The paper introduces an adaptive multi‑resolution Gaussian process framework that achieves scalable, exact inference by constructing a naturally data‑sparse covariance matrix using basis functions anchored directly to samples. By shrinking the support domains of these basis functions, the resulting matrix has limited block sizes, ensuring sparsity and enabling efficient computation of its inverse via a sparse Cholesky algorithm. The authors demonstrate that this approach yields exact inference with training cost ≠≠ O(n log^2 n) and prediction cost ≠≠ O(log^d n), while also improving predictive uncertainties through an augmented basis function.
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:2607. 07735v1 Announce Type: cross Abstract: Sparse precision matrix estimation provides an interpretable and computationally efficient framework for modeling conditional dependencies in high-dimensional, low-sample-size data.
arXiv:2511. 16340v2 Announce Type: replace Abstract: Efficient Gaussian process (GP) inference is critical for sequential decision-making tasks such as active learning, online prediction, and Bayesian optimization.
The paper introduces QuADA-GS, a method for Arbitrary-Scale Super-Resolution that dynamically densifies 2D Gaussian splatting based on low‑resolution input. By allocating Gaussians adaptively to structurally complex regions and employing a sparse communication mechanism, it balances high visual fidelity with lower computational cost. Experiments show that this approach achieves a competitive trade‑off between quality and efficiency for super‑resolution tasks.
arXiv:2607. 19498v1 Announce Type: cross Abstract: Gaussian process (GP) modeling is widely used in computational science and engineering.
arXiv:2606. 27298v1 Announce Type: cross Abstract: We study the fundamental problem of learning a high-dimensional Gaussian truncated to an unknown halfspace.
The paper introduces a transfer learning framework for structured matrix estimation when both the ambient dimension and the intrinsic representation grow over time. It models the target parameter as an embedded source component plus low‑rank innovations and sparse edits, and proposes an anchored alternating projection estimator that preserves the transferred subspace while estimating only the new components. Deterministic error bounds are derived that separate target noise, representation growth, and source estimation error, showing improved rates when rank and sparsity increments are small, and the framework is applied to Markov transition matrix estimation and structured covariance estimation with theoretical guarantees and empirical validation.
arXiv:2606. 06576v1 Announce Type: new Abstract: In the sciences, regression tasks often require predicting high-dimensional outputs from few training examples.
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:2605. 10285v2 Announce Type: replace-cross Abstract: We present a theoretically grounded Gaussian process framework that leverages neural feature maps to construct expressive kernels.
The paper presents an exact, efficient solution for the Linear Model of Co‑regionalization (LMC) multitask Gaussian Process by decoupling latent processes under a mild noise‑model assumption. It introduces a full parametrization of the resulting projected LMC, enabling linear‑time optimization and simplifying tasks such as training updates and leave‑one‑out cross‑validation. Experiments on synthetic and real data demonstrate that projected LMC is competitive with state‑of‑the‑art multitask GP models while offering greater interpretability and computational ease.
arXiv:2606. 23867v1 Announce Type: new Abstract: The exact computation of the Normalized Maximum Likelihood (NML) codelength for regular non-smooth estimators (e.