Achieving Robustness to Aleatoric Uncertainty with Heteroscedastic Bayesian Optimisation

Abstract

Bayesian optimisation is an important decision-making tool for high-stakes applications in drug discovery and materials design. An oft-overlooked modelling consideration however is the representation of input-dependent or heteroscedastic aleatoric uncertainty. The cost of misrepresenting this uncertainty as being homoscedastic could be high in drug discovery applications where neglecting heteroscedasticity in high throughput virtual screening could lead to a failed drug discovery program. In this paper, we propose a heteroscedastic Bayesian optimisation scheme which both represents and penalises aleatoric noise in the suggestions. Our scheme features a heteroscedastic Gaussian Process (GP) as the surrogate model in conjunction with two acquisition heuristics. First, we extend the augmented expected improvement (AEI) heuristic to the heteroscedastic setting and second, we introduce a new acquisition function, aleatoric-penalised expected improvement (ANPEI) based on a simple scalarisation of the performance and noise objective. Both methods penalise aleatoric noise in the suggestions and yield improved performance relative to a naive implementation of homoscedastic Bayesian optimisation on toy problems as well as a real-world optimisation problem.

Modeling the Multiwavelength Variability of Mrk 335 Using Gaussian Processes

“…Gaussian processes confer a Bayesian nonparametric framework to model general time-series data (Roberts et al 2013;Tobar et al 2015) and have proven effective in tasks such as periodicity detection (Durrande et al 2016) and spectral density estimation (Tobar 2018). More broadly, Gaussian processes (GPs) have recently demonstrated modeling success across a wide range of spatial and temporal application domains including robotics (Deisenroth & Rasmussen 2011;Greeff & Schoellig 2020), Bayesian optimization (Shahriari et al 2015;Grosnit et al 2020;Cowen-Rivers et al 2021;Grosnit et al 2021), as well as areas of the natural sciences such as molecular machine learning (Nigam et al 2021;Griffiths & Hernández-Lobato 2020;Moss & Griffiths 2020;Thawani et al 2020;Griffiths et al 2021;Hase et al 2020, Bartók et al 2010, genetics , and materials science (Cheng et al 2020;Zhang et al 2020). In the context of astrophysics there is a recent trend favoring nonparametric models such as GPs due to the flexibility afforded when specifying the underlying data modeling assumptions.…”

HEBO: An Empirical Study of Assumptions in Bayesian Optimisation

“…For instance, a homoscedastic GP suffers from misspecification when required to model data with heteroscedastic noise whilst stationary GPs fail to track non-stationary targets. The aforementioned shortcomings are not unnatural across a range of real-world problems (Kersting et al, 2007;Griffiths et al, 2021aGriffiths et al, , 2021b and hyper-parameter tuning of machine learning algorithms is no exception, as illustrated in our hypothesis tests of Section 3.2. Hence, even if one succeeds in improving computational efficiency, frequently-made assumptions such as homoscedasticity and stationarity can easily inhibit the performance of any BO-based hyper-parameter tuning algorithm.…”

“…Heteroscedasticity with output transforms: Among various approaches to handling heteroscedasticity (Kersting et al, 2007;Lázaro-Gredilla & Titsias, 2011;Kuindersma et al, 2013;Calandra, 2017;Griffiths et al, 2021a), transforming the output variables is a straightforward option giving rise to warped Gaussian processes (Snelson et al, 2004). More recently, output transformations have been extended to compositions of elementary functions (Rios & Tobar, 2019) and normalising flows (Rezende & Mohamed, 2015;Maronas et al, 2020).…”

High-Dimensional Bayesian Optimisation with Variational Autoencoders and Deep Metric Learning

“…1. Molecule and Materials Discovery: Bayesian optimisation methodologies hold great promise for accelerating the discovery of molecules and materials [80,81,82,83,84,85]. That being said, the societal effects of novel molecules and materials may range from decreased mortality due to a more diverse set of active drug molecules to a broader array of chemical and biological weapons.…”