I am currently interested in the following topics:

Logistic regression; uncertainty quantification for SMRs
Logistic regression is a standard way of risk adjustment. When the goal of the risk adjustment
model is not only to give an optimal prediction, but to assess the quality of performance, risk
factors have to be selected carefully, taking into account, on the one hand, expert knowledge
about the mechanisms underlying the risk and, on the other hand, the incentives that are set by
the evaluation method.
Once the risk adjustment model is fixed, standardized morbidity ratios (SMRs) can be computed.
How can one quantify stochastic variability of the SMR? How does one achieve a fair comparison of
SMRs when the case numbers vary considerably?

Markov bases
Together with Thomas Kahle I
maintain the Markov Bases Database. Among other things I
investigate how toric fiber products can be used to compute Markov bases of complicated models
from Markov bases of simpler models.
See arXiv:1404.6392 for recent progress.

Conditional Independence models and Robustness
CI models are sets of probability distribution with a wellunderstood probabilistic
interpretation. They can also be described by polynomial invariants. The corresponding ideals
are usually not radical, and they have interesting primary decompositions. Some of these models
are motivated by studies of robustness, initiated by the VW project
on Evolution of Networks.
See arXiv:1110.1338
and this article for examples.

Decomposing the mutual information
Different sources of information can contain the same (redundant) information or mutually
exclusive (unique) information. Furthermore, synergistic effects are possible, an effect that is
used in secret sharing and that arises, for example, with the XORfunction or with check sums. In
general, these three kinds of information (redundant, unique and synergistic information) can be
present at the same time, but mathematically it is not clear how to separate them.
This article proposes one way to
decompose the total mutual information, that two sources of information have with some target
variable.

Complex networks and random graphs
While working for the VW project on Evolution of Networks I became interested in models for random graphs and random
networks. In particular, I am working on better understanding graphons, as limits of finite
graphs, and exponential random graphs and their relationship.



Geometric Science of Information in Paris, November 7  9, 2017.

Statistische Woche in Rostock, September 19  22, 2017.

Workshop Topological and Geometrical Structures of Information at CIRM, Marseille, August 28September, 2017.

Workshop on Stochastic Models, Statistics and Their Applications at HU Berlin, February 2024, 2017.

Workshop on Partial Information Decompositions, FIAS, Frankfur,
December 2017.

AMS Sectional Meeting in Chicago, October 3  4, 2015 (invited talk).

Prague Stochastics, August 2529, 2014 (contributed talk).

Conference in Geometry and Statistics in Bath, June 23, 2014 (invited talk).

Algebraic Statistics 2014 at IIT, Chicago, May 1922, 2014 (contributed talk).

Workshop on
Exponential random network models at AIM, Palo Alto, June 17  21, 2013.

MEGA 2013 in Frankfurt, June 3
 7, 2013 (contributed talk).

Conceptual and
Mathematical Foundations of Embodied Intelligence in Leipzig, February 27  March 01, 2013.

Algebraic Statistics in
Europe at IST Austria, September 28  30, 2012 (invited talk).

WUPES '12 in Mariánské Lázně, September 12  15,
2012 (contributed talk).

Minischool on Concentration of Measures, organized by Fero Matúš at the UTIA, Prague, August 21 
23, 2012

Workshop on Graphical Models at the Fields Institute, Toronto, April 16  18, 2012
(invited talk).

Emerging Developments in Real Algebraic
Geometry in Magdeburg, February 20  24, 2012 (contributed talk).

Conference on Neural Information Processing
System (NIPS) in Granada, December 12  17, 2011 (contributed poster).

OberwolfachSeminar Affine Algebraic
Geometry and Group Actions, November 20  26, 2011.

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 67, 2010 (contributed poster).

International School on Combinatorics
“Pilar PisónCasares” 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,
August 2008 (contributed talk).

OberwolfachSeminar 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

 P. Kr. Banerjee, J. Rauh, G. Montúfar.
Computing the Unique Information.
Preprint: arXiv:1709.07487.
 N. Wang, J. Rauh, H. Massam.
Approximating faces of marginal polytopes in discrete hierarchical models.
Preprint: arXiv:1603.04843.
 J. Rauh, S. Sullivant
The Markov basis of K(3,N).
Preprint: arXiv:1406.5936.

F. Kohl, Y. Li, J. Rauh, R. Yoshida.
Semigroups  A Computational Approach.
Proceedings of the MSJ SI 2015, Eds Takayuki Hibi.

F. Mohammadi, J. Rauh.
Prime splittings of determinantal ideals.
Accepted at Communications in Algebra.

J. Rauh.
Secret Sharing and Shared Information.
Entropy 19 (11), 2017.
 G. Montúfar, J. Rauh.
Geometry of Policy Improvement.
Proceedings of Geometric Science of Information: Third International Conference 2017.

J. Rauh, P. Kr. Banerjee, E. Olbrich, E. Olbrich, J. Jost, N. Bertschinger, D. Wolpert.
CoarseGraining and the Blackwell Order.
Entropy 19 (10), 2017.

J. Rauh, P. Kr. Banerjee, E. Olbrich, E. Olbrich, J. Jost, N. Bertschinger.
On Extractable Shared Information.
Entropy 19 (7), 2017.
 G. Montúfar, J. Rauh
Hierarchical Models as Marginals of Hierarchical Models.
International Journal of Approximate Reasoning 88, 2017.
Preprint: arXiv:1508.03606.
 E. Czabarka, J. Rauh, K. Sadeghi, T. Short, L. Székely, László.
On the Number of Nonzero Elements of Joint Degree Vectors.
Electronic Journal of Combinatorics 24 (1), 2017.
Preprint: MIS Preprint 58/2012.
 J. Rauh.
The convex support of the kstar model.
Electronic Journal of Combinatorics 24 (1), 2017.
Preprint: MIS Preprint 58/2012.
 G. Montúfar, J. Rauh
Mode Poset Probability Polytopes.
Journal of Algebraic Statistics 7 (1), 2016.
Preprint: arXiv:1503.00572.
 K. GhaziZahedi, J. Rauh
Quantifying Morphological Computation Based on an
Information Decomposition of the Sensorimotor Loop.
Proceedings of the European Conference on Artificial Life 2015, p. 7077
Preprint: arXiv:1503.05113.
 J. Rauh, S. Sullivant.
Lifting Markov Bases and Higher Codimension Toric Fiber Products.
Journal of Symbolic Computation 74, p. 276307.
Preprint: arXiv:1404.6392.
 N. Bertschinger, J. Rauh.
The Blackwell relation deﬁnes no lattice.
Proceedings of ISIT 2014.
Preprint: arXiv:1401.3146.
 J. Rauh, N. Bertschinger, E. Olbrich, J. Jost.
Reconsidering unique information: Towards a multivariate information decomposition.
Proceedings of ISIT 2014.
Preprint: arXiv:1404.3146.
 T. Kahle, J. Rauh.
Toric fiber products versus Segre products.
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 84(2), p.187201 (2014).
Preprint: arXiv:1307.4029.

T. Kahle, J. Rauh, S. Sullivant.
Positive margins and primary decomposition.
Journal of Commutative Algebra 6(2), p.173208 (2014).
Preprint: arXiv:1201.2591.
 G. Montúfar, J. Rauh, N. Ay.
On the Fisher metric of conditional probability polytopes.
Entropy 16(6), p.32073233 (2014).
Preprint: arXiv:1404.0198.

G Montúfar, J. Rauh.
Scaling of model approximation errors and expected entropy distances.
Kybernetika 50 (2), p. 234–245 (2014).
Preprint: arXiv:1207.3399.

J. Rauh, N. Ay.
Robustness, Canalyzing Functions and Systems Design.
Theory in Biosciences 133 (2), p. 63–78 (2014).
Preprint: arXiv:1210.7719.
 N. Bertschinger, J. Rauh, E. Olbrich, J. Jost, N. Ay.
Quantifying unique information.
Entropy 16 (4), 2014, p. 2161–2183.
Preprint: arXiv:1404.3146.
 J. Rauh.
Optimally approximating exponential families.
Kybernetika Vol. 49, No. 2 (2013).
Preprint: MIS Preprint 73/2011.

J. Rauh.
Generalized binomial edge ideals.
Adv. Appl. Math. Vol. 50, Issue 3 (2013).
Preprint: arXiv:1210.7960.

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).
(Proceedings of WUPES'09).
Preprint: arxiv:0906.5462.

G. Boldhaus, N. Bertschinger, J. Rauh, E. Olbrich, K. Klemm.
Robustness of Boolean dynamics under knockouts.
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.

G. Montúfar, J. Rauh, N. Ay.
Maximal information divergence from statistical models defined by neural networks.
GSI 2013.
Preprint: MIS Preprint 31/2013

N. Bertschinger, J. Rauh, E. Olbrich, J. Jost.
Shared Information  New Insights and Problems in Decomposing Information
in Complex Systems.
Proceedings of ECCS 2012.
Preprint: arXiv:1210.5902.

F. Matús, J. Rauh.
Maximization of the information divergence from an exponential family and criticality.
Proceedings of ISIT 2011.
Preprint: arXiv:1210.5902.

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
