Copulas: a new insight into positive time-frequency distributions

Davy, Matthieu; Doucet, Arnaud

doi:10.1109/lsp.2003.811636

Cited by 39 publications

(15 citation statements)

References 12 publications

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“…Un resultado que utilizaremos para determinar la información mutua entre dos variables y que involucra la entropía de una cópula (Davy, 2005) es el siguiente…”

Section: Algoritmo Mimic Con Cópulasunclassified

Una extensión del algoritmo MIMIC mediante Cópulas

Gutiérrez

Aguirre

Diharce

2014

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Una nueva manera de modelar dependencias probabilísticas en el algoritmo de Maximización de Información Mutua mediante Clústeres de Entrada (MIMIC) es presentada. Mediante cópulas es posible separar la estructura de dependencia de las distribuciones marginales en una distribución conjunta. El uso de cópulas como un mecanismo para modelar distribuciones y su aplicación a MIMIC es ilustrado en la función de prueba Rosenbrock.

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“…Un resultado que utilizaremos para determinar la información mutua entre dos variables y que involucra la entropía de una cópula (Davy, 2005) es el siguiente…”

Section: Algoritmo Mimic Con Cópulasunclassified

Una extensión del algoritmo MIMIC mediante Cópulas

Gutiérrez

Aguirre

Diharce

2014

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“…If positive TFDs are desired, then the kernel must be signal-dependent [5]. Alternatively, one can use the Copulas theory-based non iterative method for constructing positive TFDs, as recently proposed in [7]. Therefore, in this paper we consider only positive TFDs (e.g.…”

Section: Time-frequency Distributionsmentioning

confidence: 99%

Contrast Functions for Blind Source Separation Based on Time-Frequency Information-Theory

Sahmoudi

Amin

Abed-Meraim

et al. 2006

Independent Component Analysis and Blind Signal Separation

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Abstract. This paper introduces new contrast functions for blind separation of sources with different time-frequency signatures. Two contrast functions based on the Kullback-Leibler and Jensen-Rényi divergences in the time-frequency (T-F) plane are introduced. Two iterative algorithms are proposed for the proposed contrasts optimization and source separation. One algorithm consists of spatial whitening and gradient-Jacobi maximization, combining Givens rotations and stochastic gradient. The second algorithm uses a quasi-Newton technique.

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“…Some copula applications started to appear in signal and image processing recently. In [17], connections between Cohen-Posch theory of positive time-frequency distributions and copula theory were established. In [18], useful copula models for image classification were used in the frame of multidimensional mixture estimation arising in the segmentation of multicomponent images.…”

Section: Introductionmentioning

confidence: 99%

Nonparametric Copula Density Estimation in Sensor Networks

Chen

2011

2011 Seventh International Conference on Mobile Ad-Hoc and Sensor Networks

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Abstract-Statistical and machine learning is a fundamental task in sensor networks. Real world data almost always exhibit dependence among different features. Copulas are full measures of statistical dependence among random variables. Estimating the underlying copula density function from distributed data is an important aspect of statistical learning in sensor networks. With limited communication capacities or privacy concerns, centralization of the data is often impossible. By only collecting the ranks of the data observed by different sensors, we estimate and evaluate the copula density on an equally spaced grid after binning the standardized ranks at the fusion center. Without assuming any parametric forms of copula densities, we estimate them nonparametrically by maximum penalized likelihood estimation (MPLE) method with a Total Variation (TV) penalty. Linear equality and positivity constraints arise naturally as a consequence of marginal uniform densities of any copulas. Through local quadratic approximation to the likelihood function, the constrained TV-MPLE problem is cast as a sequence of corresponding quadratic optimization problems. A fast gradient based algorithm solves the constrained TV penalized quadratic optimization problem. Numerical experiments show that our algorithm can estimate the underlying copula density accurately.

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Copulas: a new insight into positive time-frequency distributions

Cited by 39 publications

References 12 publications

Una extensión del algoritmo MIMIC mediante Cópulas

Una extensión del algoritmo MIMIC mediante Cópulas

Contrast Functions for Blind Source Separation Based on Time-Frequency Information-Theory

Nonparametric Copula Density Estimation in Sensor Networks

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