Proceedings ArticleDOI
On the selection of optimal nonlinearities for stochastic gradient adaptive algorithms
Tareq Y. Al-Naffouri,Ali H. Sayed,Thomas Kailath +2 more
- Vol. 1, pp 464-467
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TLDR
An expression for the optimal error nonlinearity in adaptive filter design is derived using an energy conservation relation, and some typical assumptions, by minimizing the mean-square deviation subject to a fixed rate of convergence.Abstract:
This paper derives an expression for the optimal error nonlinearity in adaptive filter design. Using an energy conservation relation, and some typical assumptions, the choice of the error function is optimized by minimizing the mean-square deviation subject to a fixed rate of convergence. The resulting optimal choice is shown to subsume earlier results as special cases.read more
Citations
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Journal ArticleDOI
Adaptive filters with error nonlinearities: mean-square analysis and optimum design
TL;DR: This paper performs stability and steady-state analysis of adaptive filters with error nonlinearities under weaker conditions than what is usually encountered in the literature, and without imposing any restriction on the color or statistics of the input.
Journal ArticleDOI
The p-norm generalization of the LMS algorithm for adaptive filtering
TL;DR: Bregman divergences are used to motivate a generalization of the least mean squared (LMS) algorithm, which can handle generalized linear models where the output of the system is a linear function combined with a nonlinear transfer function.
Journal ArticleDOI
Robust Distributed Estimation by Networked Agents
TL;DR: The robust adaptive algorithm for stand-alone agents was developed, one that semi-parametrically estimates the optimal error nonlinearity jointly with the parameter of interest is extended to solve the problem of robust distributed estimation by a network of agents.
Journal ArticleDOI
Robust Adaptation in Impulsive Noise
TL;DR: In this paper, a robust adaptive filtering algorithm is developed that effectively learns and tracks the output error distribution to improve estimation performance.
Proceedings ArticleDOI
Design of optimum error nonlinearity for channel estimation in the presence of class-A impulsive noise
TL;DR: The theoretical results are testify through simulations, to show the superiority of the designed optimum error nonlinearity in the existence of class-A impulsive noise.
References
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Journal ArticleDOI
The least mean fourth (LMF) adaptive algorithm and its family
E. Walach,Bernard Widrow +1 more
TL;DR: It is possible, therefore, that a minimum mean fourth error algorithm can do a better job of least squares estimation than a mean square error algorithm.
Journal ArticleDOI
A time-domain feedback analysis of filtered-error adaptive gradient algorithms
Markus Rupp,Ali H. Sayed +1 more
TL;DR: It is shown that an intrinsic feedback structure can be associated with the varied adaptive schemes and extended the so-called transfer function approach to a general time-variant scenario without any approximations.
Journal ArticleDOI
Stochastic gradient adaptation under general error criteria
Scott C. Douglas,Teresa H. Meng +1 more
TL;DR: It is shown that the equations governing the convergence of the nonlinear algorithm are exactly those which describe the behavior of the optimum scalar data nonlinear adaptive algorithm for white Gaussian input.
Journal ArticleDOI
On the optimum data nonlinearity in LMS adaptation
TL;DR: The effect of an arbitrary nonlinear operation on the data input to the weight update equation in the LMS adaptive algorithm is investigated for a Gaussian data model and the optimum nonlinearity is shown to be linear when the product of the algorithm step size and input power is much less than unity.
Proceedings ArticleDOI
Time-domain feedback analysis of adaptive gradient algorithms via the small gain theorem
Ali H. Sayed,Markus Rupp +1 more
TL;DR: In this paper, the authors provide a time-domain feedback analysis of gradient-based adaptive schemes with emphasis on stability and robustness issues, and show that an intrinsic feedback structure, mapping the noise sequence and the initial weight guess to the a priori estimation errors and the final weight estimate, can be associated with such schemes.
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