Related papers: On the Laplace Approximation as Model Selection Cr…
Gaussian process models are commonly used as emulators for computer experiments. However, developing a Gaussian process emulator can be computationally prohibitive when the number of experimental samples is even moderately large. Local…
We introduce a method that uses low-rank approximations of cross-correlation matrices in mixed continuous and categorical Gaussian Process models. This new method -- called Low-Rank Correlation (LRC) -- offers the ability to flexibly adapt…
Laplace approximation is a very useful tool in Bayesian inference and it claims a nearly Gaussian behavior of the posterior. \cite{SpLaplace2022} established some rather accurate finite sample results about the quality of Laplace…
In Bayesian inference, making deductions about a parameter of interest requires one to sample from or compute an integral against a posterior distribution. A popular method to make these computations cheaper in high-dimensional settings is…
A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…
Statistical applications often involve the calculation of intractable multidimensional integrals. The Laplace formula is widely used to approximate such integrals. However, in high-dimensional or small sample size problems, the shape of the…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
To address the scalability limitations of Gaussian process (GP) regression, several approximation techniques have been proposed. One such method is based on tensor networks, which utilizes an exponential number of basis functions without…
In this work, we propose a novel framework for large-scale Gaussian process (GP) modeling. Contrary to the global, and local approximations proposed in the literature to address the computational bottleneck with exact GP modeling, we employ…
We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…
We explore the estimation of generalized additive models using basis expansion in conjunction with Bayesian model selection. Although Bayesian model selection is useful for regression splines, it has traditionally been applied mainly to…
Gaussian process regression is a popular method for non-parametric probabilistic modeling of functions. The Gaussian process prior is characterized by so-called hyperparameters, which often have a large influence on the posterior model and…
Information theoretic active learning has been widely studied for probabilistic models. For simple regression an optimal myopic policy is easily tractable. However, for other tasks and with more complex models, such as classification with…
Equivariant models leverage prior knowledge on symmetries to improve predictive performance, but misspecified architectural constraints can harm it instead. While work has explored learning or relaxing constraints, selecting among…
We consider the problem of designing a sparse Gaussian process classifier (SGPC) that generalizes well. Viewing SGPC design as constructing an additive model like in boosting, we present an efficient and effective SGPC design method to…
Practitioners building classifiers often start with a smaller pilot dataset and plan to grow to larger data in the near future. Such projects need a toolkit for extrapolating how much classifier accuracy may improve from a 2x, 10x, or 50x…
Logistic Gaussian process (LGP) priors provide a flexible alternative for modelling unknown densities. The smoothness properties of the density estimates can be controlled through the prior covariance structure of the LGP, but the challenge…
In this paper we address a classification problem where two sources of labels with different levels of fidelity are available. Our approach is to combine data from both sources by applying a co-kriging schema on latent functions, which…
High-precision measurements require optimal setups and analysis tools to achieve continuous improvements. Systematic corrections need to be modeled with high accuracy and known uncertainty to reconstruct underlying physical phenomena. To…