Johannes Rauh

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 well-understood 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 XOR-function 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.

Workshops and Schools


  • 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.
Journal articles
  • 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. Coarse-Graining 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 Non-zero Elements of Joint Degree Vectors. Electronic Journal of Combinatorics 24 (1), 2017. Preprint: MIS Preprint 58/2012.
  • J. Rauh. The convex support of the k-star 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. Ghazi-Zahedi, J. Rauh Quantifying Morphological Computation Based on an Information Decomposition of the Sensorimotor Loop. Proceedings of the European Conference on Artificial Life 2015, p. 70-77 Preprint: arXiv:1503.05113.
  • J. Rauh, S. Sullivant. Lifting Markov Bases and Higher Codimension Toric Fiber Products. Journal of Symbolic Computation 74, p. 276-307. 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.187-201 (2014). Preprint: arXiv:1307.4029.
  • T. Kahle, J. Rauh, S. Sullivant. Positive margins and primary decomposition. Journal of Commutative Algebra 6(2), p.173-208 (2014). Preprint: arXiv:1201.2591.
  • G. Montúfar, J. Rauh, N. Ay. On the Fisher metric of conditional probability polytopes. Entropy 16(6), p.3207-3233 (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.
Conference Contributions
  • 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

Privacy and Legal
J.Rauh,  Version vom: 19.10.2015