Related papers: Nonparametric regression on random geometric graph…
Motivated by the need to analyze large, decentralized datasets, distributed Bayesian inference has become a critical research area across multiple fields, including statistics, electrical engineering, and economics. This paper establishes…
Here we develop a method for performing nonparametric Bayesian inference on quantiles. Relying on geometric measure theory and employing a Hausdorff base measure, we are able to specify meaningful priors for the quantile while treating the…
In nonparametric regression problems involving multiple predictors, there is typically interest in estimating an anisotropic multivariate regression surface in the important predictors while discarding the unimportant ones. Our focus is on…
Many asymptotically minimax procedures for function estimation often rely on somewhat arbitrary and restrictive assumptions such as isotropy or spatial homogeneity. This work enhances the theoretical understanding of Bayesian additive…
In the setting of nonparametric multivariate regression with unknown error variance, we study asymptotic properties of a Bayesian method for estimating a regression function f and its mixed partial derivatives. We use a random series of…
We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is…
The posterior distribution in a nonparametric inverse problem is shown to contract to the true parameter at a rate that depends on the smoothness of the parameter, and the smoothness and scale of the prior. Correct combinations of these…
Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…
Bayesian Neural Networks provide a principled framework for uncertainty quantification by modeling the posterior distribution of network parameters. However, exact posterior inference is computationally intractable, and widely used…
We analyze the statistical properties of nonparametric regression estimators using covariates which are not directly observable, but have be estimated from data in a preliminary step. These so-called generated covariates appear in numerous…
Covariate measurement error in nonparametric regression is a common problem in nutritional epidemiology and geostatistics, and other fields. Over the last two decades, this problem has received substantial attention in the frequentist…
We consider covariance estimation in the multivariate generalized Gaussian distribution (MGGD) and elliptically symmetric (ES) distribution. The maximum likelihood optimization associated with this problem is non-convex, yet it has been…
We study nonparametric Bayesian models for reversible multi-dimensional diffusions with periodic drift. For continuous observation paths, reversibility is exploited to prove a general posterior contraction rate theorem for the drift…
We study a Bayesian approach to estimating a smooth function in the context of regression or classification problems on large graphs. We derive theoretical results that show how asymptotically optimal Bayesian regularization can be achieved…
This paper considers the posterior contraction of non-parametric Bayesian inference on non-homogeneous Poisson processes. We consider the quality of inference on a rate function $\lambda$, given non-identically distributed realisations,…
We consider a non-parametric Bayesian model for conditional densities. The model is a finite mixture of normal distributions with covariate dependent multinomial logit mixing probabilities. A prior for the number of mixture components is…
This work studies nonparametric Bayesian estimation of the intensity function of an inhomogeneous Poisson point process in the important case where the intensity depends on covariates, based on the observation of a single realisation of the…
We present clustering methods for multivariate data exploiting the underlying geometry of the graphical structure between variables. As opposed to standard approaches that assume known graph structures, we first estimate the edge structure…
We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization…
This paper tackles the challenge presented by small-data to the task of Bayesian inference. A novel methodology, based on manifold learning and manifold sampling, is proposed for solving this computational statistics problem under the…