Log-Determinant Divergences Revisited: Alpha-Beta and Gamma Log-Det Divergences
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چکیده
منابع مشابه
Log-Determinant Divergences Revisited: Alpha-Beta and Gamma Log-Det Divergences
In this paper, we review and extend a family of log-det divergences for symmetric positive definite (SPD) matrices and discuss their fundamental properties. We show how to generate from parameterized Alpha-Beta (AB) and Gamma log-det divergences many well known divergences, for example, the Stein’s loss, S-divergence, called also Jensen-Bregman LogDet (JBLD) divergence, the Logdet Zero (Bhattac...
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This work presents a parametrized family of divergences, namely Alpha-Beta LogDeterminant (Log-Det) divergences, between positive definite unitized trace class operators on a Hilbert space. This is a generalization of the Alpha-Beta Log-Determinant divergences between symmetric, positive definite matrices to the infinite-dimensional setting. The family of Alpha-Beta Log-Det divergences is highl...
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The Alpha-Beta Log-Det divergences for positive definite matrices are flexible divergences that are parameterized by two real constants and are able to specialize several relevant classical cases like the squared Riemannian metric, the Steins loss, the S-divergence, etc. A novel classification criterion based on these divergences is optimized to address the problem of classification of the moto...
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We describe the underlying probabilistic interpretation of alpha and beta divergences. We first show that beta divergences are inherently tied to Tweedie distributions, a particular type of exponential family, known as exponential dispersion models. Starting from the variance function of a Tweedie model, we outline how to get alpha and beta divergences as special cases of Csiszár’s f and Bregma...
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In this paper, we extend and overview wide families of Alpha-, Betaand Gammadivergences and discuss their fundamental properties. In literature usually only one single asymmetric (Alpha, Beta or Gamma) -divergence is considered. We show in this paper that there exist families of such divergences with the same consistent properties. Moreover, we establish links and correspondences among these di...
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ژورنال
عنوان ژورنال: Entropy
سال: 2015
ISSN: 1099-4300
DOI: 10.3390/e17052988