Advancing Static and Time-Series Data Analysis: Random Matrix Theory, Causal Inference, and Mathematical Modeling

Abstract

In this talk, I will explore advanced methodologies for extracting meaningful insights from both static and time-series data. For static datasets, Principal Component Analysis (PCA) is a standard tool for identifying signals amidst noise. However, selecting the number of significant components often involves subjective judgment. I will introduce a principled approach based on Random Matrix Theory that enables objective determination of the optimal number of signals. For time-series data, causal inference techniques—such as Granger causality—are frequently applied, but they tend to suffer from high false-positive rates. I will present a novel, mathematical model-based framework for causal inference that robustly identifies underlying network structures, from molecular systems to climate dynamics. Finally, I will discuss how mathematical modeling can be applied to real-world time-series data, highlighting an example using wearable device data. In particular, I will showcase a math+AI algorithm developed to generate personalized sleep schedules, which has been implemented as a mobile application and will soon be globally serviced in collaboration with a major mobile phone company.