A tutorial on Gaussian process regression: Modelling, exploring, and exploiting functions

By Eric Schulz, Maarten Speekenbrink, Andreas Krause. bioRxiv, 2016

1,566 citations recorded by the source corpus.

This tutorial introduces the reader to Gaussian process regression as an expressive tool to model, actively explore and exploit unknown functions. Gaussian process regression is a powerful, non-parametric Bayesian approach towards regression problems that can be utilized in exploration and exploitation scenarios. This tutorial aims to provide an accessible introduction to these techniques. We will introduce Gaussian processes which generate distributions over functions used for Bayesian non-parametric regression, and demonstrate their use in applications and didactic examples including simple regression problems, a demonstration of kernel-encoded prior assumptions and compositions, a pure exploration scenario within an optimal design framework, and a bandit-like exploration-exploitation scenario where the goal is to recommend movies. Beyond that, we describe a situation modelling risk-averse exploration in which an additional constraint (not to sample below a certain threshold) needs to be accounted for. Lastly, we summarize recent psychological experiments utilizing Gaussian processes. Software and literature pointers are also provided.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/e483dc8e7ffc4668851056e57efc553102d368a7

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Citations in the corpus

AutoSeM: Automatic Task Selection and Mixing in Multi-Task Learning (2019, background): “…Bayesian approach, and it can capture a wide variety of underlying functions or relations be-tween inputs and outputs by taking advantage of the full information provided by the history of observations and is thus very data-efﬁcient (Ras-mussen, 2004; Shahriari et al., 2016; Schulz et al., 2018).”
Data-driven health estimation and lifetime prediction of lithium-ion batteries: A review (2019, background): “The Gaussian process can be seen as a collection of a limited number of random variables which have a joint multivariate Gaussian distribution [140].”
Machine Learning for Reliability Engineering and Safety Applications: Review of Current Status and Future Opportunities (2020, methodology): “e response function estimation and uncertainty quantification [86], and they are increasingly used in engineering surrogate modeling and reliability analysis, [87, 88]. The reader is referred to Ref. [89] for more details on the GPR. 3.1.2 Classification Supervised classification is widely used in f”