== 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]] ||

'''A first organizatorial meeting will be held on October 19, in room FR6048, where topics and schedule will be discussed. The first seminar will take place on October 26.'''

=== 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 ===

A participant should have basic knowledge of Commutative Algebra, Statistics and Probability Theory.
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''' ||
|| 19 October 2012 || Brief Organizatorial Meeting '''in FR6048''' || Paul Larsen and Franz Király ||
|| 26 October 2012 || Introduction into Algebraic Geometry (Chapter I of Cox) || Cevahir Demirkiran  ||
|| 02 November 2012 || Introduction into Algebraic Geometry (Chapter IV of Cox) || Cevahir Demirkiran ||
|| 09 November 2012 || Examples in Algebraic Geometry and Singular Learning Theory || Franz Király ||
|| 16 November 2012 || Local Study of Varieties; Tangent Space, Singularities || Cevahir Demirkiran ||
|| 23 November 2012 || Resolution of Singularities || Cevahir Demirkiran ||
|| 30 November 2012 || Mixture Models || Paul Larsen ||
|| 07 December 2012 || No course || Paul Larsen ||
|| 14 December 2012 || No course ||  ||
|| 21 December 2012 || No course ||  ||
|| 11 January 2013 || No course ||  ||
|| 18 January 2013 || No course ||  ||
|| 25 January 2013 || No course ||  ||
|| 01 February 2013 || Graphical Models || Paul Larsen ||
|| 08 February 2013 || Main Theorems || Robert Koppisch ||


=== Literature ===

Sumio Watanabe. Algebraic Geometry and Statistical Learning Theory. Cambridge University Press, 2009. 

David Cox, John Little, Donal O'Shea. Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra. Springer, 2006.

Ravi Vakil. [[http://math.stanford.edu/~vakil/216blog/|Foundations of Algebraic Geometry]]