Abstract

This presentation delves into the latest developments in non-parametric statistics, starting with modeling in Euclidean spaces. We will explore dimension reduction through regularization methods, supported by theoretical analysis and a genome-wide association study. Building on this, we extend our focus to the application of non-parametric statistics in various geometric spaces, including BHV spaces (phylogenetic tree spaces) and Riemannian manifolds, which offer promising insights in biological research. The presentation includes motivational examples from real-world applications, demonstrating the proposed methodologies' effectiveness and precision in addressing complex statistical challenges across multiple domains. Additionally, we will discuss the challenges involved in analyzing complex data.