Related papers: Von Mises-Fisher Elliptical Distribution
We introduce a novel family of projected distributions on the circle and the sphere, namely the circular and spherical projected Cauchy distributions, as promising alternatives for modelling circular and spherical data. The circular…
Although stochastic gradient descent (SGD) is a driving force behind the recent success of deep learning, our understanding of its dynamics in a high-dimensional parameter space is limited. In recent years, some researchers have used the…
This paper is a strongly geometrical approach to the Fisher distance, which is a measure of dissimilarity between two probability distribution functions. The Fisher distance, as well as other divergence measures, are also used in many…
Normal mean-variance mixture distributions are widely applied to simplify a model's implementation and improve their computational efficiency under the Maximum Likelihood (ML) approach. Especially for distributions with normal mean-variance…
This paper proposes a novel method to estimate the rate parameter of the Poisson distribution. The proposed method employs the Cramer-von Mises type optimization which has been commonly used in estimating parameters of continuous…
We treat the problem of estimation of orientation parameters whose values are invariant to transformations from a spherical symmetry group. Previous work has shown that any such group-invariant distribution must satisfy a restricted finite…
A $k$-modal probability distribution over the discrete domain $\{1,...,n\}$ is one whose histogram has at most $k$ "peaks" and "valleys." Such distributions are natural generalizations of monotone ($k=0$) and unimodal ($k=1$) probability…
The family of multivariate skew-normal distributions has many interesting properties. It is shown here that these hold for a general class of skew-elliptical distributions. For this class, several stochastic representations are established…
For Bayesian learning, given likelihood function and Gaussian prior, the elliptical slice sampler, introduced by Murray, Adams and MacKay 2010, provides a tool for the construction of a Markov chain for approximate sampling of the…
Circular and non-flat data distributions are prevalent across diverse domains of data science, yet their specific geometric structures often remain underutilized in machine learning frameworks. A principled approach to accounting for the…
In environmental studies, many data are typically skewed and it is desired to have a flexible statistical model for this kind of data. In this paper, we study a class of skewed distributions by invoking arguments as described by Ferreira…
We introduce a non-parametric method to recover physical probability distributions of asset returns based on their European option prices and some other sparse parametric information. Thus the main problem is similar to the one considered…
Finite mixture of skew distributions have emerged as an effective tool in modelling heterogeneous data with asymmetric features. With various proposals appearing rapidly in the recent years, which are similar but not identical, the…
We study modeling and inference with the Elliptical Gamma Distribution (EGD). We consider maximum likelihood (ML) estimation for EGD scatter matrices, a task for which we develop new fixed-point algorithms. Our algorithms are efficient and…
Probability measures on the sphere form an important class of statistical models and are used, for example, in modeling directional data or shapes. Due to their widespread use, but also as an algorithmic building block, efficient sampling…
Vertical Federated Learning (VFL) is a privacy-preserving distributed learning paradigm where different parties collaboratively learn models using partitioned features of shared samples, without leaking private data. Recent research has…
Nonlinear mixed effects models have received a great deal of attention in the statistical literature in recent years because of their flexibility in handling longitudinal studies, including human immunodeficiency virus viral dynamics,…
Elliptically symmetric distributions are widely used in portfolio modeling, as well as in signal processing applications for modeling impulsive background noises. Of particular interest are algorithms for covariance estimation and subspace…
The importance of electrostatic interactions in soft matter and biological systems can often be traced to non-uniform charge effects, which are commonly described using a multipole expansion of the corresponding charge distribution. The…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…