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 CalabiYau threefolds

ESB 4127 (host: UBC)
Mon 1 Dec 2014, 3:00pm4:00pm
Abstract
The Fukaya category of open symplectic manifolds is expected to have good localtoglobal properties. Based on this idea several people have developed sheaftheoretic 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 DyckerhoffKapranov, Nadler and SibillaTreumannZaslow. In this talk I will introduce the topological Fukaya category and explain applications to Homological Mirror Symmetry for toric CalabiYau threefolds. This is work in progress joint with James Pascaleff.
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Eran Treister, Postdoctoral Fellow
EOAS, UBC

Tue 2 Dec 2014, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

Largescale sparse inverse covariance estimation

ESB 4133 (PIMS Lounge)
Tue 2 Dec 2014, 12:30pm1:30pm
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 l1 regularized logdeterminant 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 blockcoordinate descent (BCD) approach for solving the problem for largescale data sets. Our method treats the sought matrix blockbyblock 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 l1 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.
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