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Predictive Information Rate in Discrete-time Gaussian Processes

Abdallah, SA and Plumbley, MD (2012) Predictive Information Rate in Discrete-time Gaussian Processes Technical Report. arXiv.

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Abstract

We derive expressions for the predicitive information rate (PIR) for the class of autoregressive Gaussian processes AR(N), both in terms of the prediction coefficients and in terms of the power spectral density. The latter result suggests a duality between the PIR and the multi-information rate for processes with mutually inverse power spectra (i.e. with poles and zeros of the transfer function exchanged). We investigate the behaviour of the PIR in relation to the multi-information rate for some simple examples, which suggest, somewhat counter-intuitively, that the PIR is maximised for very `smooth' AR processes whose power spectra have multiple poles at zero frequency. We also obtain results for moving average Gaussian processes which are consistent with the duality conjectured earlier. One consequence of this is that the PIR is unbounded for MA(N) processes.

Item Type: Monograph (Technical Report)
Divisions : Faculty of Engineering and Physical Sciences > Electronic Engineering > Centre for Vision Speech and Signal Processing
Authors :
AuthorsEmailORCID
Abdallah, SAUNSPECIFIEDUNSPECIFIED
Plumbley, MDUNSPECIFIEDUNSPECIFIED
Date : 1 June 2012
Uncontrolled Keywords : stat.ML, stat.ML, math.ST, stat.TH
Related URLs :
Additional Information : This is an arXiv publication.
Depositing User : Symplectic Elements
Date Deposited : 27 Jan 2016 14:32
Last Modified : 27 Jan 2016 14:32
URI: http://epubs.surrey.ac.uk/id/eprint/809732

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