This is an extension of the Fellowship 'New challenges in high-dimensional statistical inference' (EP/J017213/1). The project will involve developing methodology and theory for a range of modern statistical problems from high-dimensional and nonparametric statistical inference. Such problems lie at the heart of modern data science, an area where the UK urgently needs to grow its capacity. Specific challenges to be addressed include the development of methods for dimension reduction, variable selection and uncertainty quantification, among several others. These are some of the fundamental problems faced by practitioners in the Big Data era, and demand highly innovative solutions. Our proposed techniques will be proven to be robust via appropriate theoretical justification, and will be implemented in free, open source software so as to maximise the impact of the research.