Jacobs University Bremen
Campus Ring 12
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.