Related papers: The Power Spherical distribution
Proxy-based Deep Metric Learning (DML) learns deep representations by embedding images close to their class representatives (proxies), commonly with respect to the angle between them. However, this disregards the embedding norm, which can…
This paper focusses on robust estimation of location and concentration parameters of the von Mises-Fisher distribution in the Bayesian framework. The von Mises-Fisher (or Langevin) distribution has played a central role in directional…
We obtain discrete mixture representations for parametric families of probability distributions on Euclidean spheres, such as the von Mises--Fisher, the Watson and the angular Gaussian families. In addition to several special results we…
We consider the parameter estimation problem of a probabilistic generative model prescribed using a natural exponential family of distributions. For this problem, the typical maximum likelihood estimator usually overfits under limited…
Circular variables arise in a multitude of data-modelling contexts ranging from robotics to the social sciences, but they have been largely overlooked by the machine learning community. This paper partially redresses this imbalance by…
We propose a method to fuse posterior distributions learned from heterogeneous datasets. Our algorithm relies on a mean field assumption for both the fused model and the individual dataset posteriors and proceeds using a simple…
Variational Inference is a powerful tool in the Bayesian modeling toolkit, however, its effectiveness is determined by the expressivity of the utilized variational distributions in terms of their ability to match the true posterior…
In this paper, we present the LSF parameters by a unit vector form, which has directional characteristics. The underlying distribution of this unit vector variable is modeled by a von Mises-Fisher mixture model (VMM). With the high rate…
In this paper we introduce a new flexible class of distributions with bounded support, called reflected Generalized Topp-Leone Power Series (rGTL-PS), obtained by compounding the reflected Generalized Topp-Leone (van Drop and Kotz, 2006)…
In this paper, we present two simple approaches for deriving anisotropic distribution functions for a wide range of spherical models. The first method involves multiplying and dividing a basic augmented density with polynomials in $r$ and…
Recently the termed \emph{multimatrix variate distributions} were proposed in \citet{dgcl:24a} as an alternative for univariate and vector variate copulas. The distributions are based on sample probabilistic dependent elliptically countered…
We consider the shape of the posterior distribution to be used when fitting cosmological models to power spectra measured from galaxy surveys. At very large scales, Gaussian posterior distributions in the power do not approximate the…
We discuss generalized linear models for directional data where the conditional distribution of the response is a von Mises-Fisher distribution in arbitrary dimension or a Bingham distribution on the unit circle. To do this properly, we…
A key challenge for modern Bayesian statistics is how to perform scalable inference of posterior distributions. To address this challenge, variational Bayes (VB) methods have emerged as a popular alternative to the classical Markov chain…
The normal distribution is used as a unified probability distribution, however, our researcher found that it is not good agreed with the real-life dynamical system's data. We collected and analyzed representative naturally occurring data…
The class of $\alpha$-stable distributions enjoys multiple practical applications in signal processing, finance, biology and other areas because it allows to describe interesting and complex data patterns, such as asymmetry or heavy tails,…
We consider a class of non-conjugate priors as a mixing family of distributions for a parameter (e.g., Poisson or gamma rate, inverse scale or precision of an inverse-gamma, inverse variance of a normal distribution) of an exponential…
Long-tailed learning aims to tackle the crucial challenge that head classes dominate the training procedure under severe class imbalance in real-world scenarios. However, little attention has been given to how to quantify the dominance…
We describe an approximate statistical model for the sample variance distribution of the non-linear matter power spectrum that can be calibrated from limited numbers of simulations. Our model retains the common assumption of a multivariate…
The analysis of the Lyman-alpha forest of absorption lines in quasar spectra has emerged as a potentially powerful technique to constrain the linear matter power spectrum. In most previous work, the amplitude of the ionizing background was…