Publications
Submitted/Preprints
12. Mapping the geometry of heart rate data with J. Danciger, M. Costa, A. Goldberger, and G. Carlsson.
11. Principal Cumulant Component Analysis with L.-H. Lim.
Published
10. Relations among conditional probabilities. To appear in J. Symbolic Computation.
Some citations and discussion: Petrovic, Rinaldo, and Fienberg, Rinaldo, Petrovic, and Fienberg, Slavkovic, Zhu, and Petrovic.
9. Holographic algorithms without matchgates, with J.M. Landsberg and S. Norine. To appear in Linear Algebra and its Applications.
8. Geometry of the restricted Boltzmann machine with M. A. Cueto and B. Sturmfels. To appear in Algebraic Methods in Statistics and Probability, (eds. M. Viana and H. Wynn), American Mathematical Society, Contemporary Mathematics (2010).
7. Graphical models for correlated default, with I.O. Feliz, X.Guo, and B. Sturmfels. Mathematical Finance. doi:10.1111/j.1467-9965.2011.00499.x (2012). Slides from a talk, arXiv.
Some citations and discussion: Bayraktar and Yang , Evans and Hening.
6. Comparing pattern detection methods in microarray time series of the segmentation clock, with M. Dequeant, S. Ahnert, H. Edelsbrunner, T. Fink, E. Glynn, G. Hattem, A. Kudlicki, Y. Mileyko, A. Mushegian, L. Pachter, M. Rowicka, A. Shiu, B. Sturmfels, and O. Pourquie, PLoS ONE 3(8): e2856 doi:10.1371/journal.pone.0002856.
5. Convex rank tests and semigraphoids with L. Pachter, A. Shiu, B. Sturmfels, and O. Wienand, SIAM J. Discrete Math 23(3) 1117-1134, or here.
Some citations and discussion: Bruggemann and Patil, Derksen and Fink, Carr, Devadoss, and Forcey, Jiang, Lim, Yao, and Ye, Fink. The proof of the main theorem has recently been extended to general Coxeter groups and beyond by N. Reading.
4. The Cyclohedron test for finding periodic genes with L. Pachter, A. Shiu, and B. Sturmfels, Statistical Applications in Genetics and Molecular Biology 6 (2007) 1:21.
Some citations and discussion: Buck, Forcey and Springfield.
3. Three counterexamples on semigraphoids with R. Hemmecke, A. Shiu, B. Sturmfels and O. Wienand, Combinatorics, Probability and Computing 17 (2008) 239-257.
Some citations and discussion: Bruns, Hemmecke, Ichim, Koppe, and Soger, Kahle, Huber (forthcoming), Niepert.
2. Geometry of rank tests, with L. Pachter, A. Shiu, B. Sturmfels, and O. Wienand, in Proceedings of the Third European Workshop on Probabilistic Graphical Models, Prague, Czech Republic, September 2006.
Some citations and discussion: Postnikov, Reiner, and Williams, Billera, Jia, and Reiner, Devadoss, Agnarsson and Morris.
1. Equations defining hidden markov models, with N. Bray, Chapter 11 of Algebraic Statistics for Computational Biology, Lior Pachter and Bernd Sturmfels, ed.s. Cambridge University Press, 2005.
Our Conjecture 11.9 has reportedly been proved by Alexander Schoenhuth; see the paper.
Books and theses
Geometry of conditional independence, my dissertation.