Colloquium Mathematics - Prof. Matthias Bollhoefer

Datum 14 February 2019, 15.00 - 16.00
Lokatie 5173.0176 Linnaeusborg

Title: Large-Scale Sparse Inverse Covariance Matrix Estimation

Abstract: 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) [1] 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) [2] 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.


[1] 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.


[2] 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).



Organisator Rijksuniversiteit Groningen (email)
Geplaatst door Bernoulli Secretariaat