arXiv:2606. 06576v1 Announce Type: new Abstract: In the sciences, regression tasks often require predicting high-dimensional outputs from few training examples.
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:2607. 19498v1 Announce Type: cross Abstract: Gaussian process (GP) modeling is widely used in computational science and engineering.
arXiv:2608.30262v1 Announce Type: new Abstract: Scientific simulations generate collections of physical fields with heterogeneous statistics and dependencies, yet learned compressors often encode tho...
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:2606. 03553v1 Announce Type: cross Abstract: While principal component analysis (PCA) is a fundamental tool for dimensionality reduction, its dense representations make it ill-suited for high-dimensional data.
arXiv:2607. 18209v1 Announce Type: cross Abstract: This paper considers a multi-environment factor model in which high-dimensional covariates are collected from heterogeneous environments, with auxiliary labels available in a subset of these environments.
arXiv:2609. 21085v1 Announce Type: cross Abstract: Gaussian processes (GPs) provide principled probabilistic predictions while encoding prior knowledge, including equivariances.
arXiv:2607. 16731v1 Announce Type: new Abstract: Marine biogeochemical forecasting is increasingly important for managing marine ecosystems and the carbon cycle, yet global, seasonal forecast products lag far behind physical oceanography, held back by the complexity of the processes involved and by data scarcity.
HALO introduces a hyperspherical VAE to constrain continuous latent representations to a fixed‑radius shell, stabilizing numerical fluctuations. It then employs a masked autoregressive model that balances parallel decoding with temporal correlation learning, reducing inference steps and improving stability. Experiments show HALO achieves state‑of‑the‑art generation performance with significantly better inference efficiency compared to existing baselines.
arXiv:2412. 07041v4 Announce Type: replace-cross Abstract: Recovering incomplete multidimensional tensor-structured data is a fundamental task in many real-world applications.
HiLNO is a hierarchical latent neural operator that builds a fine‑to‑coarse‑to‑fine latent space and incorporates multi‑scale supervision and anisotropic Gaussian attention to preserve spatial information in PDE solutions with multiscale structures. The hierarchy reduces information loss during compression, while multi‑scale supervision aligns intermediate predictions with downsampled targets, and anisotropic attention facilitates feature transfer across scales. Experiments on standard PDE benchmarks and a large‑scale automotive aerodynamics task show that HiLNO achieves competitive accuracy while cutting parameter count by 84.4% and FLOPs by 69.2% compared with LinearNO, and it generalizes effectively to unseen spatial resolutions.
The paper investigates nonlinear dimensionality reduction for Bayesian optimisation (BO) by transforming high‑dimensional black‑box optimisation problems into a sequence of low‑dimensional latent‑space BO (LSBO) tasks. It extends earlier linear embedding approaches by using variational autoencoders (VAEs), deep metric loss, and adaptive retraining to better capture nonlinear structure, and couples LSBO with sequential domain reduction (SDR‑LSBO) to progressively narrow search domains. Experiments on GPU‑accelerated BoTorch with Matérn‑5/2 Gaussian‑process surrogates show that VAE‑based LSBO outperforms adaptive linear embeddings, and the authors provide a theoretical analysis of latent‑space error versus representation gap under PAC‑Bayes conditions.