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Michael Thon, PhD Student of Computer Science

Picture of Michael Thon


Jacobs University Bremen
Campus Ring 12
28759 Bremen

Office: Research I, Room 81



Research and Interests

As a mathematician by training, I am currently working in the field of machine learning. Concretely, I am investigating observable operator models (OOM) and their learning algorithms. These are models for stochastic processes that generalize hidden Markov models (HMM). My main contributions to the field are:

  • Showing that OOMs, as well as the related input-output OOMs (IO-OOM) and predictive state representations (PSR), are all special cases of multiplicity automata.
  • Using this to formulate a spectral learning framework for these models that unifies many of the known learning algorithms.
  • Introducing weights into the estimation procedure to further improve the statistical efficiency.
  • A spectral learning algorithm for OOMs that can deal with missing values.
  • tom, a C++/Python toolkit for observable operator modeling.

Apart from this, I have also worked with echo state networks, especially using control inputs to the network in order to control or stabilize certain features of the generated signal.

Furthermore, I have been involved in teaching Mathematics to talented high school students through the clubs Mathematik in Bremen! and Talentförderung Mathematik, and have taught three one-week intensive workshops on "Mathematical logic and Gödel's theorem", "Cryptography", as well as "Mathematics and Magic" as part of previous Bremen summer academies.

Previously, I have also worked on holomorphic dynamics, combinatorial game theory and computational geometry (map labeling).

Awards and Competitions

  • 11th/230 and 19th/261 places at the ICFP 72 h team programming contests, 2004 and 2006
  • 15th place at the ACM NWERC team programming contest, 2003
  • Fellowship of the Studienstiftung des Deutschen Volkes 2000-2005
  • Final round "Bundeswettbewerb Mathematik" German national Mathematics competition, 1998
  • 3rd prizes German national Mathematics Olympiads, 1997 and 1998
  • 2nd place "Baltic Way" international Mathematics team competition, 1997


  • M. Thon, H. Jaeger (2015): Links between multiplicity automata, observable operator models and predictive state representations — a unified learning framework. Journal of Machine Learning Research 16, 103-147 (pdf)
  • M. Zhao, H. Jaeger, M. Thon (2009): Making The Error Controlling Algorithm of Observable Operator Models Constructive. Neural Computation 22(12), 3460-3486 (Preprint pdf)
  • M. Zhao, H. Jaeger, M. Thon (2009): A Bound on Modeling Error in Observable Operator Models and an Associated Learning Algorithm. Neural Computation 21(9), 2687-2712 (Preprint pdf)
  • M. Thon (2009): Ein einfacher Kartentrick und erstaunlich viel Mathematik. In: Schiemann, S. (ed.), Talentförderung Mathematik: Ein Tagungsband anlässlich des 25-jährigen Jubiläums der Schülerförderung. LIT Verlag Münster, 99-113
  • M. Thon (2008): Input-Output OOMs. Technical report 16, Jacobs University Bremen, Germany (pdf)
  • K. Bach, K. Hanig, T. Hoffmann, W. Kresse, J. Löcherbach, P. Rosenthal, S. Rudnick, P. Schreiber, M. Thon, A. Wolff (2002): Beschriftungsalgorithmen in Theorie & Praxis. Institut für Mathematik und Informatik, Universität Greifswald
  • A. Wolff, M. Thon, Y. Xu (2002): A simple factor-2/3 approximation algorithm for two-circle point labeling. International Journal of Computational Geometry and Applications 12 (4), 269-281 (pdf)
  • M. Thon, A. Wolff, Y. Xu (2000): Ein neuer Algorithmus zur Beschriftung von Punkten mit je zwei Kreisen. In: Gesellschaft für Informatik e.V. (ed.), Tagungsband der Informatiktage, Bad Schussenried. 
  • A. Wolff, M. Thon, Y. Xu (2000): A better lower bound for two-circle point labeling. Proceedings of the 11th International Symposium on Algorithms and Computation (ISAAC), 422-431 (pdf)

Talks and Conferences

  • 2014: Academic visit to the Computational Molecular Biology group, FU Berlin, Germany, where I assisted applying OOMs to molecular dynamics modeling.
  • 2013: NIPS, Workshop on Spectral Learning, Lake Tahoe, USA. Talk: Weighted Spectral Learning and the Efficiency Sharpening algorithm.
  • 2009, 2010, 2011: Interdisciplinary College, Günne at Lake Möhne, Germany. Poster (2011):
    Observable operator models don’t need to hide from hidden Markov models.
  • 2009: Workshop on Reinforcement Learning, McGill University (Canada), Barbados. Talk: OOMs, PSRs, S-MAs and a statistically efficient learning algorithm.
  • 2008: 25th Anniversary "Talentförderung Mathematik e.V.", University of Hannover, Germany. Talk: A simple card trick and amazing mathematics.
  • 2006: Workshop on Ergodic Theory and Dynamical Systems, Wroclaw University, Poland.
  • 2006: Workshop on Discrete Probability, Erwin Schrödinger Institute, Vienna, Austria.
  • 2004: Workshop on Holomorphic Dynamics, University of Warwick, UK. Talk: Hausdorff dimension of escaping points of transcendental entire functions.
  • 2000, 2001, 2004: Summer Academies of the Studienstiftung des Deutschen Volkes, Olang and La Villa, Italy; Rot a.d. Rot, Germany. Topics: Models of Reality, Combinatorial Game Theory, Quantum Information Theory.
  • 2002: Summer School on Computational Algebraic Geometry, Emi-Noether-Institute, Israel
  • 2000: Fall School of the European Graduate Program "Combinatorics, Geometry and Computation" on Bioinformatics, FU Berlin, Germany.
  • 2000: Informatiktage, Bad Schussenried, Germany. Talk: A new algorithm for two-circle point labeling.