Exponentiality test based on alpha-divergence and gamma-divergence

Ahrari, Vahideh; Habibirad, Arezou; Bajgiran, Simindokht Baratpour

doi:10.1080/03610918.2017.1406511

Cited by 5 publications

(2 citation statements)

References 30 publications

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“…The α-divergences are widely used in information sciences, see [22][23][24][25][26][27] just to cite a few applications. The singly parametric α-divergences have also been generalized to biparametric families of divergences such as the (α, β)-divergences [6] or the αβ-divergences [28].…”

Section: Introduction 1statistical Divergences and α-Divergencesmentioning

confidence: 99%

Generalizing the Alpha-Divergences and the Oriented Kullback–Leibler Divergences with Quasi-Arithmetic Means

Nielsen

2022

Algorithms

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The family of α-divergences including the oriented forward and reverse Kullback–Leibler divergences is often used in signal processing, pattern recognition, and machine learning, among others. Choosing a suitable α-divergence can either be done beforehand according to some prior knowledge of the application domains or directly learned from data sets. In this work, we generalize the α-divergences using a pair of strictly comparable weighted means. Our generalization allows us to obtain in the limit case α→1 the 1-divergence, which provides a generalization of the forward Kullback–Leibler divergence, and in the limit case α→0, the 0-divergence, which corresponds to a generalization of the reverse Kullback–Leibler divergence. We then analyze the condition for a pair of weighted quasi-arithmetic means to be strictly comparable and describe the family of quasi-arithmetic α-divergences including its subfamily of power homogeneous α-divergences. In particular, we study the generalized quasi-arithmetic 1-divergences and 0-divergences and show that these counterpart generalizations of the oriented Kullback–Leibler divergences can be rewritten as equivalent conformal Bregman divergences using strictly monotone embeddings. Finally, we discuss the applications of these novel divergences to k-means clustering by studying the robustness property of the centroids.

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Section: Introduction 1statistical Divergences and α-Divergencesmentioning

confidence: 99%

Generalizing the Alpha-Divergences and the Oriented Kullback–Leibler Divergences with Quasi-Arithmetic Means

Nielsen

2022

Algorithms

View full text Add to dashboard Cite

show abstract

“…The α-divergences are widely used in information sciences, see [3,8,38,22,17,1] just to cite a few applications. The singly-parametric α-divergences have also been generalized to bi-parametric families of divergences like the (α, β)-divergences [2] or the αβ-divergences [37].…”

Section: Introduction 1statistical Divergencesmentioning

confidence: 99%

The α-divergences associated with a pair of strictly comparable quasi-arithmetic means

Nielsen

2020

Preprint

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We generalize the family of α-divergences using a pair of strictly comparable weighted means. In particular, we obtain the 1-divergence in the limit case α → 1 (a generalization of the Kullback-Leibler divergence) and the 0-divergence in the limit case α → 0 (a generalization of the reverse Kullback-Leibler divergence). We state the condition for a pair of quasi-arithmetic means to be strictly comparable, and report the formula for the quasi-arithmetic α-divergences and its subfamily of bipower homogeneous α-divergences which belong to the Csisár's f -divergences. Finally, we show that these generalized quasi-arithmetic 1-divergences and 0-divergences can be decomposed as the sum of generalized cross-entropies minus entropies, and rewritten as conformal Bregman divergences using monotone embeddings.

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