The Laplace Distribution and Generalizations

Kotz, Samuel; Kozubowski, Tomaz J.; Podgórski, Krzysztof

doi:10.1007/978-1-4612-0173-1

Cited by 680 publications

(322 citation statements)

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“…This is done by maximizing the continuous (Shannon) entropy subject to the empirical moments of the data. This yields the most conservative (closest to uniform) post data density (Zellner [14,[40][41][42][43]; Zellner and Tobias [15]). In that way the BMOM uses only assumptions on the realized error terms which are used to derive the post data density.…”

Section: Comparison With the Bayesian Methods Of Moments (Bmom)mentioning

confidence: 99%

An Entropic Estimator for Linear Inverse Problems

Golan

Gzyl

2012

Entropy

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In this paper we examine an Information-Theoretic method for solving noisy linear inverse estimation problems which encompasses under a single framework a whole class of estimation methods. Under this framework, the prior information about the unknown parameters (when such information exists), and constraints on the parameters can be incorporated in the statement of the problem. The method builds on the basics of the maximum entropy principle and consists of transforming the original problem into an estimation of a probability density on an appropriate space naturally associated with the statement of the problem. This estimation method is generic in the sense that it provides a framework for analyzing non-normal models, it is easy to implement and is suitable for all types of inverse problems such as small and or ill-conditioned, noisy data. First order approximation, large sample properties and convergence in distribution are developed as well. Analytical examples, statistics for model comparisons and evaluations, that are inherent to this method, are discussed and complemented with explicit examples.

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Section: Comparison With the Bayesian Methods Of Moments (Bmom)mentioning

confidence: 99%

An Entropic Estimator for Linear Inverse Problems

Golan

Gzyl

2012

Entropy

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“…where W Exp(1) and V N(0, Σ) is independent of W (Kotz, Kozubowski, and Podgorski 2001;Franczak et al 2014). It follows that W | x has a generalized inverse Gaussian distribution (Barndorff-Nielsen 1997); accordingly, the E-steps in the associated EM algorithm are highly tractable (see Franczak et al 2014, for details).…”

Section: Mixtures Of Asymmetric Componentsmentioning

confidence: 99%

Model-Based Clustering

McNicholas

2016

J Classif

181

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Abstract:The notion of defining a cluster as a component in a mixture model was put forth by Tiedeman in 1955; since then, the use of mixture models for clustering has grown into an important subfield of classification. Considering the volume of work within this field over the past decade, which seems equal to all of that which went before, a review of work to date is timely. First, the definition of a cluster is discussed and some historical context for model-based clustering is provided. Then, starting with Gaussian mixtures, the evolution of model-based clustering is traced, from the famous paper by Wolfe in 1965 to work that is currently available only in preprint form. This review ends with a look ahead to the next decade or so.

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“…The bivariate Laplacian distribution has heavier tails than the bivariate Gaussian distribution and its PDF is defined by [41] (A.4) where is the modified Bessel function of the second kind. In the data fitting process, we decide two parameters and by adopting the approach of method of moments [42], [43].…”

Section: Bivariate Laplacian Distributionmentioning

confidence: 99%

“…According to the property of Laplacian distribution [41], a linear combination is one-dimensional Laplacian distribution if and are jointly Laplacian. Hence, the term (A.5) is also Laplacian distributed.…”

Section: Bivariate Laplacian Distributionmentioning

confidence: 99%

Fast Bi-Directional Prediction Selection in H.264/MPEG-4 AVC Temporal Scalable Video Coding

Lin

Hang

Peng

2011

IEEE Trans. on Image Process.

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Abstract-In this paper, we propose a fast algorithm that efficiently selects the temporal prediction type for the dyadic hierarchical-B prediction structure in the H.264/MPEG-4 temporal scalable video coding (SVC). We make use of the strong correlations in prediction type inheritance to eliminate the superfluous computations for the bi-directional (BI) prediction in the finer partitions, , by referring to the best temporal prediction type of 16 16. In addition, we carefully examine the relationship in motion bit-rate costs and distortions between the BI and the uni-directional temporal prediction types. As a result, we construct a set of adaptive thresholds to remove the unnecessary BI calculations. Moreover, for the block partitions smaller than 8 8, either the forward prediction (FW) or the backward prediction (BW) is skipped based upon the information of their 8 8 partitions. Hence, the proposed schemes can efficiently reduce the extensive computational burden in calculating the BI prediction. As compared to the JSVM 9.11 software, our method saves the encoding time from 48% to 67% for a large variety of test videos over a wide range of coding bit-rates and has only a minor coding performance loss.Index Terms-Bi-directional prediction, bi-directionally predictive frame, encoder optimization, hierarchical prediction structure, H.264/MPEG-4 AVC scalable video coding, temporal scalability.

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The Laplace Distribution and Generalizations

Cited by 680 publications

References 0 publications

An Entropic Estimator for Linear Inverse Problems

An Entropic Estimator for Linear Inverse Problems

Model-Based Clustering

Fast Bi-Directional Prediction Selection in H.264/MPEG-4 AVC Temporal Scalable Video Coding

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