The article introduces a partial information decomposition (PID) for multivariate Gaussian systems using the Blackwell order, which determines when one channel is more informative than another. It shows that Gaussian channels optimally extract redundant and union information, providing a geometric interpretation and an efficient numerical algorithm. The authors derive closed‑form expressions for two‑source cases, compare their Blackwell redundancy to the BROJA measures, and demonstrate scalability to systems with up to a thousand dimensions or sources, including an application to an optimal control problem.
By Artemy Kolchinsky
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.
By Mads Greisen H{\o}jlund, August Smart Lykke-M{\o}ller, Henry Moss, Ove Christiansen
arXiv:2606. 27298v1 Announce Type: cross Abstract: We study the fundamental problem of learning a high-dimensional Gaussian truncated to an unknown halfspace.
By Haitong Liu, Deepak Narayanan Sridharan, David Steurer, Manuel Wiedmer
The paper studies the numerical solution of the Beurling‑LASSO (BLASSO) for estimating Gaussian mixture models (GMMs) with unknown numbers of components and unknown diagonal covariance matrices. It introduces a Conic Particle Gradient Descent (CPGD) algorithm that incorporates Riemannian gradient descent to respect the Fisher‑Rao geometry of Gaussian distributions. The authors provide theoretical convergence guarantees, including exponential local convergence under a non‑degeneracy condition related to component separation, and demonstrate through numerical experiments that CPGD is more robust to overspecification of components than the EM algorithm.
By Romane Giard, Yohann De Castro, Roland Denis, Cl\'ement Marteau
arXiv:2606. 31390v1 Announce Type: cross Abstract: Low-rank matrix optimization is often carried out via the Burer-Monteiro (BM) formulation, but choosing the factorization rank $r$ is delicate and can substantially slow optimization.
By Yudong Wei, Liang Zhang, Bingcong Li, Niao He
arXiv:2402.03809v2 Announce Type: replace-cross
Abstract: Gaussian processes are a widely embraced technique for regression due to their good prediction accuracy, analytical tractability, and built-i...
By Mickael Binois (ACUMES), Victor Picheny
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.
By Yanchuang Cao, Jun Liu, Tengchao Yu, Heng Yong
arXiv:2609.37308v1 Announce Type: cross
Abstract: This paper introduces a hybrid joint-selective optimization (HJSO) framework for large-scale numerical problems in which a small subset of trainable...
By Muhammad Luthfi Shahab, Gabriella Alfa Indahsari, Imam Mukhlash, Hadi Susanto
The paper proposes using the $q$Gaussian distribution, derived from Tsallis entropy maximization, to address the shortcomings of Gaussian assumptions in sparse learning with correlated and heterogeneous data. It introduces a new framework that adapts numerical equilibrium methods to composite optimization problems, applying it to the Hager‑Zhang conjugate gradient algorithm to create a stable, efficient sparse learning algorithm. The work offers both theoretical insights into alternative statistical distributions and practical tools for data analysis in fields like biostatistics.
By Kai Yang, Masoud Asgharian, Celia M. T. Greenwood
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.
By Olivier Truffinet (CEA Saclay), Karim Ammar (CEA Saclay), Jean-Philippe Argaud (EDF R&D), Bertrand Bouriquet (EDF)
The paper introduces a two‑stage method for estimating sparse high‑dimensional partial correlation matrices and inverse covariance matrices with non‑asymptotic guarantees. It leverages the link between inverse covariance and linear regression while ensuring positive semi‑definiteness, and provides an efficient proximal splitting algorithm for computation. The authors demonstrate the method’s effectiveness on synthetic and real‑world datasets.
By Samuel Erickson, Tobias Ryd\'en
arXiv:2512.03579v2 Announce Type: replace
Abstract: Optimal transport (OT) and Gromov-Wasserstein (GW) alignment provide interpretable geometric frameworks for comparing, transforming, and aggregatin...
By Sanjit Dandapanthula, Aleksandr Podkopaev, Shiva Prasad Kasiviswanathan, Aaditya Ramdas, Ziv Goldfeld