Related papers: Optimal Bayesian estimation in random covariate de…

We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…

While Gaussian processes are a mainstay for various engineering and scientific applications, the uncertainty estimates don't satisfy frequentist guarantees and can be miscalibrated in practice. State-of-the-art approaches for designing…

Deep Gaussian processes have recently been proposed as natural objects to fit, similarly to deep neural networks, possibly complex features present in modern data samples, such as compositional structures. Adopting a Bayesian nonparametric…

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…

In this work, we investigate Gaussian process regression used to recover a function based on noisy observations. We derive upper and lower error bounds for Gaussian process regression with possibly misspecified correlation functions. The…

In this article, we investigate posterior convergence in nonparametric regression models where the unknown regression function is modeled by some appropriate stochastic process. In this regard, we consider two setups. The first setup is…

Gaussian processes are a fully Bayesian smoothing technique that allows for the reconstruction of a function and its derivatives directly from observational data, without assuming a specific model or choosing a parameterization. This is…

Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…

Whilst deep neural networks have shown great empirical success, there is still much work to be done to understand their theoretical properties. In this paper, we study the relationship between random, wide, fully connected, feedforward…

Statistical physics approaches can be used to derive accurate predictions for the performance of inference methods learning from potentially noisy data, as quantified by the learning curve defined as the average error versus number of…

Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…

Bayesian optimization through Gaussian process regression is an effective method of optimizing an unknown function for which every measurement is expensive. It approximates the objective function and then recommends a new measurement point…

We introduce a random partition model for Bayesian nonparametric regression. The model is based on infinitely-many disjoint regions of the range of a latent covariate-dependent Gaussian process. Given a realization of the process, the…

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…

Gaussian processes (GPs) are widely used metamodels for approximating expensive computer simulations, particularly in engineering design and spatial prediction. However, their performance can deteriorate significantly when covariance…

Gaussian process (GP) regression is a powerful interpolation technique due to its flexibility in capturing non-linearity. In this paper, we provide a general framework for understanding the frequentist coverage of point-wise and…

We develop a semiparametric Bayesian approach for estimating the mean response in a missing data model with binary outcomes and a nonparametrically modelled propensity score. Equivalently we estimate the causal effect of a treatment,…

We consider Bayesian nonparametric density estimation using a Pitman-Yor or a normalized inverse-Gaussian process kernel mixture as the prior distribution for a density. The procedure is studied from a frequentist perspective. Using the…

Bayesian inference and uncertainty quantification in a general class of non-linear inverse regression models is considered. Analytic conditions on the regression model $\{\mathscr G(\theta): \theta \in \Theta\}$ and on Gaussian process…

We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior…