I am interested in the geometry of statistical models arising in statistical learning theory, computational biology, and finance.
8. Relations among conditional probabilities. In preparation.
7. Graphical models for credit default, with I.O. Feliz, X.Guo, and B. Sturmfels. In preparation.
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, Submitted to PLoS Genetics.
5. 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.
4. Convex rank tests and semigraphoids with L. Pachter, A. Shiu, B. Sturmfels, and O. Wienand. Submitted to SIAM J DIscrete Math.
3. Three counterexamples on semigraphoids with R. Hemmecke, A. Shiu, B. Sturmfels and O. Wienand, 16 pp., to appear in Combinatorics, Probability and Computing.
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.
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.
See the supplementary material and software for 2,3,4, and 5.
Relations among conditional probabilities, AMS Special Session on Combinatorial Enumeration, Optimization, Geometry, and Statistics at the Murfreesboro, Tennessee meeting, 11/03/07.
Schur modules in algebraic statistics, U.C. Berkeley Special Algebraic Statistics Seminar, 7/2/07.
How to Write Down Polynomials I and II (on using Schur-Weyl Duality to decompose ideals), Special Geometry Seminar at Texas A&M, 6/4/07 and 6/6/07.
Geometry of Rank Tests, poster at IMA session on Applications of Algebraic Geometry (Applications in Biology, Dynamics, and Statistics), 3/5/07.
The Toric Geometry of Conditional Probability, U. C. Berkeley Student Algebraic Statistics Seminar, 11/13/06.
Semigraphoids and the Permutohedron, MIT Combinatorics Seminar, 10/6/06
Geometry of Rank Tests, Texas A&M Algebra and Combinatorics Seminar, 9/29/06
Geometry of Rank Tests, Third European Workshop on Probabilistic Graphical Models, Prague 9/14/06
Rank Tests for Microarray Data, Duke Systems Biology Seminar, 8/31/06
Geometry of Rank Tests, MSRI Summer Graduate Workshop on Mathematical aspects of computational biology, 6/27/06
Co-organizer (with J.M. Landsberg and Lek-Heng Lim) of an MSRI Graduate Workshop (July 7-19, 2008): Geometry and Representation Theory of Tensors for Computer Science, Statistics, and other areas. The workshop will be based around Computational complexity and algebraic statistics via geometry and representation theory, a draft book by J.M. Landsberg and myself. This is in part a lead up to the following AIM conference.
Co-organizer (with J.M. Landsberg, Lek-Heng Lim, and Jerzy Weyman) of an AIM Conference (July 21-26, 2008): Geometry and representation theory of tensors for computer science, statistics and other areas. The goal of this workshop is to implement advanced techniques from geometry and representation theory to problems in several areas of research. Each of the problems relates to varieties in spaces of tensors. The areas include: computational complexity, statistical learning theory, signal processing, and scientific data analysis. The main goal of the workshop is getting researchers in very different areas, working on problems with similar underlying mathematics, to share knowledge and work together to advance projects.
"Geometric Aspects of Conditional Independence and Information" at the Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany, 13-14 March 2008.
European Science Foundation (ESF) Exploratory Workshop: Multivariate Interpolation - Its Relation To Algebraic Statistics, Classical Algebraic Geometry And Computational Complexity Theory, Sestri Levante, Italy, 16 - 19 October 2007.