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A generalized Levinson algorithm for covariance extension with application to multiscale autoregressive modeling

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3 Author(s)
A. B. Frakt ; Health Services Res. & Evaluation, Abt Assoc. Inc., Cambridge, MA, USA ; H. Lev-Ari ; A. S. Willsky

Efficient computation of extensions of banded, partially known covariance matrices is provided by the classical Levinson algorithm. One contribution of this paper is the introduction of a generalization of this algorithm that is applicable to a substantially broader class of extension problems. This generalized algorithm can compute unknown covariance elements in any order that satisfies certain graph-theoretic properties, which we describe. This flexibility, which is not provided by the classical Levinson algorithm, is then harnessed in a second contribution of this paper, the identification of a multiscale autoregressive (MAR) model for the maximum-entropy (ME) extension of a banded, partially known covariance matrix. The computational complexity of MAR model identification is an order of magnitude below that of explicitly computing a full covariance extension and is comparable to that required to build a standard autoregressive (AR) model using the classical Levinson algorithm.

Published in:

IEEE Transactions on Information Theory  (Volume:49 ,  Issue: 2 )