# Derivation of Output Correlation Inferences for Multi-Output (aka Multi-Task) Gaussian Process

arXiv: https://arxiv.org/abs/2501.07964 · HTML: https://mlsanity.com/paper/2501.07964/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 42 references that are in the map.
- First posted on arXiv 14 Jan 2025.

## Builds on (most cited first, 19 of 19)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [BOHB: Robust and Efficient Hyperparameter Optimization at Scale](https://mlsanity.com/paper/1807.01774/) (2018)
- [SMAC3: A Versatile Bayesian Optimization Package for Hyperparameter Optimization](https://mlsanity.com/paper/2109.09831/) (2021)
- [Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2006.05078/) (2020)
- [Tree-Structured Parzen Estimator: Understanding Its Algorithm Components and Their Roles for Better Empirical Performance](https://mlsanity.com/paper/2304.11127/) (2023)
- [Efficiently Sampling Functions from Gaussian Process Posteriors](https://mlsanity.com/paper/2002.09309/) (2020)
- [Multi-fidelity Bayesian Optimisation with Continuous Approximations](https://mlsanity.com/paper/1703.06240/) (2017)
- [Bayesian Optimization with Unknown Constraints](https://mlsanity.com/paper/1403.5607/) (2014)
- [Multi-Objective Bayesian Optimization over High-Dimensional Search Spaces](https://mlsanity.com/paper/2109.10964/) (2021)
- [Scalable Constrained Bayesian Optimization](https://mlsanity.com/paper/2002.08526/) (2020)
- [A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1811.00755/) (2018)
- [Scalable Log Determinants for Gaussian Process Kernel Learning](https://mlsanity.com/paper/1711.03481/) (2017)
- [Bayesian Optimization with High-Dimensional Outputs](https://mlsanity.com/paper/2106.12997/) (2021)
- [Multi-fidelity Gaussian Process Bandit Optimisation](https://mlsanity.com/paper/1603.06288/) (2016)
- [Practical Transfer Learning for Bayesian Optimization](https://mlsanity.com/paper/1802.02219/) (2018)
- [Supervising the Multi-Fidelity Race of Hyperparameter Configurations](https://mlsanity.com/paper/2202.09774/) (2022)
- [Scaling Gaussian Processes for Learning Curve Prediction via Latent Kronecker Structure](https://mlsanity.com/paper/2410.09239/) (2024)
- [c-TPE: Tree-structured Parzen Estimator with Inequality Constraints for Expensive Hyperparameter Optimization](https://mlsanity.com/paper/2211.14411/) (2022)
- [Speeding Up Multi-Objective Hyperparameter Optimization by Task Similarity-Based Meta-Learning for the Tree-Structured Parzen Estimator](https://mlsanity.com/paper/2212.06751/) (2022)

## Built on by (most cited first, 1 of 1)

- [From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems](https://mlsanity.com/paper/2506.15906/) (2025)

## Abstract (arXiv)

Gaussian process (GP) is arguably one of the most widely used machine learning algorithms in practice. One of its prominent applications is Bayesian optimization (BO). Although the vanilla GP itself is already a powerful tool for BO, it is often beneficial to be able to consider the dependencies of multiple outputs. To do so, Multi-task GP (MTGP) is formulated, but it is not trivial to fully understand the derivations of its formulations and their gradients from the previous literature. This paper serves friendly derivations of the MTGP formulations and their gradients.