Related papers: Density estimates and concentration inequalities w…
Likelihood analysis is typically limited to normally distributed noise due to the difficulty of determining the probability density function of complex, high-dimensional, non-Gaussian, and anisotropic noise. This is a major limitation for…
Group-invariant probability distributions appear in many data-generative models in machine learning, such as graphs, point clouds, and images. In practice, one often needs to estimate divergences between such distributions. In this work, we…
Underdamped Langevin Monte Carlo (ULMC) is an algorithm used to sample from unnormalized densities by leveraging the momentum of a particle moving in a potential well. We provide a novel analysis of ULMC, motivated by two central questions:…
We provide posterior contraction rates for constrained deep Gaussian processes in non-parametric density estimation and classication. The constraints are in the form of bounds on the values and on the derivatives of the Gaussian processes…
For a difference approximations of multidimensional diffusion, the truncated local limit theorem is proved. Under very mild conditions on the distribution of the difference terms, this theorem provides that the transition probabilities of…
We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…
Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Maatouk and Bay (2017)…
In this paper, we extend Walsh's stochastic integral with respect to a Gaussian noise, white in time and with some homogeneous spatial correlation, in order to be able to integrate some random measure-valued processes. This extension turns…
We provide general conditions to derive posterior concentration rates for Aalen counting processes. The conditions are designed to resemble those proposed in the literature for the problem of density estimation, for instance in Ghosal et…
We study various generalizations of concentration of measure on the unit sphere, in particular by means of log-Sobolev inequalities. First, we show Sudakov-type concentration results and local semicircular laws for weighted random matrices.…
We develop a theory of Malliavin calculus for Banach space valued random variables. Using radonifying operators instead of symmetric tensor products we extend the Wiener-Ito isometry to Banach spaces. In the white noise case we obtain two…
By means of the Malliavin calculus, integral representations for the likelihood function and for the derivative of the log-likelihood function are given for a model based on discrete time observations of the solution to equation…
Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular non-parametric density estimators, the mean integrated square error converges…
The random convex hull of a Poisson point process in $\mathbb{R}^d$ whose intensity measure is a multiple of the standard Gaussian measure on $\mathbb{R}^d$ is investigated. The purpose of this paper is to invent a new viewpoint on these…
We study Malliavin differentiability for the solutions of a stochastic differential equation with drift of super-linear growth. Assuming we have a monotone drift with polynomial growth, we prove Malliavin differentiability of any order. As…
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…
We present the Gaussian process density sampler (GPDS), an exchangeable generative model for use in nonparametric Bayesian density estimation. Samples drawn from the GPDS are consistent with exact, independent samples from a distribution…
We consider the stochastic integrals of multivariate point processes and study their concentration phenomena. In particular, we obtain a Bernstein type of concentration inequality through Dol\'eans-Dade exponential formula and a uniform…
The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the…
In this paper, based on the techniques of Malliavin calculus, we provide some new concentration inequalities for the running supremum of the It\^o stochastic integral with unbounded integrands. Several applications and examples are provided…