Related papers: Variable Selection Consistency of Gaussian Process…

To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of…

We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable to deal with single-output as well as multiple-output linear regressions, in small or high dimension, enforcing either…

We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data. We develop a general recipe for analyzing the convergence of iterative algorithms…

Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these…

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…

We propose a new Bayesian strategy for adaptation to smoothness in nonparametric models based on heavy tailed series priors. We illustrate it in a variety of settings, showing in particular that the corresponding Bayesian posterior…

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a…

In this paper, we prove almost surely consistency of a Survival Analysis model, which puts a Gaussian process, mapped to the unit interval, as a prior on the so-called hazard function. We assume our data is given by survival lifetimes $T$…

Given a sequence of observable variables $\{(x_1, y_1), \ldots, (x_n, y_n)\}$, the conformal prediction method estimates a confidence set for $y_{n+1}$ given $x_{n+1}$ that is valid for any finite sample size by merely assuming that the…

We study the posterior contraction rates of a Bayesian method with Gaussian process priors in nonparametric regression and its plug-in property for differential operators. For a general class of kernels, we establish convergence rates of…

A general theory for Gaussian mean estimation that automatically adapts to unknown sparsity under arbitrary norms is proposed. The theory is applied to produce adaptively minimax rate-optimal estimators in high dimensional regression and…

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…

We consider Bayesian model selection in generalized linear models that are high-dimensional, with the number of covariates p being large relative to the sample size n, but sparse in that the number of active covariates is small compared to…

In nonparameteric Bayesian approaches, Gaussian stochastic processes can serve as priors on real-valued function spaces. Existing literature on the posterior convergence rates under Gaussian process priors shows that it is possible to…

In a regression model, prediction is typically performed after model selection. The large variability in the model selection makes the prediction unstable. Thus, it is essential to reduce the variability in model selection and improve…

In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…

Aleatoric uncertainty captures the inherent randomness of the data, such as measurement noise. In Bayesian regression, we often use a Gaussian observation model, where we control the level of aleatoric uncertainty with a noise variance…

We derive non-asymptotic bounds for the minimax risk of variable selection under expected Hamming loss in the Gaussian mean model in $\mathbb{R}^d$ for classes of $s$-sparse vectors separated from 0 by a constant $a > 0$. In some cases, we…

Gaussian processes that can be decomposed into a smooth mean function and a stationary autocorrelated noise process are considered and a fully automatic nonparametric method to simultaneous estimation of mean and auto-covariance functions…

We develop a fast and accurate grouped penalized credible region approach for variable selection and prediction in Bayesian high-dimensional linear regression. Most existing Bayesian methods either are subject to high computational costs…