Related papers: Jointly Robust Prior for Gaussian Stochastic Proce…
In the context of the expected-posterior prior (EPP) approach to Bayesian variable selection in linear models, we combine ideas from power-prior and unit-information-prior methodologies to simultaneously produce a minimally-informative…
This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. We consider a sparse projection of input variables and a general stationary covariance model that depends on the Euclidean distance…
Any classifier can be "smoothed out" under Gaussian noise to build a new classifier that is provably robust to $\ell_2$-adversarial perturbations, viz., by averaging its predictions over the noise via randomized smoothing. Under the…
A key challenge in spatial statistics is the analysis for massive spatially-referenced data sets. Such analyses often proceed from Gaussian process specifications that can produce rich and robust inference, but involve dense covariance…
The paper discusses shrinkage priors which impose increasing shrinkage in a sequence of parameters. We review the cumulative shrinkage process (CUSP) prior of Legramanti et al. (2020), which is a spike-and-slab shrinkage prior where the…
We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP)…
Gaussian Process (GP) regression is shown to be effective for learning unknown dynamics, enabling efficient and safety-aware control strategies across diverse applications. However, existing GP-based model predictive control (GP-MPC)…
Doubly intractable problems occur when both the likelihood and the posterior are available only in unnormalised form, with computationally intractable normalisation constants. Bayesian inference then typically requires direct approximation…
Bayesian optimisation requires fitting a Gaussian process model, which in turn requires specifying prior on the unknown black-box function -- most of the theoretical literature assumes this prior is known. However, it is common to have more…
The vast quantity of information brought by big data as well as the evolving computer hardware encourages success stories in the machine learning community. In the meanwhile, it poses challenges for the Gaussian process (GP) regression, a…
Gaussian processes are a flexible Bayesian nonparametric modelling approach that has been widely applied but poses computational challenges. To address the poor scaling of exact inference methods, approximation methods based on sparse…
Despite their promise and ubiquity, Gaussian processes (GPs) can be difficult to use in practice due to the computational impediments of fitting and sampling from them. Here we discuss a short R package for efficient multivariate normal…
Smoothing classifiers and probability density functions with Gaussian kernels appear unrelated, but in this work, they are unified for the problem of robust classification. The key building block is approximating the $\textit{energy…
As is well known, both sampling from the posterior and computing the mean of the posterior in Gaussian process regression reduces to solving a large linear system of equations. We study the use of stochastic gradient descent for solving…
Multifidelity models integrate data from multiple sources to produce a single approximator for the underlying process. Dense low-fidelity samples are used to reduce interpolation error, while sparse high-fidelity samples are used to…
Gaussian processes (GPs) are powerful and widely used probabilistic regression models, but their effectiveness in practice is often limited by the choice of kernel function. This kernel function is typically handcrafted from a small set of…
The computational efficiency of approximate Bayesian computation (ABC) has been improved by using surrogate models such as Gaussian processes (GP). In one such promising framework the discrepancy between the simulated and observed data is…
Bayesian simulation-based inference (SBI) methods are used in statistical models where simulation is feasible but the likelihood is intractable. Standard SBI methods can perform poorly in cases of model misspecification, and there has been…
We propose a nested Gaussian process (nGP) as a locally adaptive prior for Bayesian nonparametric regression. Specified through a set of stochastic differential equations (SDEs), the nGP imposes a Gaussian process prior for the function's…
The Gaussian process is a standard tool for building emulators for both deterministic and stochastic computer experiments. However, application of Gaussian process models is greatly limited in practice, particularly for large-scale and…