Reading Seminar on Algebraic Geometry and Singular Learning Theory
Time: 
Friday, 10:00  12:00 
Room: FR 6046 

Organizers: 
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
Singular Learning Theory is the study of singular parametric estimation, where naive application of classical learning and model selection methods like MaxLikelihood, 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 Algebraic Geometry and Statistical Learning Theory, by 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. Foundations of Algebraic Geometry