EMG | Dr. Simon Pepin lehalleur | Singular learning theory I: Bayesian statistics

EMG | Dr. Simon Pepin lehalleur | Singular learning theory I: Bayesian statistics Speaker: Dr Simon Pepin lehalleur (Universiteit van Amsterdam) Date: 27th Mar 2024 - 14:00 to 15:00 Venue: INI Seminar Room 2 Title: Singular learning theory I: Bayesian statistics Event: (EMG) New equivariant methods in algebraic and differential geometry Abstract: The asymptotic performance of many statistical models is controlled byproperties of the singularities of certain associated real analyticfunctions. The goal of these two lectures is to give this idea aprecise mathematical form (due to Sumio Watanabe) in the context ofBayesian statistics, and to explain recent applications to theinterpretability problem of machine learning models. In the firstlecture, I will explain Watanabe's central results, which connect themain quantities of Bayesian statistical learning theory (posteriordistribution, free energy, generalization error) to the reallog-canonical threshold of the relative entropy between the model andthe data-generating process. This is a generalization of classicalresults like the Bernstein-Von Mises theorem, which require Fisherregularity assumptions not satisfied for typical machine learningmodels. I will start with a quick overview of Bayesian statistics andof real log-canonical thresholds. 👉 Want to learn more about the talks in this stream? Seminar Link:https://www.newton.ac.uk/seminar/42502/ Programme: https://www.newton.ac.uk/event/emg/ ------------------- FOLLOW US 🌐| Website: https://www.newton.ac.uk 🎥| Main Channel:    / @isaacnewtoninstitute   🐦| Twitter:   / newtoninstitute   💬| Facebook:   / newton.institute   📷| Instagram:   / isaacnewtoninstitute   🔗| LinkedIn:   / isaac-newton-institute-for-mathematical-sc...   SEMINAR ROOMS 🥇| INI Seminar Room 1:    / @iniseminarroom1   🥈| INI Seminar Room 2:    / @iniseminarroom2   🛰️| INI Satellite Events:    / @inisatellite   ABOUT The Isaac Newton Institute is a national and international visitor research institute. It runs research programmes on selected themes in mathematics and the mathematical sciences with applications over a wide range of science and technology. It attracts leading mathematical scientists from the UK and overseas to interact in research over an extended period. 👉 Learn more about us and our events here: https://www.newton.ac.uk