# Heteroscedastic Treed Bayesian Optimisation

arXiv: https://arxiv.org/abs/1410.7172 · HTML: https://mlsanity.com/paper/1410.7172/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Oct 2014.

## Built on by (most cited first, 9 of 9)

- [PFNs4BO: In-Context Learning for Bayesian Optimization](https://mlsanity.com/paper/2305.17535/) (2023)
- [Bayesian Optimization with Conformal Prediction Sets](https://mlsanity.com/paper/2210.12496/) (2022)
- [Efficient Robust Bayesian Optimization for Arbitrary Uncertain Inputs](https://mlsanity.com/paper/2310.20145/) (2023)
- [Optimal Online Generalized Linear Regression with Stochastic Noise and Its Application to Heteroscedastic Bandits](https://mlsanity.com/paper/2202.13603/) (2022)
- [Robust expected improvement for Bayesian optimization](https://mlsanity.com/paper/2302.08612/) (2023)
- [Predicting the utility of search spaces for black-box optimization: a simple, budget-aware approach](https://mlsanity.com/paper/2112.08250/) (2021)
- [Bayesian Optimization with Informative Covariance](https://mlsanity.com/paper/2208.02704/) (2022)
- [Searching in the Forest for Local Bayesian Optimization](https://mlsanity.com/paper/2111.05834/) (2021)
- [Applications of Gaussian Processes at Extreme Lengthscales: From Molecules to Black Holes](https://mlsanity.com/paper/2303.14291/) (2023)

## Abstract (arXiv)

Optimising black-box functions is important in many disciplines, such as tuning machine learning models, robotics, finance and mining exploration. Bayesian optimisation is a state-of-the-art technique for the global optimisation of black-box functions which are expensive to evaluate. At the core of this approach is a Gaussian process prior that captures our belief about the distribution over functions. However, in many cases a single Gaussian process is not flexible enough to capture non-stationarity in the objective function. Consequently, heteroscedasticity negatively affects performance of traditional Bayesian methods. In this paper, we propose a novel prior model with hierarchical parameter learning that tackles the problem of non-stationarity in Bayesian optimisation. Our results demonstrate substantial improvements in a wide range of applications, including automatic machine learning and mining exploration.