相关论文: On information projections between multivariate el…

We show that the $f$-divergence between any two densities of potentially different location-scale families can be reduced to the calculation of the $f$-divergence between one standard density with another location-scale density. It follows…

We first extend the result of Ali and Silvey [Journal of the Royal Statistical Society: Series B, 28.1 (1966), 131-142] who first reported that any $f$-divergence between two isotropic multivariate Gaussian distributions amounts to a…

In this paper we propose a family of multivariate asymmetric distributions over an arbitrary subset of set of real numbers which is defined in terms of the well-known elliptically symmetric distributions. We explore essential properties,…

We develop a "multifocal" approach to reveal spatial dissimilarities in cities, from the most local scale to the metropolitan one. Think for instance of a statistical variable that may be measured at different scales, eg ethnic group…

There are many applications that benefit from computing the exact divergence between 2 discrete probability measures, including machine learning. Unfortunately, in the absence of any assumptions on the structure or independencies within…

Cities are characterized by the coexistence of general aggregate patterns, along with many local variations. This poses challenges for analyses of urban phenomena, which tend to be either too aggregated or too local, depending on the…

We introduce a rank-statistic approximation of $f$-divergences that avoids explicit density-ratio estimation by working directly with the distribution of ranks. For a resolution parameter $K$, we map the mismatch between two univariate…

This paper describes a generalization of the Hellinger distance which we call the S -Hellinger distance; this general family connects the Hellinger distance smoothly with the $L_2$-divergence by a tuning parameter $\alpha$ and is indeed a…

This paper proposes a unified class of generalized location-scale mixture of multivariate elliptical distributions and studies integral stochastic orderings of random vectors following such distributions. Given a random vector…

When performing classification tasks, raw high dimensional features often contain redundant information, and lead to increased computational complexity and overfitting. In this paper, we assume the data samples lie on a single underlying…

M-estimators offer simple robust alternatives to the maximum likelihood estimator. Much of the robustness literature, however, has focused on the problems of location, location-scale and regression estimation rather than on estimation of…

Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple…

The manifold of empirical mean values of statistical data ad infinitum has a geometric shape that depends on the probability measure that governs the generating model. Large deviation theory produces entropy functions that depend on both…

Distributed learning of probabilistic models from multiple data repositories with minimum communication is increasingly important. We study a simple communication-efficient learning framework that first calculates the local maximum…

We present DUAL-LOCO, a communication-efficient algorithm for distributed statistical estimation. DUAL-LOCO assumes that the data is distributed according to the features rather than the samples. It requires only a single round of…

We consider a space structured population model generated by two point clouds: a homogeneous Poisson process $M$ with intensity $n\to\infty$ as a model for a parent generation together with a Cox point process $N$ as offspring generation,…

We propose new small-sphere distributional families for modeling multivariate directional data on $(\mathbb{S}^{p-1})^K$ for $p \ge 3$ and $K \ge 1$. In a special case of univariate directions in $\Re^3$, the new densities model random…

Skew-symmetric densities recently received much attention in the literature, giving rise to increasingly general families of univariate and multivariate skewed densities. Most of those families, however, suffer from the inferential drawback…

We develop and analyze $M$-estimation methods for divergence functionals and the likelihood ratios of two probability distributions. Our method is based on a non-asymptotic variational characterization of $f$-divergences, which allows the…

In information geometry, generalized exponential families and statistical manifolds with curvature are under active investigation in recent years. In this paper we consider the statistical manifold induced by a logarithmic…