Related papers: On a method to construct exponential families by r…
The paper is devoted to the study of exact curves on Arborealized Liouville surfaces. We introduce the notion of a generating family for such curves. Our main statement is a hamiltonian lifting property: the set of curves admitting a…
In a seminal paper in 2009, Borcea, Br\"and\'en, and Liggett described the connection between probability distributions and the geometry of their generating polynomials. Namely, they characterized that stable generating polynomials…
In a range of fields including the geosciences, molecular biology, robotics and computer vision, one encounters problems that involve random variables on manifolds. Currently, there is a lack of flexible probabilistic models on manifolds…
This article studies exponential families $\mathcal{E}$ on finite sets such that the information divergence $D(P\|\mathcal{E})$ of an arbitrary probability distribution from $\mathcal{E}$ is bounded by some constant $D>0$. A particular…
In this paper we study the problem of explicitly describing the space of invariant linear forms on induced distinguished representations in terms of invariant linear forms on the inducing representation. More precisely, for certain tempered…
Generating images from a single sample, as a newly developing branch of image synthesis, has attracted extensive attention. In this paper, we formulate this problem as sampling from the conditional distribution of a single image, and…
We study the algebraic framework in which one can define, in the manner of the theta correspondence, a correspondence between representations of two locally profinite groups $H_1$, $H_2$. In particular, we examine when and how such a…
One of the key ingredients in the recent construction of the generalized doubling method is a new class of models, called $(k,c)$ models, for local components of generalized Speh representations. We construct a family of $(k,c)$…
The aim of this article is to show the existence, and also give an explicit construction, of infinite sets of orthogonal exponentials for certain families of convex polytopes which include simple-rational polytopes and also non simple…
There is considerable current interest in applications of generalised Lie algebras graded by an abelian group $\Gamma$ with a commutative factor $\omega$. This calls for a systematic development of the theory of such algebraic structures.…
This document describes concisely the ubiquitous class of exponential family distributions met in statistics. The first part recalls definitions and summarizes main properties and duality with Bregman divergences (all proofs are skipped).…
Bayesian inference on structured models typically relies on the ability to infer posterior distributions of underlying hidden variables. However, inference in implicit models or complex posterior distributions is hard. A popular tool for…
Let G be a reductive complex algebraic group and V a finite-dimensional G-module. From elements of the invariant algebra C[V]^G we obtain by polarization elements of C[kV]^G, where k\geq 1 and kV denotes the direct sum of k copies of V. For…
Mixtures of experts probabilistically divide the input space into regions, where the assumptions of each expert, or conditional model, need only hold locally. Combined with Gaussian process (GP) experts, this results in a powerful and…
The first known families of cages arised from the incidence graphs of generalized polygons of order $q$, $q$ a prime power. In particular, $(q+1,6)$--cages have been obtained from the projective planes of order $q$. Morever, infinite…
We develop a class of integrals on a manifold M called exponential iterated integrals, an extension of K. T. Chen's iterated integrals. It is shown that the matrix entries of any upper triangular representation of the fundamental group of M…
In this work some advances in the theory of curvature of two-dimensional probability manifolds corresponding to families of distributions are proposed. It is proved that location-scale distributions are hyperbolic in the Information…
Generating functions, which are widely used in combinatorics and probability theory, encode function values into the coefficients of a polynomial. In this paper, we explore their use as a tractable probabilistic model, and propose…
Given some observed data and a probabilistic generative model, Bayesian inference aims at obtaining the distribution of a model's latent parameters that could have yielded the data. This task is challenging for large population studies…
Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. Method for general construction of star product is presented. Corresponding twist, expressed in terms of phase space…