Related papers: Estimation of high dimensional Gamma convolutions …
Estimation of a multivariate regression function from independent and identically distributed data is considered. An estimate is defined which fits a deep neural network consisting of a large number of fully connected neural networks, which…
This article provides a general expression for infinitely divisible multivariate gamma distributions defined by their Laplace transforms, as well as the conditional Laplace transform of infinitely divisible multivariate gamma…
Scale invariance (fractality) is a prominent feature of the large-scale behavior of many stochastic systems. In this work, we construct an algorithm for the statistical identification of the Hurst distribution (in particular, the scaling…
Stochastic localization is a pathwise analysis technique originating from convex geometry. This paper explores certain algorithmic aspects of stochastic localization as a computational tool. First, we unify various existing stochastic…
A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using…
We consider component-wise equivariant estimation of order restricted location/scale parameters of a general bivariate distribution under quite general conditions on underlying distributions and the loss function. This paper unifies various…
The generalized Ridge penalty is a powerful tool for dealing with overfitting and for high-dimensional regressions. The generalized Ridge regression can be derived as the mean of a posterior distribution with a Normal prior and a given…
We study the peak height distribution of certain non-stationary Gaussian random fields. The explicit peak height distribution of smooth, non-stationary Gaussian processes in 1D with general covariance is derived. The formula is determined…
A number of recent studies have estimated the inter-galactic void probability function and investigated its departure from various random models. We study a family of parametric statistical models based on gamma distributions, which do give…
We propose a general framework using spike-and-slab prior distributions to aid with the development of high-dimensional Bayesian inference. Our framework allows inference with a general quasi-likelihood function. We show that highly…
A generalization of expectiles for d-dimensional multivariate distribution functions is introduced. The resulting geometric expectiles are unique solutions to a convex risk minimization problem and are given by d-dimensional vectors. They…
Although there is much recent work developing flexible variational methods for Bayesian computation, Gaussian approximations with structured covariance matrices are often preferred computationally in high-dimensional settings. This paper…
We present a multivariate Gaussian process regression approach for parameter field reconstruction based on the field's measurements collected at two different scales, the coarse and fine scales. The proposed approach treats the parameter…
In this article, we develop a distributed variable screening method for generalized linear models. This method is designed to handle situations where both the sample size and the number of covariates are large. Specifically, the proposed…
Copulas are a powerful tool to model dependence between the components of a random vector. One well-known class of copulas when working in two dimensions is the Farlie-GumbelMorgenstern (FGM) copula since their simple analytic shape enables…
In this work we study the estimation of the density of a totally positive random vector. Total positivity of the distribution of a random vector implies a strong form of positive dependence between its coordinates and, in particular, it…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
Deep generative models provide a systematic way to learn nonlinear data distributions, through a set of latent variables and a nonlinear "generator" function that maps latent points into the input space. The nonlinearity of the generator…
In this paper, we consider projection estimates for L\'evy densities in high-frequency setup. We give a unified treatment for different sets of basis functions and focus on the asymptotic properties of the maximal deviation distribution for…
Clustering mixtures of Gaussian distributions is a fundamental and challenging problem that is ubiquitous in various high-dimensional data processing tasks. While state-of-the-art work on learning Gaussian mixture models has focused…