# Near-Optimal Active Learning of Multi-Output Gaussian Processes

arXiv: https://arxiv.org/abs/1511.06891 · HTML: https://mlsanity.com/paper/1511.06891/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2015.

## Built on by (most cited first, 10 of 10)

- [Safe Active Learning for Multi-Output Gaussian Processes](https://mlsanity.com/paper/2203.14849/) (2022)
- [Training-Free Neural Active Learning with Initialization-Robustness Guarantees](https://mlsanity.com/paper/2306.04454/) (2023)
- [ROOT: Rethinking Offline Optimization as Distributional Translation via Probabilistic Bridge](https://mlsanity.com/paper/2509.16300/) (2025)
- [Amortized Safe Active Learning for Real-Time Data Acquisition: Pretrained Neural Policies From Simulated Nonparametric Functions](https://mlsanity.com/paper/2501.15458/) (2025)
- [Convolutional Normalizing Flows for Deep Gaussian Processes](https://mlsanity.com/paper/2104.08472/) (2021)
- [Practical Privacy-Preserving Gaussian Process Regression via Secret Sharing](https://mlsanity.com/paper/2306.14498/) (2023)
- [Global Safe Sequential Learning via Efficient Knowledge Transfer](https://mlsanity.com/paper/2402.14402/) (2024)
- [Improved active output selection strategy for noisy environments](https://mlsanity.com/paper/2101.03499/) (2021)
- [Exact and general decoupled solutions of the LMC Multitask Gaussian Process model](https://mlsanity.com/paper/2310.12032/) (2023)
- [Novel Pivoted Cholesky Decompositions for Efficient Gaussian Process Inference](https://mlsanity.com/paper/2507.20678/) (2025)

## Abstract (arXiv)

This paper addresses the problem of active learning of a multi-output Gaussian process (MOGP) model representing multiple types of coexisting correlated environmental phenomena. In contrast to existing works, our active learning problem involves selecting not just the most informative sampling locations to be observed but also the types of measurements at each selected location for minimizing the predictive uncertainty (i.e., posterior joint entropy) of a target phenomenon of interest given a sampling budget. Unfortunately, such an entropy criterion scales poorly in the numbers of candidate sampling locations and selected observations when optimized. To resolve this issue, we first exploit a structure common to sparse MOGP models for deriving a novel active learning criterion. Then, we exploit a relaxed form of submodularity property of our new criterion for devising a polynomial-time approximation algorithm that guarantees a constant-factor approximation of that achieved by the optimal set of selected observations. Empirical evaluation on real-world datasets shows that our proposed approach outperforms existing algorithms for active learning of MOGP and single-output GP models.