Model fitting for small skin permeability data sets: hyperparameter optimisation in Gaussian Process Regression

Objectives
The aim of this study was to investigate how to improve predictions from Gaussian Process models by optimising the model hyperparameters.

Methods
Optimisation methods, including Grid Search, Conjugate Gradient, Random Search, Evolutionary Algorithm and Hyper-prior, were evaluated and applied to previously published data. Data sets were also altered in a structured manner to reduce their size, which retained the range, or ‘chemical space’ of the key descriptors to assess the effect of the data range on model quality.

Key findings
The Hyper-prior Smoothbox kernel results in the best models for the majority of data sets, and they exhibited significantly better performance than benchmark quantitative structure–permeability relationship (QSPR) models. When the data sets were systematically reduced in size, the different optimisation methods generally retained their statistical quality, whereas benchmark QSPR models performed poorly.

Conclusions
The design of the data set, and possibly also the approach to validation of the model, is critical in the development of improved models. The size of the data set, if carefully controlled, was not generally a significant factor for these models and that models of excellent statistical quality could be produced from substantially smaller data sets.