Colloquium Mathematics - Prof. M. Bollhoefer
|When:||Th 14-02-2019 15:00 - 16:00|
The estimation of large sparse inverse covariance matrices is an
ubiquitous statistical problem in many application areas such as
mathematical finance or geology or many others. Numerical approaches
typically rely on the maximum likelihood estimation or its negative
log-likelihood function. When the Gaussian mean random field is
expected to be sparse, regularization techniques which add a sparsity
prior have become popular to address this issue. Recently a quadratic
approximate inverse covariance method (QUIC)  has been proposed.
The hallmark of this method is its superlinear to quadratic convergence
which makes this algorithm to be among the most competitive methods.
In this talk we present a sparse version (SQUIC)  of this method
and we will demonstrate that using advanced sparse matrix technology
the sparse version of QUIC is easily able to deal with problems of
size one million within a few minutes on modern multicore computers.
 C.J. Hsieh, M.A. Sustik, I.S. Dhillon, and P.K. Ravikumar.
Sparse inverse covariance matrix estimation using quadratic approximation,
in Advances in Neural Information Processing Systems, J. Shawe-Taylor,
R. Zemel, P. Bartlett, F. Pereira, and K. Weinberger, eds., vol. 24, Neural
Information Processing Systems Foundation, 2011, pp. 2330-2338.
 M. Bollhoefer, A. Eftekhari, S. Scheidegger, and O. Schenk. Large-Scale
Sparse Inverse Covariance Matrix Estimation. SIAM J. Sci. Comput., to appear
This is joined work with O.Schenk, A. Eftekhari (USI Lugano) and S. Scheidegger (EPFL Lausanne).