Related papers: Heavy-tailed Bayesian nonparametric adaptation
We consider deep neural networks in a Bayesian framework with a prior distribution sampling the network weights at random. Following a recent idea of Agapiou and Castillo (2023), who show that heavy-tailed prior distributions achieve…
The large variety of functions encountered in nonparametric statistics, calls for methods that are flexible enough to achieve optimal or near-optimal performance over a wide variety of functional classes, such as Besov balls, as well as…
We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…
In this paper we present a novel methodology to perform Bayesian model selection in linear models with heavy-tailed distributions. We consider a finite mixture of distributions to model a latent variable where each component of the mixture…
A novel statistical method is proposed and investigated for estimating a heavy tailed density under mild smoothness assumptions. Statistical analyses of heavy-tailed distributions are susceptible to the problem of sparse information in the…
We consider priors for several nonparametric Bayesian models which use finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…
In a general class of Bayesian nonparametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process. Our results apply to nonparametric exponential family that contains both Gaussian and…
We derive rates of contraction of posterior distributions on nonparametric models resulting from sieve priors. The aim of the paper is to provide general conditions to get posterior rates when the parameter space has a general structure,…
We investigate an empirical Bayesian nonparametric approach to a family of linear inverse problems with Gaussian prior and Gaussian noise. We consider a class of Gaussian prior probability measures with covariance operator indexed by a…
We study Bayesian linear regression models with skew-symmetric scale mixtures of normal error distributions. These kinds of models can be used to capture departures from the usual assumption of normality of the errors in terms of heavy…
Despite the successes of probabilistic models based on passing noise through neural networks, recent work has identified that such methods often fail to capture tail behavior accurately, unless the tails of the base distribution are…
Our goal is to develop a Bayesian model averaging technique in linear regression models that accommodates heavier tailed error densities than the normal distribution. Motivated by the use of the Huber loss function in the presence of…
We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this…
Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…
We study posterior contraction rates for a class of deep Gaussian process priors applied to the nonparametric regression problem under a general composition assumption on the regression function. It is shown that the contraction rates can…
Robots rely on motion planning to navigate safely and efficiently while performing various tasks. In this paper, we investigate motion planning through Bayesian inference, where motion plans are inferred based on planning objectives and…
In the study of heavy tail data, several models have been introduced. If the interest is in the tail of the distribution, block maxima or excess over thresholds are the typical approaches, wasting relevant information in the bulk of the…
We consider nonparametric estimation of a mixed discrete-continuous distribution under anisotropic smoothness conditions and possibly increasing number of support points for the discrete part of the distribution. For these settings, we…
We investigate two empirical Bayes methods and a hierarchical Bayes method for adapting the scale of a Gaussian process prior in a nonparametric regression model. We show that all methods lead to a posterior contraction rate that adapts to…
We study high-dimensional Bayesian linear regression with a general beta prime distribution for the scale parameter. Under the assumption of sparsity, we show that appropriate selection of the hyperparameters in the beta prime prior leads…