Related papers: Standardizing densities on Gaussian spaces
We study the regularity of densities of distributions that are polynomial images of the standard Gaussian measure on $\mathbb{R}^n$. We assume that the degree of a polynomial is fixed and that each variable enters to a power bounded by…
Through a reformulation of the local limit theorem and law of small numbers, which is obtained by working in the spaces naturally associated to the limiting distributions, we discover a general and abstract framework for the investigation…
We study a statistical model for infinite dimensional Gaussian random variables with unknown parameters. For this model we derive linear estimators for the mean and the variance of the Gaussian distribution. Furthermore, we construct…
Consider the random sequential packing model with infinite input and in any dimension. When the input consists of non-zero volume convex solids we show that the total number of solids accepted over cubes of volume $\lambda$ is…
We consider finite dimensional rough differential equations driven by centered Gaussian processes. Combining Malliavin calculus, rough paths techniques and interpolation inequalities, we establish upper bounds on the density of the…
We introduce new finite-dimensional spaces specifically designed to approximate the solutions to high-frequency Helmholtz problems with smooth variable coefficients in dimension $d$. These discretization spaces are spanned by Gaussian…
In this paper we examine the deviations from Gaussianity for two types of random variable converging to a normal distribution, namely sums of random variables generated by a deterministic discrete time map and a linearly damped variable…
We introduce fully scalable Gaussian processes, an implementation scheme that tackles the problem of treating a high number of training instances together with high dimensional input data. Our key idea is a representation trick over the…
This short review is devoted to measures on infinite dimensional spaces. We start by discussing product measures and projective techniques. Special attention is paid to measures on linear spaces, and in particular to Gaussian measures.…
A Gaussian variational approximation is often used to study interfaces in random media. By considering the 1+1 dimensional directed polymer in a random medium, it is shown here that the variational Ansatz typically leads to a negative…
Inertial particles in 2D driven by a Gaussian white noise forcing are considered. For two examples of the forcing (compressible and incompressible) upper and lower bounds are found for the mean number of caustics as a function of Stokes…
Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…
Finite mixture of Gaussian distributions provide a flexible semi-parametric methodology for density estimation when the variables under investigation have no boundaries. However, in practical applications variables may be partially bounded…
We establish Gaussian limits for general measures induced by binomial and Poisson point processes in d-dimensional space. The limiting Gaussian field has a covariance functional which depends on the density of the point process. The general…
One of the fundamental problems in Bayesian statistics is the approximation of the posterior distribution. Gibbs sampler and coordinate ascent variational inference are renownedly utilized approximation techniques that rely on stochastic…
This paper presents a new Bayesian framework for quantifying discretization errors in numerical solutions of ordinary differential equations. By modelling the errors as random variables, we impose a monotonicity constraint on the variances,…
The aim of this paper is to establish the uniform convergence of the densities of a sequence of random variables, which are functionals of an underlying Gaussian process, to a normal density. Precise estimates for the uniform distance are…
We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…
Bayesian variable selection has gained much empirical success recently in a variety of applications when the number $K$ of explanatory variables $(x_1,...,x_K)$ is possibly much larger than the sample size $n$. For generalized linear…
Density estimation is an interdisciplinary topic at the intersection of statistics, theoretical computer science and machine learning. We review some old and new techniques for bounding the sample complexity of estimating densities of…