Related papers: Statistical exponential families: A digest with fl…
We consider the challenging problem of statistical inference for exponential-family random graph models based on a single observation of a random graph with complex dependence. To facilitate statistical inference, we consider random graphs…
The mathematical properties of a family of generalized beta distribution, including beta-normal, skewed-t, log-F, beta-exponential, beta-Weibull distributions have recently been studied in several publications. This paper applies these…
There are given characterizations of the exponential distribution by the properties of the independence of linear forms with random coefficients. Related results based on the constancy of regression of one statistic on a linear form are…
This paper develops methods to study the distribution of Eulerian statistics defined by second-order recurrence relations. We define a random process to decompose the statistics over compositions of integers. It is shown that the numbers of…
We describe \textit{deep exponential families} (DEFs), a class of latent variable models that are inspired by the hidden structures used in deep neural networks. DEFs capture a hierarchy of dependencies between latent variables, and are…
Statistical inference may follow a frequentist approach or it may follow a Bayesian approach or it may use the minimum description length principle (MDL). Our goal is to identify situations in which these different approaches to statistical…
Recently, Ehrenborg and Van Willenburg defined a class of bipartite graphs that correspond naturally to Ferrers diagrams, and proved several results about them. We give bijective proofs for the (already known) expressions for the number of…
Directional data emerges in a wide array of applications, ranging from atmospheric sciences to medical imaging. Modeling such data, however, poses unique challenges by virtue of their being constrained to non-Euclidean spaces like…
In this paper we present various new inequalities for tail proabilities for distributions that are elements of the most improtant exponential families. These families include the Poisson distributions, the Gamma distributions, the binomial…
The $\lambda$-exponential family generalizes the standard exponential family via a generalized convex duality motivated by optimal transport. It is the constant-curvature analogue of the exponential family from the information-geometric…
Sampling algorithms, hypergraph degree sequences, and polytopes play a crucial role in statistical analysis of network data. This article offers a brief overview of open problems in this area of discrete mathematics from the point of view…
We start from a parametrized system of $d$ generalized polynomial equations (with real exponents) for $d$ positive variables, involving $n$ generalized monomials with $n$ positive parameters. Existence and uniqueness of a solution for all…
Probability distributions supported on the simplex enjoy a wide range of applications across statistics and machine learning. Recently, a novel family of such distributions has been discovered: the continuous categorical. This family enjoys…
In the field of statistics, many kind of divergence functions have been studied as an amount which measures the discrepancy between two probability distributions. In the differential geometrical approach in statistics (information…
We present a method for learning max-weight matching predictors in bipartite graphs. The method consists of performing maximum a posteriori estimation in exponential families with sufficient statistics that encode permutations and data…
A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…
We investigate a family of one dimensional maps for which the bifurcation diagram looks differently than the usual ones. We describe and exemplify various unique and interesting phenomena arising for this family of maps.
We characterize the exponential distribution as the only one which satisfies a regression condition. This condition involves the regression function of a fixed record value given two other record values, one of them being previous and the…
Exponential-family random graph models (ERGMs) provide a principled and flexible way to model and simulate features common in social networks, such as propensities for homophily, mutuality, and friend-of-a-friend triad closure, through…
The lower bound of Cramer and Rao is generalized to pairs of families of probability distributions, one of which is escort to the other. This bound is optimal for certain families, called phi-exponential in the paper. Their dual structure…