Related papers: $\alpha$-Geodesical Skew Divergence
Modern data is customarily of multimodal nature, and analysis tasks typically require separation into the single components. Although a highly ill-posed problem, the morphological difference of these components sometimes allow a very…
Skewed probit regression is but one example of a statistical model that generalizes a simpler model, like probit regression. All skew-symmetric distributions and link functions arise from symmetric distributions by incorporating a skewness…
We propose a new simple and explicit numerical scheme for time-homogeneous stochastic differential equations. The scheme is based on sampling increments at each time step from a skew-symmetric probability distribution, with the level of…
The assumption of normality in data has been considered in the field of statistical analysis for a long time. However, in many practical situations, this assumption is clearly unrealistic. It has recently been suggested that the use of…
The goal of inversion is to estimate the model which generates the data of observations with a specific modeling equation. One general approach to inversion is to use optimization methods which are algebraic in nature to define an objective…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
We present a rectangle-based segmentation algorithm that sets up a graph and performs a graph cut to separate an object from the background. However, graph-based algorithms distribute the graph's nodes uniformly and equidistantly on the…
It is well known that adding any skew symmetric matrix to the gradient of Langevin dynamics algorithm results in a non-reversible diffusion with improved convergence rate. This paper presents a gradient algorithm to adaptively optimize the…
We consider the theory of \emph{twisted symmetries} of differential equations, in particular $\lambda$ and $\mu$-symmetries, and discuss their geometrical content. We focus on their interpretation in terms of gauge transformations on the…
Statistical divergence is widely applied in multimedia processing, basically due to regularity and interpretable features displayed in data. However, in a broader range of data realm, these advantages may no longer be feasible, and…
Various optimal gradient-based algorithms have been developed for smooth nonconvex optimization. However, many nonconvex machine learning problems do not belong to the class of smooth functions and therefore the existing algorithms are…
In this paper we introduce five different algorithms based on method of moments, maximum likelihood and full Bayesian estimation for learning the parameters of the Inverse Gamma distribution. We also provide an expression for the KL…
This article deals with quantitative error analysis resulting from ellipsometric data obtained from measurement on curved surfaces including the influence of non-collimated beams. Numerical model based on the combination of geometrical and…
Distributive skew lattices satisfying $x\wedge (y\vee z)\wedge x = (x\wedge y\wedge x) \vee (x\wedge z\wedge x)$ and its dual are studied, along with the larger class of linearly distributive skew lattices, whose totally preordered…
Divergences are fundamental to the information criteria that underpin most signal processing algorithms. The alpha-beta family of divergences, designed for non-negative data, offers a versatile framework that parameterizes and continuously…
Kullback-Leibler (KL) divergence is a fundamental concept in information theory that quantifies the discrepancy between two probability distributions. In the context of Variational Autoencoders (VAEs), it serves as a central regularization…
Although there is ample work in the literature dealing with skewness in the multivariate setting, there is a relative paucity of work in the matrix variate paradigm. Such work is, for example, useful for modelling three-way data. A matrix…
Let $K$ be a field and $E$ be a graph. Let $L_K(E)$ be the Leavitt path algebra of $E$ over $K$ with the standard involution $^\star$. We investigate the set of skew-symmetric elements, $\mathbf{K}_{L_K(E)}=\{x\in L_K(E) : x^{\star}=-x\}$,…
$\alpha$-posteriors and their variational approximations distort standard posterior inference by downweighting the likelihood and introducing variational approximation errors. We show that such distortions, if tuned appropriately, reduce…
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 Bregman divergences as…