On Computing Jeffrey's Divergence Between Time-Varying Autoregressive Models

Autoregressive (AR) and time-varying AR (TVAR) models are widely used in various applications, from speech processing to biomedical signal analysis. Various dissimilarity measures such as the Itakura divergence have been proposed to compare two AR models. However, they do not take into account the v...

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Bibliographic Details
Published in:IEEE signal processing letters 2015-07, Vol.22 (7), p.915-919
Main Authors: Magnant, Clement, Giremus, Audrey, Grivel, Eric
Format: Article
Language:English
Subjects:
Analogies
Analytical models
Asymptotic properties
Autoregressive process
Autoregressive processes
Biological system modeling
Biomedical measurement
Computation
Computational modeling
Computer Science
Divergence
Gaussian
Itakura divergence
Jeffrey's divergence
Joints
Mathematical model
Mathematical models
Signal and Image Processing
Speech processing
time-varying autoregressive process
Vectors
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Summary:Autoregressive (AR) and time-varying AR (TVAR) models are widely used in various applications, from speech processing to biomedical signal analysis. Various dissimilarity measures such as the Itakura divergence have been proposed to compare two AR models. However, they do not take into account the variances of the driving processes and only apply to stationary processes. More generally, the comparison between Gaussian processes is based on the Kullback-Leibler (KL) divergence but only asymptotic expressions are classically used. In this letter, we suggest analyzing the similarities of two TVAR models, sample after sample, by recursively computing the Jeffrey's divergence between the joint distributions of the successive values of each TVAR model. Then, we show that, under some assumptions, this divergence tends to the Itakura divergence in the stationary case.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2014.2377473