Research

    I use geometric and topological tools both within pure Math and in Computer Science. My main area of research is Machine Learning (statistical machine learning, topological data analysis) but I also work on certain problems in Contact/Symplectic Geometry as well as Computational Geometry. My focus in Machine Learning is its interaction with Neuroscience - understanding theoretical principles governing both artificial and biological learning, developing data-analytic tools for neuroscience data, and taking inspiration from biological learning to develop machine learning algorithms. Google Scholar entry.

Recent publications and preprints

  1. N. Denis, M. Fraser, Landmark Options Via Reflection (LOVR) in Multi-Task Lifelong Reinforcement Learning NIPS Hierarchical Reinforcement Learning Workshop (oral presentation and poster; non-proceedings pdf), December 2017.

  2. M. Fraser, L. Polterovich, D. Rosen, On Sandon-type metrics for contactomorphism groups. Ann. Math. Québec, 2017. online-doi. (arxiv version)

  3. M. Fraser, Contact non-squeezing at large scale in ℝ2n x S1. International Journal of Mathematics, (27)13, pp. 60-85, 2017. (arxiv version)

  4. M. Fraser, Multi-step learning and underlying structure in statistical models. NIPS 2016. (proceedings pdf)

  5. M. Fraser, Contact non-squeezing via generating functions: A low-tech proof in the language of persistence modules Poster in Summer School 2016 on Symplectic Topology, Sheaves and Mirror Symmetry, Paris IJM-PRG, 2016. (poster)

  6. M. Fraser, Contact spectral invariants and persistence, preprint 2015. (arxiv version)

  7. M. Fraser, Group Actions in Topological Data Analysis and Hierarchical Learning. PhD Thesis, Dept. of Computer Science, University of Chicago, August 2013.

  8. M. Fraser, Tight Linear Lower Memory Bound for Local Routing in Planar Digraphs. In Proceedings of Canadian Conference on Computational Geometry (CCCG12), August 2012. (proceedings pdf)

  9. M. Fraser, Persistent Homology of filtered covers. 2012. (arxiv version)

  10. M. Fraser, Local Routing in Graphs Embedded on Surfaces of Arbitrary Genus. 2012. (arxiv version)

  11. M. Fraser, Structural Observations on Neural Networks for Hierarchically Derived Reproducing Kernels. University of Chicago Master's thesis, November 2011. (revised version) (slides)

  12. M. Fraser, Two Extensions to Manifold Learning Algorithms Using α-Complexes. Dept. of Computer Science, University of Chicago, Technical Report TR-2010-07, 2010.
  13. A. Fraser, D. Fraser, M. Fraser, Curvature Revisited and the Bayes-Frequentist Divergence. In Journal of Statistical Research, Vol 44 number 2, 2010. (pdf)

  14. Y. Eliashberg and M. Fraser, Topologically Trivial Legendrian Knots. In Journal of Symplectic Geometry, Vol. 7, pp.77-127, 2009. (arxiv version)

  15. E. Chávez, M. Fraser and H. Tejeda, Proximal Labeling for Oblivious Routing in Wireless Ad Hoc Networks. In Proceedings of ADHOC-NOW 2009, Springer Verlag LNCS 5793, pp. 360-365.

  16. M. Fraser, E. Kranakis, J. Urrutia, Memory Requirements for Local Geometric Routing or Traversal in Digraphs. In Proceedings of Canadian Conference on Computational Geometry (CCCG08), August 2008. (proceedings pdf)

  17. M. Fraser, Local Routing on Tori (extended, invited version of next paper). In Ad Hoc and Sensor Wireless Networks, journal issue dedicated to ADHOC-NOW 2007, Vol. 6, pp. 179-196, 2008.

  18. M. Fraser, Local Routing on Tori. In proceedings of ADHOC-NOW 2007, Springer Verlag LNCS 4686, pp. 153-166, E. Kranakis and J. Opatrny (Eds.), Morelia, September 2007.

Teaching

  • MAT4376B/5314: Statistical Machine Learning
  • MAT1741: Algèbre linéaire
  • MAT3153: Introduction to Topology (using this textbook)

Previously at University of Toronto:
TA'ing at University of Chicago: