Veranstalter: Graduiertenschule Computational Engineering
Referent: Prof. Dr. Matthias Bollhöfer
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., 41(1), A380-A401, 2019.