In the past decade there has been a massive increase in the volume of biological sequence data, driven by massively parallel sequencing technologies. This has enabled data-driven statistical analyses using non-parametric predictive models (including those from machine learning) to complement more traditional, hypothesis-driven approaches. This thesis addresses several challenges that arise when applying non-parametric predictive models to biological sequence data.

Some of these challenges arise due to the nature of the biological system of interest. For example, in the study of the human microbiome the phylogenetic relationships between microorganisms are often ignored in statistical analyses. This thesis outlines a novel approach to modelling phylogenetic similarity using string kernels and demonstrates its utility in the two-sample test and host-trait prediction.

Other challenges arise from limitations in our understanding of the models themselves. For example, calculating variable importance (a key task in biomedical applications) is not possible for many models. This thesis describes a novel extension of an existing approach to compute importance scores for grouped variables in a Bayesian neural network. It also explores the behaviour of random forest classifiers when applied to microbial datasets, with a focus on the robustness of the biological findings under different modelling assumptions.