https://mp.weixin.qq.com/s/CZOqCD9WoqebVikkBb6A_Ahttps://ymsc.tsinghua.edu.cn/info/1050/2855.htm
短期课程报名：信息几何引论
YMSC 清华大学丘成桐数学科学中心 2022-06-28 15:38 发表于北京
短期课程
Introduction to Information Geometry
Speaker
Jun Zhang 张俊
密歇根大学
图片
Jun Zhang, PhD, is Professor of Mathematics, Statistics, and Psychology in the College of Literature, Science, and the Arts at the University of Michigan, Ann Arbor. Prof. Zhang develops algebraic and geometric methods for data analysis.His interests include mathematical psychology and computational neuroscience, broadly defined to include neural network theory and reinforcement learning, dynamical analysis of nervous system (single neuron activity and event-related potential), computational vision, choice-reaction time model, Bayesian decision theory and game theory.
# Time
July 4 – August 1, 2022, Mondays/Fridays, 8:30-10:00am (Lectures), Wednesdays 9:00-10:00pm (Practicum/Project)
# Venue
Zoom Meeting ID: 999 8991 2497 Passcode: YMSC (Mon/Fri only)
# Abstract
This short course will give a comprehensive introduction to the emerging interdisciplinary field of Information Geometry. Information Geometry provides a differential geometric characterization of probability models. Starting with the concept of divergence functions (such as Kullback-Leibler divergence and Bregman divergence), a manifold of the probability functions is constructed with Fisher information as the Riemannian metric and a family of affine connections with dualistic structures. The course explains dually-flat (“Hessian”) geometry of exponential family, with e- and m-projections, for maximum entropy inference, and their generalizations. The course also presents several new research directions, including deformation theory, which constructs a conformal Hessian structure based on deforming the exponential/logarithm function, and the link of information geometry to optimal transport, which is another framework for the manifold of probability measures and both are used in machine learning, neural network, statistical inference, signal processing, optimization, etc.
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