Jose Israel Rodriguez
jo dot ro at ND dot edu
University of Notre Dame, Department of Applied and Computational Mathematics and Statistics,
Advisors and Mentors
Research and Writings
The maximum likelihood degree of rank 2 matrices via Euler characteristics. Preprint. We use Euler characteristics to prove an outstanding conjecture by Hauenstein, the first author, and Sturmfels; we prove a closed form expression for the ML degree of 3 by n rank 2 matrices. More broadly, we show how these techniques give a recursive expression for the ML degree of m by n rank 2 matrices.
Critical points via monodromy and local methods. Submitted. We use the numerical algebraic geometry tool of monodromy and local methods to compute critical points of the likelihood function and Euclidean distance function.
Data discriminants of likelihood equations. To appear in the ISSAC'15. We develop an algebraic probability 1 algorithm for computing data discriminants. Experimental results show that, for the benchmarks we have tried, the algebraic probability 1 algorithm is more efficient than the standard elimination algorithm. Based on the computational results, we propose the real root classification conjecture for the 3 by 3 symmetric matrix model.
Maximum likelihood for dual varieties. SNC '14 Proceedings of the 2014 Symposium on Symbolic-Numeric Computation (2014) Pages 43-49. MLE for statistical models with discrete data is studied from an algebraic statistics viewpoint. A reformulation of the MLE problem in terms of dual varieties and conormal varieties is given.
Maximum likelihood geometry in the presence of data zeros. ISSAC '14 Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation (2014) Pages 232-239. We consider discrete algebraic statistical models and study the solutions to the likelihood equations when the data contain zeros. We give new lower bounds for Maximum Likelihood degreesBertini for Macaulay2. Submitted. Numerical algebraic geometry is the field of computational mathematics concerning the numerical solution of polynomial systems of equations. Bertini, a popular software package for computational applications of this field, includes implementations of a variety of algorithms based on polynomial homotopy continuation. The Macaulay2 package Bertini.m2 provides an interface to Bertini. Maximum Likelihood Duality for Determinantal Varieties. Int Math Res Notices (2014) 2014(20): 5648-5666.
We prove that the maximum-likelihood degree of the variety of rank-r matrices equals that of the variety of co-rank (r-1)-matrices; and also establish variants for symmetric and skew-symmetric matrices. Maximum Likelihood for Matrices with Rank Constraints. Journal of Algebraic Statistics 5 (2014) 18-38. We use numerical algebraic geometry to find maximum likelihood degrees of determinantal varieties and show these techniques can be useful for statisticians.
Combinatorial Excess Intersection. Journal of Symbolic Computation 68 (2015) 297-307.
A novel method for the solution of the forward displacement problem of spherical parallel manipulators.
ZAMM Z. Angew. Math. Mech. 93 (2013), no. 1, 73-82.
Bounding The Degree of Belyi Polynomials. J. Number Theory vol. 133 (2013), no. 9, 2892-2900.
In May 2014 I graduated from UC Berkeley with a PhD in mathematics. My thesis is titled Numerical algebraic geometry for maximum likelihood estimation, and my advisor was Bernd Sturmfels. Last summer I was in Korea, participating in the 2014 NIMS thematic program on applied algebraic geometry. Now, I am an NSF postdoc working with Jonathan Hauenstein at Notre Dame. My interests are in applied algebraic geometry and algebraic statistics. In particular, I am interested in solving systems of polynomial equations numerically.Here is a link to a talk at the Simons Institute about my thesis work: Link.
My Future and Recent Whereabouts Mathematics Colloquium: December 1, 2014 UT Dallas.
Top Com Seminar: January 7, 2015 Freie Universität Berlin.
Algebraic Geometry and Number Theory Seminar: February 3, 2015 Rice University, Houston.
Algebraic Geometry/Commutative Algebra Seminar: February 25, 2015 University of Notre Dame.
Algebraic Geometry Seminar: March 13, 2015 University of Wisconsin-Madison.
Algebra, Geometry, and Combinatorics Seminar: May 1, 2015 UIUC.
GOAL workshop: May 18-19, 2015 University of California, Berkeley.
UC Berkeley Commencement: May 22-23, 2015 University of California, Berkeley.
Tropical Doener Workshop: May 27-28, 2015 Freie Universität Berlin, Germany.
Workshop on Non-Linear Algebra: May 29-30, 2015 in Berlin, Germany.
GAeL XXIII: June 1-5, 2015 KU Leuven, Belgium.
Algebraic Statistics 2015: June 8-11, 2015 in Genoa, Italy.
MEGA 2015: Effective Methods in Algebraic Geometry: June 15-19, 2015 at The University of Trento, Povo (Trento), Italy.
Theory and applications of syzygies: July 1-3, 2015 Universität des Saarlandes, Saarbrücken, Germany. (Tentative)
ISSAC 2015: July 7-9, 2015 The University of Bath, Bath, UK.
SWAAG: July 13-17, 2015 NIMS, Daejeon, Korea.
AMS Sectional Meeting: Algebraic statistics and its interactions with combinatorics, computation, and network science session: October 3-4, 2015 Loyola University Chicago, Chicago, IL.
Workshop on Algebra, Geometry and Proofs in Symbolic: December 6-13, 2015 The Fields Institute-Toronto, Canada.
Books I like Numerically Solving Polynomial Systems with Bertini
Teaching and Mentoring Sections of Math 1B with Professor Serganova (Fall 2013): Techniques of integration; applications of integration. Infinite sequences and series. First-order ordinary differential equations. Second-order ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations. Sections of Math 1B with Professor Christ (Spring 2013): Techniques of integration; applications of integration. Infinite sequences and series. First-order ordinary differential equations. Second-order ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations. Berkeley Science Network The UC Berkeley McNair Scholars Program University of Notre Dame ACMS Department Events
Invited Talks and Seminars - (December 2015) Workshop on Algebra, Geometry and Proofs in Symbolic Computation, The Fields Institute-Toronto, Canada.
- (August 2015) SIAM Conference on Applied Algebraic Geometry Mini-symposium: Maximum Likelihood Degrees and Critical Points Mini-Symposium, National Institute for Mathematical Sciences-Daejeon, South Korea.
- (August 2015) SIAM Conference on Applied Algebraic Geometry Mini-symposium:Group actions in algebraic geometry and commutative algebra , National Institute for Mathematical Sciences-Daejeon, South Korea.
- (July 2015) Seminar Week on Applied Algebraic Geometry , National Institute for Mathematical Sciences-Daejeon, South Korea.
- (June 2015) Algebraic Statistics, Genoa, Italy.
- (June 2015) Algebra and Geometry Seminar, University in Leuven, Belgium.
- (May 2015) GOAL Workshop, University of California, Berkeley.
- (May 2015) Algebra, Geometry, and Combinatorics Seminar, University of Illinois at Urbana–Champaign.
- (March 2015) Algebraic Geometry Seminar, University of Wisconsin-Madison.
- (February 2015) Algebraic Geometry/Commutative Algebra Seminar, University of Notre Dame.
- (February 2015) Algebraic Geometry and Number Theory Seminar, Rice University.
- (January 2015) Topology and Combinatorics Seminar, Freie Universität Berlin.
- (December 2014) Colloquium, University of Texas at Dallas.
- (October 2014) Algebraic Statistics Special Section, AMS Fall Western Sectional Meeting.
- (October 2014) Computational Algebraic Geometry and Applications in Science and Engineering Special Section, AMS Fall Western Sectional Meeting, SS17A.
- (October 2014) Solving Polynomial Equations Conference, Simons Institute, Berkeley, California.
- (August 2014) ICMS 2014 Session: Software for Numerical Algebraic Geometry, Hanyang University, Seoul, Korea.
- (July 2014) Symbolic Numeric Computation 2014, East China Normal University, Shanghai, China.
- (July 2014) International Symposium on Symbolic and Algebraic Computation 2014, Kobe, Japan.
- (June 2014) Algebraic Geometry Seminar, Korea Institute for Advanced Study, Seoul, Korea.
- (June 2014) Optimization and Algebraic Geometry, NIMS at Daejeon, South Korea.
- (May 2014) Applied Algebra Days 2, University of Madison at Wisconsin.
- (April 2014) Tropical April, University of California at Berkeley.
- (April 2014) Algebraic Statistics Seminar, Illinois Institute of Technology.
- (March 2014) Algebraic Statistics Seminar, University of California at Berkeley.
- (August 2013) Symbolic Computation Seminar, North Carolina State University.
- (August 2013) Algebra Seminar, Georgia Institute of Technology, Atlanta.
- (August 2013) SIAM Conference of Applied Algebraic Geometry , Colorado State University.
- (July 2013) Computational Algebra Seminar, Max Planck Institute for Mathematics, Bonn.
- (July 2013) Algebra Seminar, Universitat des Saarlandes.
- (July 2013) Discrete Mathematics Seminar, Goethe-Universitat.
- (July 2013) Algebra Seminar, Universitat Konstanz.
- (June 2013) Effective Methods in Algebraic Geometry, Goethe-Universitat.
- (April 2013) Graduate Student Combinatorics Conference, University of Minnesota, Twin Cities.
- (March 2013) Math/ICES Center of Numerical Analysis Seminar, University of Texas at Austin.
- (March 2013) Colloquium, Sam Houston State University.
- (March 2013) AVID Program Seminar, Grand Prairie High School.
- (March 2013) SIAM Student Chapter Seminar, Texas Tech University.
- (March 2013) Colloquium, Southern Methodist University.
- (March 2013) Algebraic Statistics Workshop, University of California at Berkeley.
- (March 2013) AGC Seminar, San Francisco State University.
- (March 2013) Algebra and Discrete Mathematics, University of California at Davis.
- (February 2013) SIAM Student Chapter Seminar, University of California at Berkeley.
- (February 2013) FRAGMENT Seminar, Colorado State University.
- (February 2013) Colloquium, University of Colorado at Boulder.
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