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: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:2608.29349v1 Announce Type: new Abstract: Gaussian process (GP) regression with a single global GP (GP-glo) incurs cubic computational cost, limiting scalability to large datasets. Product-of-e...
arXiv:2608. 11917v1 Announce Type: new Abstract: Multi-output Gaussian process regression scales cubically in the number of observations times outputs, and dense kernel-matrix methods need bespoke handling whenever different outputs are observed at different inputs.
arXiv:2603. 22050v2 Announce Type: replace-cross Abstract: Supervised machine learning describes the practice of fitting a parameterized model to labeled input-output 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 tackles the challenge of predicting multiple high‑dimensional physical fields that must satisfy linear equality constraints, a common scenario in physics‑informed machine learning. It critiques the conventional approach of deducing one field from others, showing its sensitivity to arbitrary choices and its impact on accuracy and uncertainty. To address this, the authors introduce a symmetric framework that first applies a row‑wise PCA to preserve constraints in a latent space, then trains a linearly‑constrained multi‑output Gaussian process using a specially parametrized kernel, and validate the method on population dynamics and CFD problems involving Reynolds stress tensors.
arXiv:2606. 27298v1 Announce Type: cross Abstract: We study the fundamental problem of learning a high-dimensional Gaussian truncated to an unknown halfspace.
arXiv:2608. 13793v1 Announce Type: cross Abstract: Machine learning (ML) has become an indispensable part of modern engineering design workflows.
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:2607. 09073v1 Announce Type: new Abstract: Bayesian optimization routinely warm-starts a target experiment with data from related source tasks, and the multi-task Gaussian process is the textbook surrogate for the job.
arXiv:2412. 08147v2 Announce Type: replace-cross Abstract: Pareto fronts are useful to find good task-mixing strategies for multitask finetuning, but they are also costly to compute.
arXiv:2607. 01689v1 Announce Type: cross Abstract: Model merging aims to combine existing single-task solutions into a multi-task solution without additional data-driven fine-tuning.