Singular Learning Theory - Bayesian Statistics and Real Log-Canonical Thresholds - Part 1

Explore a comprehensive lecture on singular learning theory and its applications in Bayesian statistics, delivered by Dr. Simon Pepin lehalleur from the Universiteit van Amsterdam. Delve into the mathematical foundations of how singularities in real analytic functions influence statistical model performance. Learn about Watanabe's groundbreaking findings connecting Bayesian statistical learning theory elements - including posterior distribution, free energy, and generalization error - to the real log-canonical threshold of relative entropy between model and data-generating process. Understand how these concepts extend beyond classical results like the Bernstein-Von Mises theorem, particularly in their application to machine learning models. Begin with foundational concepts in Bayesian statistics and real log-canonical thresholds before exploring their deeper connections to modern statistical learning challenges and model interpretability.