Information Geometry

Elementary statistics

Fisher Information

  • Fisher Information (28/8/08)
  • Natural gradient
  • Applications to neural networks
  • Application to ICA

Differential geometry

  • Elementary differential geometry
  • Riemannian Manifolds
  • Affine connections
  • Curvature

Information geometry

  • Geometry of statistical models (Amari Ch. 2)
  • Dual connections (Amari Ch. 3)
  • Statistical inference (Amari Ch. 4)
  • Linear systems (Amari Ch. 5)

Resources

Books

  • Yudi Pawitan (2001) In All Likelihood. Oxford Science.
  • R. E. Kass, P. W. Vos (1997) Geometrical Foundations of Asymptotic Inference, Wiley.
  • M. K. Murray, J. W. Rice (1993) Differential Geometry and Statistics. CRC Press.
  • S. Amari, H. Nagaoka (2000) Methods of Information Geometry, AMS Bookstore.
  • S. Amari (1987) Differential Geometry in Statistical Inference. IMS.
  • D. R. Cox, D. V. Hinkley, N. Reid, E. J. Snell (1991) Statistical Theory and Modelling. Chapman and Hall.
  • N. N. Cencov (1982) Statistical Decisions Rules and Optimal Inference. American Mathematical Society.
  • Khadiga Arwini, C.T.J. Dodson (2008) Information Geometry. Springer LNM. (appears 27/8/08)

-- MichaelH - 14 Aug 2008

Topic revision: r4 - 21 Aug 2008 - 10:55:53 - MichaelH
 
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