S2. Information Geometry and Deformed Statistics

Special Session organized by J. Zhang and H. Matsuzoe

Information geometry provides a suite of differential geometric tools for studying statistical inference, information theory, and machine learning models. Key notions such as statistical manifolds (with Fisher information as to its Riemannian metric), Hessian geometry, biorthogonal coordinates have links to statistical mechanics, thermodynamics, geometric mechanics, etc. As sequel to the special session (organized by Johnston, Matsuzoe, Ruppeiner, and Wada) at SigmaPhi2017, this Session at SigmaPhi2020 will explore differential geometric characterizations of probabilistic models arising from a variety of setting including stochastic thermodynamics, condensed matter physics, cosmology and high-energy physics, etc. Of particular interest are deformed statistical models, models which deviate from exponential family through parameterization (e.g., kappa-exponential model, q-exponential model, Renyi model) and their associated deformed entropy, cross-entropy, and divergences. The Session will also welcome contributions from related disciplines of statistical machine learning, dynamics and control, optimal transport and Wasserstein geometry, etc.