Reading Seminar on Algebraic Geometry and Singular Learning Theory


Friday, 10:00 - 12:00

Room: FR 6046


Dr. Franz Király, 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.


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.


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.


The topic list refers to the book Algebraic Geometry and Statistical Learning Theory, by Sumio Watanabe.



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


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

IDA Wiki: Main/WS12_AGSLT (last edited 2013-02-04 12:21:03 by FranzKiraly)