How Bayesian Should Bayesian Optimisation Be?

This is the author accepted manuscript. The final version is available from ACM via the DOI in this recordBayesian optimisation (BO) uses probabilistic surrogate models - usually Gaussian processes (GPs) - for the optimisation of expensive black-box functions. At each BO iteration, the GP hyperparameters are fit to previously-evaluated data by maximising the marginal likelihood. However, this fails to account for uncertainty in the hyperparameters themselves, leading to overconfident model predictions. This uncertainty can be accounted for by taking the Bayesian approach of marginalising out the model hyperparameters. We investigate whether a fully-Bayesian treatment of the Gaussian process hyperparameters in BO (FBBO) leads to improved optimisation performance. Since an analytic approach is intractable, we compare FBBO using three approximate inference schemes to the maximum likelihood approach, using the Expected Improvement (EI) and Upper Confidence Bound (UCB) acquisition functions paired with ARD and isotropic Matern kernels, across 15 well-known benchmark problems for 4 observational noise settings. FBBO using EI with an ARD kernel leads to the best performance in the noise-free setting, with much less difference between combinations of BO components when the noise is increased. FBBO leads to over-exploration with UCB, but is not detrimental with EI. Therefore, we recommend that FBBO using EI with an ARD kernel as the default choice for BO.Innovate U

Statistical and Stochastic Learning Algorithms for Distributed and Intelligent Systems

In the big data era, statistical and stochastic learning for distributed and intelligent systems focuses on enhancing and improving the robustness of learning models that have become pervasive and are being deployed for decision-making in real-life applications including general classification, prediction, and sparse sensing. The growing prospect of statistical learning approaches such as Linear Discriminant Analysis and distributed Learning being used (e.g., community sensing) has raised concerns around the robustness of algorithm design. Recent work on anomalies detection has shown that such Learning models can also succumb to the so-called \u27edge-cases\u27 where the real-life operational situation presents data that are not well-represented in the training data set. Such cases have been the primary reason for quite a few mis-classification bottleneck problems recently. Although initial research has begun to address scenarios with specific Learning models, there remains a significant knowledge gap regarding the detection and adaptation of learning models to \u27edge-cases\u27 and extreme ill-posed settings in the context of distributed and intelligent systems. With this motivation, this dissertation explores the complex in several typical applications and associated algorithms to detect and mitigate the uncertainty which will substantially reduce the risk in using statistical and stochastic learning algorithms for distributed and intelligent systems