Computational Information Geometry Wonderland

In 2005, I released a book on visual computing:

The book has been used for teaching in several universities. For example

• Cardiff U, UK
• Salzburg U, Austria
• Beira Interior U, Portugal
• Electro-Communications U, Japan
• Polytechnic Madrid U, Spain
• MPI, Germany
• Braunschweig University of Technology, Germany
• Ecole Polytechnique, France
• etc...

See the table of contents
It contains a set of 50 source codes in C++: source codes in C++.
Nowadays, I am more Java(TM) and Processing oriented, and I am refreshing many of the demos. Stay tuned...

Recently, I have been engrossed in coding and postponed blogging. However, today I received my complimentary copy of the book entitled Connected at Infinity II. Here are pictures of the front and back cover pages.

The chapter on Cramer-Rao Lower Bound and Information Geometry is also available here.

@incollection{CRIG-2013,
  author      = {Frank Nielsen},
  title       = {Cram\'er-Rao Lower Bound and Information Geometry},
  page              = {18-37},
  editor      = {Rajendra Bhatia and C. S. Rajan and Ajit Iqbal Singh},
  booktitle   = {Connected at Infinity {II}: A selection of mathematics by {I}ndians},
  publisher   = {Hindustan Book Agency (Texts and Readings in Mathematics, TRIM)},
  note          = {arxiv 1301.3578}
  year        = {2013},
  url                   = {http://www.hindbook.com/}
}

For some reasons, the book price in France dropped significanly. A mere 10 dollars, compared to the US 50 dollars price!!! You are welcome to check this

• Amazon FR
• Amazon US

I am teaching this course now at Master 1 level:
Visual Computing
The book home page is here.

Students shall do an internship from April to August 2011, so feel free to send proposal if you would like to host one of them.

Frank.

Recently, there have been a few books introducing information geometry and applications. They are all worth reading and present different vantage points.

• Algebraic and Geometric Methods in Statistics is a collective edited book that shows information geometry alive with new research directions.

• Algebraic Geometry and Statistical Learning Theory : You first get your hands on the statistical manifold of a 2-mixture of Gaussians, and realize it has singularities (degenerate Fisher information). How to proceed then? The book investigates the singularities and show how to elegantly tackle them through Hironaka blow-up techniques.

• Information Geometry: Near Randomness and Near Independence: This book investigates the alpha-geometry theory and provides application chapters. It is well illustrated and applications range from bioinfo to galaxy distributions.

• The geometry of Hessian structures: It is the english translation of a former book published in japanese (2001). It investigates the Codazzi equation to define Hessian structures. Relationships with Kahler manifolds are explicited. Again, very well-written, and information geometry is explained as an application of the more general formalism.

... and here are the bibtex entries for those books:

@book{hessianstructure-2007,
      author       = "Shima , Hirohiko",
      title        = "The geometry of Hessian structures",
      publisher    = "World Scientific",
      year         = "2007",
}
    
    
@book{infogeo-2008,
      author       = " Khadiga Arwini and C T J Dodson",
      title        = " Information Geometry: Near Randomness and Near Independence ",
      publisher    = "Lecture Notes in Mathematics 1953",
      year         = "2008",
}

@book{alginfogeo-2009,
      author       = "Gibilisco, Paolo and Riccomagno, Eva and Rogantin, Maria Piera and Wynn, Henry P",
      title        = "Algebraic and Geometric Methods in Statistics",
      publisher    = "Cambridge Univ. Press",
      address      = "Leiden",
      year         = "2009",
}

@book{singularinfogeo-2009,
 author = {Watanabe, Sumio},
 title = {Algebraic Geometry and Statistical Learning Theory},
 year = {2009},
 isbn = {0521864674, 9780521864671},
 publisher = {Cambridge University Press}
 }

Happy readings, Frank.