# Active Learning of Linear Embeddings for Gaussian Processes

arXiv: https://arxiv.org/abs/1310.6740 · HTML: https://mlsanity.com/paper/1310.6740/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2013.

## Built on by (most cited first, 30 of 34)

- [High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspaces](https://mlsanity.com/paper/2103.00349/) (2021)
- [Vanilla Bayesian Optimization Performs Great in High Dimensions](https://mlsanity.com/paper/2402.02229/) (2024)
- [Local Latent Space Bayesian Optimization over Structured Inputs](https://mlsanity.com/paper/2201.11872/) (2022)
- [High-Dimensional Bayesian Optimisation with Variational Autoencoders and Deep Metric Learning](https://mlsanity.com/paper/2106.03609/) (2021)
- [LassoBench: A High-Dimensional Hyperparameter Optimization Benchmark Suite for Lasso](https://mlsanity.com/paper/2111.02790/) (2021)
- [SMT 2.0: A Surrogate Modeling Toolbox with a focus on Hierarchical and Mixed Variables Gaussian Processes](https://mlsanity.com/paper/2305.13998/) (2023)
- [Bayesian Optimization over High-Dimensional Combinatorial Spaces via Dictionary-based Embeddings](https://mlsanity.com/paper/2303.01774/) (2023)
- [A survey and benchmark of high-dimensional Bayesian optimization of discrete sequences](https://mlsanity.com/paper/2406.04739/) (2024)
- [Safe Active Learning for Multi-Output Gaussian Processes](https://mlsanity.com/paper/2203.14849/) (2022)
- [Posterior Inference with Diffusion Models for High-dimensional Black-box Optimization](https://mlsanity.com/paper/2502.16824/) (2025)
- [Scalable Gaussian-process regression and variable selection using Vecchia approximations](https://mlsanity.com/paper/2202.12981/) (2022)
- [High-dimensional mixed-categorical Gaussian processes with application to multidisciplinary design optimization for a green aircraft](https://mlsanity.com/paper/2311.06130/) (2023)
- ["Noisier" Noise Contrastive Eestimation is (Almost) Maximum Likelihood](https://mlsanity.com/paper/2405.16730/) (2024)
- [Bayesian optimization for mixed variables using an adaptive dimension reduction process: applications to aircraft design](https://mlsanity.com/paper/2504.08682/) (2025)
- [Towards Universal Offline Black-Box Optimization via Learning Language Model Embeddings](https://mlsanity.com/paper/2506.07109/) (2025)
- [Global optimization using random embeddings](https://mlsanity.com/paper/2107.12102/) (2021)
- [High-dimensional Bayesian Optimization via Covariance Matrix Adaptation Strategy](https://mlsanity.com/paper/2402.03104/) (2024)
- [Sensitivity Prewarping for Local Surrogate Modeling](https://mlsanity.com/paper/2101.06296/) (2021)
- [Hierarchical-Hyperplane Kernels for Actively Learning Gaussian Process Models of Nonstationary Systems](https://mlsanity.com/paper/2303.10022/) (2023)
- [Active Cost-aware Labeling of Streaming Data](https://mlsanity.com/paper/2304.06808/) (2023)
- [Bayesian Optimization with Informative Covariance](https://mlsanity.com/paper/2208.02704/) (2022)
- [Leveraging Axis-Aligned Subspaces for High-Dimensional Bayesian Optimization with Group Testing](https://mlsanity.com/paper/2504.06111/) (2025)
- [Enhancing Trust-Region Bayesian Optimization via Newton Methods](https://mlsanity.com/paper/2508.18423/) (2025)
- [Informed Initialization for Bayesian Optimization and Active Learning](https://mlsanity.com/paper/2510.23681/) (2025)
- [Linear Embedding-based High-dimensional Batch Bayesian Optimization without Reconstruction Mappings](https://mlsanity.com/paper/2211.00947/) (2022)
- [Combining additivity and active subspaces for high-dimensional Gaussian process modeling](https://mlsanity.com/paper/2402.03809/) (2024)
- [Global Optimisation of Black-Box Functions with Generative Models in the Wasserstein Space](https://mlsanity.com/paper/2407.11917/) (2024)
- [Safe Active Learning for Gaussian Differential Equations](https://mlsanity.com/paper/2412.09053/) (2024)
- [Amortized Active Learning for Nonparametric Functions](https://mlsanity.com/paper/2407.17992/) (2024)
- [Sample-Constrained Black Box Optimization for Audio Personalization](https://mlsanity.com/paper/2507.12773/) (2025)

## Abstract (arXiv)

We propose an active learning method for discovering low-dimensional structure in high-dimensional Gaussian process (GP) tasks. Such problems are increasingly frequent and important, but have hitherto presented severe practical difficulties. We further introduce a novel technique for approximately marginalizing GP hyperparameters, yielding marginal predictions robust to hyperparameter mis-specification. Our method offers an efficient means of performing GP regression, quadrature, or Bayesian optimization in high-dimensional spaces.