Advanced Probabilistic Modeling for Data Science

This graduate course develops the probabilistic foundations that underlie modern data science, with a strong emphasis on rigor, precision, and critical reasoning. The course is organized around two central themes: (1) high-dimensional probability and concentration phenomena, and (2) stochastic processes and their applications. Throughout the semester, theoretical results are complemented by examples from real-world applications, such as generative AI, population genomics, biological and ecological modeling, and random network analysis, illustrating how probabilistic principles shape contemporary data-driven methodologies.