The paper introduces CUTS-GPR, a method for exact Gaussian Process Regression (GPR) in high-dimensional settings. It achieves near-linear scaling in the number of training points and low-order polynomial scaling in dimensionality by using an additive kernel on an incomplete grid, enabling efficient kernel matrix-vector products. Benchmarks demonstrate scalability to billions of data points and thousands of dimensions, with full GPR runs on up to 4.5 million points in 500 dimensions and practical application to ten high-dimensional potential energy surfaces completed in hours.
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.
arXiv:2606. 02909v1 Announce Type: cross Abstract: Gradient observations can substantially improve Gaussian process (GP) surrogates, particularly in high-dimensional settings where function evaluations are expensive.
arXiv:2609. 21085v1 Announce Type: cross Abstract: Gaussian processes (GPs) provide principled probabilistic predictions while encoding prior knowledge, including equivariances.
arXiv:2606. 23867v1 Announce Type: new Abstract: The exact computation of the Normalized Maximum Likelihood (NML) codelength for regular non-smooth estimators (e.
arXiv:2610.02395v1 Announce Type: new Abstract: Streaming GPU solvers for entropic optimal transport (EOT), such as FlashSinkhorn, avoid storing the dense kernel but still evaluate all $n\times m$ po...
arXiv:2607. 19498v1 Announce Type: cross Abstract: Gaussian process (GP) modeling is widely used in computational science and engineering.
arXiv:2608. 10523v1 Announce Type: cross Abstract: \texttt{TensorSketch} by~\cite{pham2013fast,kar2012random} provides efficient sketching algorithms for high-dimensional polynomial kernels $\vec{x}^{\otimes p} \in \R^{d^p}$.
\texttt{TensorSketch} by~\cite{pham2013fast,kar2012random} provides efficient sketching algorithms for high-dimensional polynomial kernels $\vec{x}^{\otimes p} \in \R^{d^p}$. \cite{kar2012random} uses dense Johnson-Lindenstrauss (JL)-type projections with computational cost $O(pDd)$, where $D$ denotes the sketch dimension, whereas~\cite{pham2013fast} extends the sparse \texttt{CountSketch}~\citep{count_sketch} algorithm, yielding a faster algorithm for high-dimensional sparse inputs with running time $O\big(p(\nnz{\vec{x}} + D \log D)\big)$.
arXiv:2610.28256v1 Announce Type: cross Abstract: Sparse variational Gaussian processes (SVGPs) are a widely used, principled approach to scalable Gaussian process modelling. Their success stems from...
arXiv:2606. 27298v1 Announce Type: cross Abstract: We study the fundamental problem of learning a high-dimensional Gaussian truncated to an unknown halfspace.
arXiv:2610.10428v1 Announce Type: cross Abstract: Gradient observations promise more accurate Gaussian process (GP) surrogates, but the cost of incorporating them has long stood in the way of realizi...
The paper presents a neural hierarchical‑matrix preconditioner designed for real‑time GPU solves of sparse symmetric positive‑definite systems that change each frame. By training a graph‑and‑attention network to predict an SPD approximate inverse in H²‑matrix format, the method achieves linear‑time inference and application, outperforming traditional multigrid setup times and local preconditioners. Experiments on 3D mesh diffusion problems show the preconditioner reduces conjugate‑gradient iterations from 116 to 33 and enables 120 fps real‑time performance for up to 3,647 unknowns.