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A Global Gradient Noise Covariance Expression for Stationary Real Gaussian Inputs

An, P.E., Brown, M. and Harris, C.J. (1995) A Global Gradient Noise Covariance Expression for Stationary Real Gaussian Inputs IEEE Trans. on Neural Networks, 6, (6)

Record type: Article

Abstract

Supervised parameter adaptation in many artificial neural networks is largely based on an instantaneous version of gradient descent called the Least-Mean-Square (LMS) algorithm. As the gradient is estimated using single samples of the input ensemble, its convergence properties generally deviate significantly from that of the true gradient descent because of the noise in the gradient estimate. It is thus important to study the gradient noise characteristics so that the convergence of the LMS algorithm can be analyzed from a new perspective. This paper considers only neural models which are linear with respect to their adaptable parameters, and has two major contributions. Firstly, it derives an expression for the gradient noise covariance under the assumption that the input samples are real, stationary, Gaussian distributed but can be partially correlated. This expression relates the gradient correlation and input correlation matrices to the gradient noise covariance, and explains why the gradient noise generally correlates maximally with the steepest principal axis and minimally with the one of the smallest curvature, regardless of the magnitude of the weight error. Secondly, a recursive expression for the weight error correlation matrix is derived in a straightforward manner using the gradient noise covariance, and comparisons are drawn with the complex LMS algorithm.

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More information

Published date: 1995
Additional Information: accepted for publication
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 250282
URI: http://eprints.soton.ac.uk/id/eprint/250282
PURE UUID: 87d7d06d-7b40-450b-979e-6d710033f65c

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Date deposited: 04 May 1999
Last modified: 18 Jul 2017 10:43

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Contributors

Author: P.E. An
Author: M. Brown
Author: C.J. Harris

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