Related papers: Discrete Gaussian distributions via theta function…
Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…
In this paper, an alternative Discrete skew Logistic distribution is proposed, which is derived by using the general approach of discretizing a continuous distribution while retaining its survival function. The properties of the…
We study the degree of the Gauss map of the theta divisor of principally polarised complex abelian varieties. We use this to obtain a bound on the multiplicity of the theta divisor along irreducible components of its singular locus, and…
We consider two-dimensional N=(2,2) supersymmetric gauge theory on discretized Riemann surfaces. We find that the discretized theory can be efficiently described by using graph theory, where the bosonic and fermionic fields are regarded as…
Given a single observation from a Gaussian distribution with unknown mean $\theta$, we design computationally efficient procedures that can approximately generate an observation from a different target distribution $Q_{\theta}$ uniformly…
Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete…
A symmetric random variable is called a Gaussian mixture if it has the same distribution as the product of two independent random variables, one being positive and the other a standard Gaussian random variable. Examples of Gaussian mixtures…
We present a novel way of constructing the Gaussian Free Field on a weighted graph via a dynamical expansion of the Green function along an expanding family of subgraphs. Along the way we obtain the discrete analogue of the classical…
We propose a numerical accountant for evaluating the tight $(\varepsilon,\delta)$-privacy loss for algorithms with discrete one dimensional output. The method is based on the privacy loss distribution formalism and it uses the recently…
We demonstrate the parallel between the properties of Gaussian vectors and the Euclidean geometry. In particular we study the Markov property and give various equivalent Euclidean and probabilistic characterizations. We also give a simple…
We introduce a class of distributions originating from an exponential family and having a property related to the strict stability property. A characteristic function representation for this family is obtained and its properties are…
We investigate the complex Gaussian as well as non-Gaussian distributed random analytical and entire functions (complex entire random field) and calculate their domain of definiteness (radius of convergence) as well as some important…
In this paper we focus on the finite n probability distribution function of the largest eigenvalue in the classical Gaussian Ensemble of n by n matrices (GEn). We derive the finite n largest eigenvalue probability distribution function for…
A Wright function based framework is proposed to combine and extend several distribution families. The $\alpha$-stable distribution is generalized by adding the degree of freedom parameter. The PDF of this two-sided super distribution…
We study a basic private estimation problem: each of $n$ users draws a single i.i.d. sample from an unknown Gaussian distribution, and the goal is to estimate the mean of this Gaussian distribution while satisfying local differential…
There is a need for new models for characterizing dependence in multivariate data. The multivariate Gaussian distribution is routinely used, but cannot characterize nonlinear relationships in the data. Most non-linear extensions tend to be…
The present work investigates the Lesche stability (experimental robustness), the thermodynamic stability, the Legendre structure of thermodynamics, and derives the Maximum Entropy distribution of the one--parametric ``nonextensive…
Convex analysis and Gaussian probability are tightly connected, as mostly evident in the theory of linear regression. Our work introduces an algebraic perspective on such relationship, in the form of a diagrammatic calculus of string…
We consider Gaussian distributions on certain Riemannian symmetric spaces. In contrast to the Euclidean case, it is challenging to compute the normalization factors of such distributions, which we refer to as partition functions. In some…
The Weibull distribution can be obtained using a power transformation from the standard exponential distribution. In this article, we will consider a symmetrized power transformation of a random variable with the standard normal…