arXiv:2512. 06143v2 Announce Type: replace Abstract: Despite a large corpus of recent work on scaling up Gaussian processes, a stubborn trade-off between computational speed, prediction and uncertainty quantification accuracy, and customizability persists.
The paper introduces a scalable Bayesian method for conditional density estimation using a logistic Gaussian process. It models the log conditional density with a separable covariance— a Matérn kernel on the response dimension and a Nyström-feature kernel on covariates— and samples the latent field via kinetic Langevin dynamics instead of traditional approximations. Experiments on photometric‑redshift data with up to 3.9 million observations show the approach matches state‑of‑the‑art tabular foundation models on density and calibration metrics.
The paper argues against using the Gaussian (squared exponential/RBF) kernel as a default in Gaussian process regression, citing its brittleness. Two key issues are highlighted: the kernel produces unrealistically small conditional variances leading to overconfident predictions, and it causes numerical ill‑conditioning that necessitates ad‑hoc fixes like nugget terms. The authors attribute these problems to the kernel’s analytic, infinitely smooth nature, suggesting that analytic stationary kernels in general should be avoided.
The paper argues against using the Gaussian (squared exponential/RBF) kernel as a default in Gaussian process regression, citing its brittleness. It shows that the kernel leads to unrealistically small conditional variances, causing overconfidence in predictive uncertainty, and that this small variance induces numerical ill‑conditioning, necessitating tricks like nugget terms that alter the model. The authors attribute these issues to the kernel’s analytic, highly smooth nature and suggest that analytic stationary kernels in general should be avoided.
arXiv:2607. 21823v1 Announce Type: new Abstract: We show that, up to isotropic scaling, the Gaussian RBF reproducing kernel Hilbert space (RKHS) is asymptotically isometric to Euclidean space in the large bandwidth limit.
The monograph explores the relationships between Gaussian processes and reproducing kernel Hilbert spaces (RKHS), two widely used approaches that rely on positive definite kernels. It examines how these frameworks connect and are equivalent across key topics such as regression, interpolation, numerical integration, distributional discrepancies, statistical dependence, and Gaussian process sample path properties. By establishing a unifying perspective based on the equivalence between the Gaussian Hilbert space and the RKHS, the work aims to bridge methods developed independently by the machine learning, statistics, and numerical analysis communities.
arXiv:2606. 03559v1 Announce Type: new Abstract: For nonconvex optimization problems whose objective is the prediction function of a trained Support Vector Regression (SVR) model with the Gaussian radial basis function (RBF) kernel (RBF-SVR), we present a framework that applies the difference of convex functions (DC) algorithm (DCA) by exploiting the analytical structure of the RBF kernel to construct an explicit DC decomposition.
arXiv:2610.03201v1 Announce Type: cross Abstract: Gaussian Processes (GPs) are a powerful tool for modelling and quantifying uncertainty in functional relationships. However, they require practitione...
The paper introduces improvements to FlowGP, a method for conditional sampling from Gaussian processes outside the linear-Gaussian regime. It adds kernel approximations to scale to high-resolution domains and a new technique for computing marginal likelihood by measuring the work required to steer diffusion toward conditioning statements. These advances enable hyperparameter optimisation within FlowGP and are demonstrated on tasks such as probabilistic downscaling, PDE solution inference on irregular domains, and sea level anomaly field recovery from non-Gaussian satellite data.
arXiv:2610.19925v1 Announce Type: cross Abstract: Efficient global optimization aims to identify a global optimum of an expensive black-box function within a limited evaluation budget $N$. We investi...
The paper proposes three information‑theoretic criteria for selecting the most relevant basis functions in sparse Gaussian process regression, tailored to different levels of prior knowledge. Experiments on six UCI regression datasets and three basis families (HSGP, VFF, VISH) show that the no‑data criterion is a robust default, often outperforming simple truncation, while the data‑aware criteria yield significant improvements for HSGP. The study demonstrates that careful basis‑function selection can lead to better performance without increasing computational cost.
arXiv:2604. 07635v2 Announce Type: replace-cross Abstract: This research considers a scalable inference for spatial data modeled through Gaussian intrinsic conditional autoregressive (ICAR) structures.