I am currently interested in the following topics:

• Complex networks and random graphs

  As part of the VW project on Evoluation of Networks I investigate models for random graphs and random networks. In particular, I am interested in graphons, as limits of finite graphs, and exponential random graphs.

• Markov bases

  Together with Thomas Kahle I maintain the Markov Bases Database.

• Conditional Independence models and Robustness

  I'm interested in CI models, their algebraic descriptions and primary decompositions. Some of these models are motivated by studies of robustness, initiated by the VW project on Evoluation of Networks. See this preprint for examples.

• Algebraic Statistical Models and Exponential Families

  Many statistical models have an algebraic structure that can be exploited in statistics and information theory. For some examples see this article in IJAR and my thesis.

• Information Geometry: Maximizing the Information Divergence

  Probability distributions that maximize the information divergence from an exponential family have peculiar properties. Studying this maximization problem was the main subject of my thesis. See the group homepage and my thesis for more information.

Workshops and Schools

• SIAM Conference on Applied Algebraic Geometry in Raleigh, NC, October 6 - 9, 2011 (contributed talk).
• IEEE International Symposium on Information Theory in St. Petersburg, July 31 - August 5, 2011 (contributed talk).
• Combinatorial Methods in Algebraic Geometry and Commutative Algebra in Leipzig, July 5 - 7, 2011
• Spring School on Limits of finite graphs in Leipzig, April 26 - 30, 2011
• Workshop on Geometric and Algebraic Statistics 3 at the University of Warwick, April 5 - 7, 2011 (contributed talk).
• COSA Workshop in Munich, March 14 - 15, 2011
• Summer School in Algorithmic Mathematics in Berlin, August 16 - 20, 2010
• Information Geometry and its Applications III in Leipzig, August 2 - 06, 2010 (contributed talk and poster).
• Quantum Information and Quantum Entanglement in Leipzig, July 16 - 17, 2010
• Minischool on Quantum Information Theory and Quantum Computing, organized by Arleta Szkoła and myself, in Leipzig, May 31 - June 02, 2010.
• Workshop on Geometric and Algebraic Statistics 2 at the University of Warwick, April 6-7, 2010 (contributed poster).
• International School on Combinatorics “Pilar Pisón-Casares” in Sevilla, January 2010 (contributed talk).
• WUPES ’09 in Liblice, September 2009 (contributed talk).
• 32nd Autumn School in Algebraic Geometry on “Algebraic Torus Actions” in Łukęcin, September 2009
• Minischool on Oriented Matroids, organized by Fero Matúš at the UTIA, Prague, May 25 - 26, 2009
• Model Selection Days in Berlin, Leipzig, Magdeburg, Prague, 2008 and 2009
• Workshop on Algebraic Statistics at the MSRI, December 2008
• Workshop on Polytopes and Algebraic Statistics at KTH Stockholm (organized by Alexander Engström and Thomas Kahle, August 2008 (contributed talk).
• Oberwolfach-Seminar Algebraic Statistics, May 2008
• International School on Neural Nets “E.R. Caianiello” in Erice, December 2007
• Buildings 2007 in Münster, Oktober 2007 (contributed talk).
• Buildings and Groups in Ghent, May 2007

Publications

Preprints

• J. Rauh, Optimally approximating exponential families. Preprint: MIS Preprint 73/2011
• J. Rauh, N. Ay, Robustness and Conditional Independence Ideals. Preprint: arXiv:1110.1338

Journal articles

• J. Rauh. Finding the Maximizers of the Information Divergence from an Exponential Family. IEEE Trans. Inf. Theory Vol. 57, No. 6 (2011). Preprint: arXiv:0912.4660.
• J. Rauh, T. Kahle, N. Ay. Support Sets in Exponential Families and Oriented Matroid Theory. Int. J. Approx. Reas. Vol 52, Issue 5 (2011), Workshop on Uncertainty Processing (WUPES'09). Preprint: arxiv:0906.5462.
• G. Boldhaus, N. Bertschinger, J. Rauh, E. Olbrich, K. Klemm. Knockouts, Robustness and Cell Cycles. Phys. Rev. E 82, 021916 (2010). Preprint: arXiv:1003.0104.
• J. Herzog, T. Hibi, F. Hreinsdóttir, T. Kahle, J. Rauh. Binomial Edge Ideals and Conditional Independence Statements. Adv. Appl. Math. Vol. 45, Issue 3 (2010). Preprint: arxiv:0909.4717.

Conference Contributions

• N. Ay, G. Montúfar, J. Rauh, Selection Criteria for Neuromanifolds of Stochastic Dynamics. ICCN 2011. Preprint: MIS Preprint 15/2011
• G. Montúfar, J. Rauh, N. Ay, Expressive Power and Approximation Errors of Restricted Boltzmann Machines. NIPS 2011. Preprint: MIS Preprint 27/2011

Other

• J. Rauh, Maximizing the Information Divergence from an Exponential Family, dissertation, University of Leipzig.