arXiv:2607. 19498v1 Announce Type: cross Abstract: Gaussian process (GP) modeling is widely used in computational science and engineering.
Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.
arXiv:2609. 21085v1 Announce Type: cross Abstract: Gaussian processes (GPs) provide principled probabilistic predictions while encoding prior knowledge, including equivariances.
arXiv:2601.21831v3 Announce Type: replace Abstract: We propose a geometric latent-subspace framework for generative modeling of discrete data. Specifically, we introduce latent subspaces in the expon...
arXiv:2606. 06576v1 Announce Type: new Abstract: In the sciences, regression tasks often require predicting high-dimensional outputs from few training examples.
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.
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 introduces the Sparse Landmark Embedding (SLE) kernel, a new framework that removes the need for conditionally negative definite (CND) distance measures in kernel methods and Gaussian Processes. By embedding each input into a sparse feature vector using compactly supported bump functions centered at all training points, any standard positive semi-definite (PSD) kernel can be applied in this embedding space, guaranteeing PSD for arbitrary distance measures. The authors provide theoretical guarantees on PSD, sparsity, stability, and universal approximation, and show through experiments with geodesic and Wasserstein distances that the SLE kernel matches or surpasses domain-specific baselines in predictive accuracy and uncertainty quantification.