arXiv Machine Learning
Bayesian Optimization on Function Spaces via Sparse RKHS Manifolds
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
Related stories
arXiv Machine Learning
Jul 7
Local Constrained Bayesian Optimization
arXiv:2603. 07965v2 Announce Type: replace-cross Abstract: Bayesian optimization (BO) for high-dimensional constrained problems remains a significant challenge due to the curse of dimensionality.
arXiv Machine Learning
Sep 14
Nonlinear Dimensionality Reduction Techniques for Bayesian Optimization
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 Machine Learning
Jul 22
Information Theoretic Bayesian Optimization over the Probability Simplex
arXiv:2603. 09793v2 Announce Type: replace Abstract: Bayesian optimization is a data-efficient technique that has been shown to be extremely powerful to optimize expensive, black-box, and possibly noisy objective functions.
arXiv Machine Learning
Sep 16
A Weighted Kernel Method for Approximation that Adapts to Learned Multivariable Structure
The paper introduces Total Sensitivity Kernels (TSKs), a weighted ANOVA kernel framework that learns the importance of individual inputs and their interactions for approximating a multivariable black-box function from limited data. By selecting an RKHS where the target function has minimum norm, the authors derive a unique solution and prove consistency for finite-data interpolation. Numerical experiments show that adapting the kernel to the learned multivariable structure can significantly improve approximation accuracy compared to a standard product kernel.
arXiv AI
Aug 6
Out-Of-The-Loop Multi-Fidelity Bayesian Optimization
arXiv:2608. 04113v1 Announce Type: cross Abstract: Black-box optimization is a ubiquitous problem in science and engineering, often dealing with expensive objective functions with cheaper lower-fidelity proxies available.
arXiv Machine Learning
Aug 27
Functional linear regression from sparse to dense designs: a pooling-ridge method and minimax optimality
The paper introduces a pooling‑ridge estimation method for functional linear regression that handles data observed at discrete times, ranging from sparse to dense designs. By combining pooling strategies with RKHS‑based techniques, the authors achieve minimax‑optimal prediction risk for both scalar‑on‑function and function‑on‑function models. The study identifies distinct phase transitions in convergence behavior, with up to three transitions for function‑on‑function regression, and validates the approach through simulations and real data examples.