Geometric structures for statistical models

• Fisher-Rao manifolds: 2403.10089, 2302.08175
• Hilbert/Birkhoff geometry:
  • Simplex domain (categorical distributions): 2203.11434
  • Elliptope domain (correlation matrices): 1704.00454
  • Symmetric positive-definite cone (SPDs, MVNs): 2307.10644
  • Siegel domain, complex domain including SPD: 2004.08160
• Bregman manifolds:
  • Dual geometry of convex conjugate functions: 1910.03935
  • Applications to mixture families (Jensen-Shannon centroid): 1912.00610
  • Applications to exponential families (Chernoff information): 2207.03745 2207.03745
• Dual statistical structures:
  • PDF "The many faces of information geometry." Not. Am. Math. Soc 69.1 (2022): 36-45.
  • PDF "An elementary introduction to information geometry." Entropy 22.10 (2020): 1100.
• Semi-Riemannian structures (stochastic NNs, singularities): 1905.11027