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ICASSP
2009
IEEE

Maximum-likelihood estimation of autoregressive models with conditional independence constraints

10 years 4 months ago
Maximum-likelihood estimation of autoregressive models with conditional independence constraints
We propose a convex optimization method for maximum likelihood estimation of autoregressive models, subject to conditional independence constraints. This problem is an extension to times series of the classical covariance selection problem in graphical modeling. The conditional independence constraints impose quadratic equalities on the autoregressive model parameters, which makes the maximum likelihood estimation problem nonconvex and difficult to solve. We formulate a convex relaxation and prove that it is exact when the sample covariance matrix is block-Toeplitz. We also observe experimentally that in practice the relaxation is exact under much weaker conditions. We discuss applications to topology selection in graphical models of time series, by enumerating all possible topologies, and ranking them using information-theoretic model selection criteria. The method is illustrated by an example of air pollution data.
Jitkomut Songsiri, Joachim Dahl, Lieven Vandenberg
Added 21 May 2010
Updated 21 May 2010
Type Conference
Year 2009
Where ICASSP
Authors Jitkomut Songsiri, Joachim Dahl, Lieven Vandenberghe
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