== Reading Seminar on Algebraic Geometry and Singular Learning Theory ==

||<|2> '''Time:''' ||Friday, 10:00 - 12:00 ||
|| '''Room:''' FR 6046 ||
|| '''Organizers:''' || [[http://www.ml.tu-berlin.de/menue/mitglieder/franz_kiraly/|Dr. Franz Király]], [[http://www-irm.mathematik.hu-berlin.de/~larsen/|Dr. Paul Larsen]] ||

=== Summary ===

[[http://watanabe-www.math.dis.titech.ac.jp/users/swatanab/singular-learning-theory.html|Singular Learning Theory]] is the study of singular parametric estimation, where naive application of classical learning and model selection methods like Max-Likelihood, Bayes Learning, AIC or BIC fails. As virtually all meaningful and practically relevant learning machines like Neural Networks, Mixture Models, Hidden Markov Models or Boltzmann Machines are singular, the analysis of their singular properties is of high practical relevance. Sumio Watanabe has developed generalizations of Bayes Learning Theory and Bayes Model Selection for the singular case; the aim of this seminar is the study of his work and its ramifications.

=== Prerequisites ===

Knowledge in Algebraic Geometry, Singularity Theory, Parametric Statistics and Bayes Estimation Theory is useful, but not necessary; all relevant basics will be discussed in the course.


=== Schedule ===
The topic list refers to the book
[[http://watanabe-www.math.dis.titech.ac.jp/users/swatanab/ag-slt.html|Algebraic Geometry and Statistical Learning Theory]], by [[http://watanabe-www.math.dis.titech.ac.jp/users/swatanab/index.html|Sumio Watanabe]].

|| '''Date''' || '''Topic''' || '''Discussion leader''' ||
|| 20 April 2012 || Organizatorial Meeting and Overview on Singular Learning || Duncan Blythe and Paul Larsen ||
|| 11 May 2012 || Chapter 1: Learning Theory and Singular Parametric Models || Franz Király ||
|| 18 May 2012 || No Seminar ||  ||
|| 25 May 2012 || Chapter 1: Singular Examples, Learning and Generalization Error || Franz Király ||
|| 1 June 2012 || Chapter 1: Evidence and the Bayes quartet || Paul Larsen ||
|| 8 June 2012 || No Seminar ||  ||
|| 15 June 2012 || Chapter 1: The Zeta Function || Duncan Blythe ||
|| 22 June 2012 || Algebraic Geometry Basics ||  ||