum mechanicTrace distancemeasurement theoryStatistical physicsEntanglement and quantum nonlocalityQuantum Physics (quant-ph)QuantumCondensed Matter - Statistical MechanicsMathematical PhysicsData Analysis Statistics and Probability (physics.data-an)
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Dynamics of geometric and entropic quantifiers of correlations in open quantum systems

2012

We extend the Hilbert-Schmidt (square norm) distance, previously used to define the geometric quantum discord, to define also geometric quantifiers of total and classical correlations. We then compare the dynamics of geometric and entropic quantifiers of the different kinds of correlations in a non-Markovian open two-qubit system under local dephasing. We find that qualitative differences occur only for quantum discords. This is taken to imply that geometric and entropic discords are not, in general, equivalent in describing the dynamics of quantum correlations. We then show that also geometric and entropic quantifiers of total correlations present qualitative disagreements in the state spa…

PhysicsQuantum correlationsQuantum PhysicsQuantum discordQuantum decoherenceKullback–Leibler divergenceDephasingFOS: Physical sciencesAtomic and Molecular Physics and OpticsSettore FIS/03 - Fisica Della MateriaMeasurement theoryNorm (mathematics)Quantum mechanicsOpen quantum systemOpen quantum systems; Quantum correlationsStatistical physicsQuantum Physics (quant-ph)Quantum
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Tetrolet-based reduced reference image quality assessment approach

2014

In this paper, we propose a new reduced reference image quality assessment (RRIQA) scheme. For this purpose, we use a statistical-based method in a new adaptive Haar wavelet transform domain, called Tetrolet. Firstly, we decompose the reference and distorted images and we obtain the Tetrolet coefficients for each image. Secondly, we use a marginal Generalized Gaussian Density (GGD) to model each subband coefficients. Finally, the distortion measure is computed using the Kullback Leibler Divergence (KLD) between GGD Probability density function (PDFs). Experimental results show the efficiency of the proposed method when comparing to those reported in the literature.

Reference imageKullback–Leibler divergencebusiness.industryComputer scienceDistortionPattern recognitionProbability density functionArtificial intelligencebusinessMeasure (mathematics)Domain (mathematical analysis)Haar waveletImage (mathematics)2014 International Conference on Multimedia Computing and Systems (ICMCS)
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Analysis of a parabolic cross-diffusion population model without self-diffusion

2006

Abstract The global existence of non-negative weak solutions to a strongly coupled parabolic system arising in population dynamics is shown. The cross-diffusion terms are allowed to be arbitrarily large, whereas the self-diffusion terms are assumed to disappear. The last assumption complicates the analysis since these terms usually provide H 1 estimates of the solutions. The existence proof is based on a positivity-preserving backward Euler–Galerkin approximation, discrete entropy estimates, and L 1 weak compactness arguments. Furthermore, employing the entropy–entropy production method, we show for special stationary solutions that the transient solution converges exponentially fast to its…

Self-diffusioneducation.field_of_studyKullback–Leibler divergenceRelative entropyStrong cross-diffusionApplied MathematicsMathematical analysisPopulationLong-time behavior of solutionsWeak competitionArbitrarily largeCompact spaceExponential growthPopulation modelEntropy (information theory)Global-in-time existence of weak solutionseducationPopulation equationsAnalysisMathematicsJournal of Differential Equations
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Usage of HMM-Based Speech Recognition Methods for Automated Determination of a Similarity Level Between Languages

2019

The problem of automated determination of language similarity (or even defining of a distance on the space of languages) could be solved in different ways – working with phonetic transcriptions, with speech recordings or both of them. For the recordings, we propose and test a HMM-based one: in the first part of our article we successfully try language detection, afterwards we are trying to calculate distances between HMM-based models, using different metrics and divergences. The Kullback-Leibler divergence is the only one we got good results with – it means that the calculated distances between languages correspond to analytical understanding of similarity between them. Even if it does not …

Space (punctuation)Kullback–Leibler divergenceLanguage identificationSimilarity (network science)Computer scienceSpeech recognitionComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)Hidden Markov modelUSableDivergence (statistics)
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Generalization of Jeffreys Divergence-Based Priors for Bayesian Hypothesis Testing

2008

Summary We introduce objective proper prior distributions for hypothesis testing and model selection based on measures of divergence between the competing models; we call them divergence-based (DB) priors. DB priors have simple forms and desirable properties like information (finite sample) consistency and are often similar to other existing proposals like intrinsic priors. Moreover, in normal linear model scenarios, they reproduce the Jeffreys–Zellner–Siow priors exactly. Most importantly, in challenging scenarios such as irregular models and mixture models, DB priors are well defined and very reasonable, whereas alternative proposals are not. We derive approximations to the DB priors as w…

Statistics and ProbabilityKullback–Leibler divergenceMarkov chainMarkov chain Monte CarloBayes factorMixture modelsymbols.namesakePrior probabilityEconometricssymbolsApplied mathematicsStatistics Probability and UncertaintyDivergence (statistics)Statistical hypothesis testingMathematicsJournal of the Royal Statistical Society Series B: Statistical Methodology
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Selecting the tuning parameter in penalized Gaussian graphical models

2019

Penalized inference of Gaussian graphical models is a way to assess the conditional independence structure in multivariate problems. In this setting, the conditional independence structure, corresponding to a graph, is related to the choice of the tuning parameter, which determines the model complexity or degrees of freedom. There has been little research on the degrees of freedom for penalized Gaussian graphical models. In this paper, we propose an estimator of the degrees of freedom in $$\ell _1$$ -penalized Gaussian graphical models. Specifically, we derive an estimator inspired by the generalized information criterion and propose to use this estimator as the bias term for two informatio…

Statistics and ProbabilityStatistics::TheoryKullback–Leibler divergenceKullback-Leibler divergenceComputer scienceGaussianInformation Criteria010103 numerical & computational mathematicsModel complexityModel selection01 natural sciencesTheoretical Computer Science010104 statistics & probabilitysymbols.namesakeStatistics::Machine LearningGeneralized information criterionEntropy (information theory)Statistics::MethodologyGraphical model0101 mathematicsPenalized Likelihood Kullback-Leibler Divergence Model Complexity Model Selection Generalized Information Criterion.Model selectionEstimatorStatistics::ComputationComputational Theory and MathematicsConditional independencesymbolsPenalized likelihoodStatistics Probability and UncertaintySettore SECS-S/01 - StatisticaAlgorithmStatistics and Computing
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