Print Friendly printer friendly
 Events
UBC
Mon 1 Dec 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
The topological Fukaya category and mirror symmetry for toric Calabi-Yau threefolds
ESB 4127 (host: UBC)
Mon 1 Dec 2014, 3:00pm-4:00pm

Abstract

The Fukaya category of open symplectic manifolds is expected to have good local-to-global properties. Based on this idea several people have developed sheaf-theoretic models for the Fukaya category of punctured Riemann surfaces: the name topological Fukaya category appearing in the title refers to the (equivalent) constructions due to Dyckerhoff-Kapranov, Nadler and Sibilla-Treumann-Zaslow. In this talk I will introduce the topological Fukaya category and explain applications to Homological Mirror Symmetry for toric Calabi-Yau threefolds. This is work in progress joint with James Pascaleff.
hide
Eran Treister, Postdoctoral Fellow
EOAS, UBC
Tue 2 Dec 2014, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Large-scale sparse inverse covariance estimation
ESB 4133 (PIMS Lounge)
Tue 2 Dec 2014, 12:30pm-1:30pm

Abstract

The sparse inverse covariance estimation problem arises in many statistical applications in machine learning and signal processing. In this problem, the inverse of a covariance matrix of a multivariate normal distribution is estimated, assuming that it is sparse. An l-1 regularized log-determinant optimization problem is typically solved to approximate such matrices. Because of memory limitations, most existing algorithms are unable to handle large scale instances of this problem. 
 
In this talk we present two contributions. First, we present a new block-coordinate descent (BCD) approach for solving the problem for large-scale data sets. Our method treats the sought matrix block-by-block using quadratic approximations, and we show that this approach has advantages over existing methods in several aspects. Next, we present an iterative multilevel framework for accelerating the solution of general convex optimization problems with sparsity promoting l-1 regularization. Taking advantage of the typical sparseness of the solution, we create a multilevel hierarchy of similar problems, which are traversed back and forth in order to accelerate the optimization process. We demonstrate this framework for solving the sparse inverse covariance estimation problem.  Numerical experiments on both synthetic and real gene expression data sets demonstrate our BCD and multilevel approaches for solving both medium and large scale instances of this problem. 
 
Collaborators:
Javier Turek & Irad Yavneh, CS dept. Technion Israel Institute of Technology.
hide
 
Top