$α$-Geodesical Skew Divergence
The asymmetric skew divergence smooths one of the distributions by mixing it, to a degree determined by the parameter $\lambda$, with the other distribution. Such divergence is an approximation of the KL divergence that does not require the target distribution to be absolutely continuous with respect to the source distribution. In this paper, an information geometric generalization of the skew divergence called the $\alpha$-geodesical skew divergence is proposed, and its properties are studied.
Code (1)
Similar Papers 제목 키워드 기반
Generalized Bregman and Jensen divergences which include some f-divergences
In this paper, we introduce new classes of divergences by extending the definitions of the Bregman divergence and the skew Jensen divergence. These new divergence classes (g-Bregman divergence and skew g-Jensen divergenc…
$\alpha$-VAEs : Optimising variational inference by learning data-dependent divergence skew
The {\em skew-geometric Jensen-Shannon divergence} $\left(\textrm{JS}^{\textrm{G}_{\alpha}}\right)$ allows for an intuitive interpolation between forward and reverse Kullback-Leibler (KL) divergence based on the skew pa…
DenoisingVariational InferenceDivergences induced by dual subtractive and divisive normalizations of exponential families and their convex deformations
Exponential families are statistical models which are the workhorses in statistics, information theory, and machine learning among others. An exponential family can either be normalized subtractively by its cumulant or f…
Accelerated First-order Methods for Geodesically Convex Optimization on Riemannian Manifolds
In this paper, we propose an accelerated first-order method for geodesically convex optimization, which is the generalization of the standard Nesterov's accelerated method from Euclidean space to nonlinear Riemannian spa…
A note on the quasiconvex Jensen divergences and the quasiconvex Bregman divergences derived thereof
We first introduce the class of strictly quasiconvex and strictly quasiconcave Jensen divergences which are oriented (asymmetric) distances, and study some of their properties. We then define the strictly quasiconvex Bre…