Hernan Rey

A Nonparametric VSS NLMS Algorithm

The aim of a variable step size normalized least-mean-square (VSS-NLMS) algorithm is to try to solve the conflicting requirement of fast convergence and low misadjustment of the NLMS algorithm. Numerous VSS-NLMS algorithms can be found in the literature with a common point for most of them: they may not work very reliably since they depend on several parameters that are not simple to tune in practice. The objective of this letter is twofold. First, we explain a simple and elegant way to derive VSS-NLMS-type algorithms. Second, a new nonparametric VSS-NLMS is proposed that is easy to control and gives good performances in the context of acoustic echo cancellation

A New Robust Variable Step-Size NLMS Algorithm

A new framework for designing robust adaptive filters is introduced. It is based on the optimization of a certain cost function subject to a time-dependent constraint on the norm of the filter update. Particularly, we present a robust variable step-size NLMS algorithm which optimizes the square of the a posteriori error. We also show the link between the proposed algorithm and another one derived using a robust statistics approach. In addition, a theoretical model for predicting the transient and steady-state behavior and a proof of almost sure filter convergence are provided. The algorithm is then tested in different environments for system identification and acoustic echo cancelation applications.

Variable Explicit Regularization in Affine Projection Algorithm: Robustness Issues and Optimal Choice

A variable regularized affine projection algorithm (VR-APA) is introduced, without requiring the classical step size. Its use is supported from different points of view. First, it has the property of being Hinfin optimal and it satisfies certain error energy bounds. Second, the time-varying regularization parameter is obtained by maximizing the speed of convergence of the algorithm. Although we first derive the VR-APA for a linear time invariant (LTI) system, we show that the same expression holds if we consider a time-varying system following a first-order Markov model. We also find expressions for the power of the steady-state error vector for the VR-APA and the standard APA with no regularization parameter. Particularly, we obtain quite different results with and without using the independence assumption between the a priori error vector and the measurement noise vector. Simulation results are presented to test the performance of the proposed algorithm and to compare it with other schemes under different situations. An important conclusion is that the former independence assumption can lead to very inaccurate steady-state results, especially when high values of the projection order are used

Fast communication: A robust variable step-size affine projection algorithm

We present a robust variable step-size affine projection algorithm (RVSS-APA) using a recently introduced new framework for designing robust adaptive filters. The algorithm is the result of minimizing the square norm of the a posteriori error vector subject to a time-dependent constraint on the norm of the filter update. The RVSS-APA is then successfully tested in different environments for system identification and acoustic echo cancellation applications.

A Fast Robust Recursive Least-Squares Algorithm

We present a fast robust recursive least-squares (FRRLS) algorithm based on a recently introduced new framework for designing robust adaptive filters. The algorithm is the result of minimizing a cost function subject to a time-dependent constraint on the norm of the filter update. Although the characteristics of the exact solution to this problem are known, there is no closed-form solution in general. However, the approximate solution we propose is very close to the optimal one. We also present some theoretical results regarding the asymptotic behavior of the algorithm. The FRRLS is then tested in different environments for system identification and acoustic echo cancellation applications.

A Family of Robust Algorithms Exploiting Sparsity in Adaptive Filters

We introduce a new family of algorithms to exploit sparsity in adaptive filters. It is based on a recently introduced new framework for designing robust adaptive filters. It results from minimizing a certain cost function subject to a time-dependent constraint on the norm of the filter update. Although in general this problem does not have a closed-form solution, we propose an approximate one which is very close to the optimal solution. We take a particular algorithm from this family and provide some theoretical results regarding the asymptotic behavior of the algorithm. Finally, we test it in different environments for system identification and acoustic echo cancellation applications.

Optimum Variable Explicit Regularized Affine Projection Algorithm

A variable regularized affine projection algorithm (VR-APA) is introduced, which does not require the classical step size. Its use is supported from different points of view. First, it has the property of being Hinfin optimal, providing robust behavior against perturbations and model uncertainties. Second, the time varying regularization parameter is obtained by maximizing the speed of convergence of the algorithm. At each time step, it needs knowledge of the power of the estimation error vector, which can be estimated by averaging observable quantities. Although we first derive it for a linear time invariant (LTI) system, we show that the same expression holds if we consider a time varying system following a first order Markov model. Simulation results are presented to test the performance of the proposed algorithm and to compare it with other schemes under different situations

Stability analysis of adaptive filters with regression vector nonlinearities

We present a unified framework to analyze the mean and mean-square stability of a large class of adaptive filters. We do this without obtaining a full transient model, allowing us to acquire sufficient conditions on the stability without assuming a given statistical distribution for the input regressors. We also apply the proposed framework to some popular adaptive filtering schemes, showing that in some cases the sufficient conditions derived are very tight and even necessary too.

Neuronal mechanisms underlying exploration-exploitation strategies in operant learning

One of the most valuable mechanisms in animal self-adaptation is the ability to switch between exploration and exploitation strategies. In this work, we present a computational model that learns visual discrimination paradigms and adapts its behavior whereupon rules change. In the model, dopamine and norepinephrine neurons are proposed as detectors of changes in the environment. Dopamine modulates the excitability and plasticity of artificial neurons in the prefrontal cortex and motor-related structures. These neurons change their synaptic weights following a Hebbian or anti-Hebbian rule depending on the amount of released dopamine and, as the reward rate increases, it induces exploitative behaviors. On the other hand, tonic levels of norepinephrine modulate both, information flows towards motor structures and the excitability of dopaminergic neurons, facilitating the switch from exploitation to exploration strategies. The computational model predicts behavioral and physiological results and provides a computational framework to the exploration-exploitation dilemma in self-adaptive agents.

A biologically plausible model for same/different discrimination

Abstract rules can be learned by several species (not only humans). We propose a biologically plausible model for same/different discrimination, that can point towards the neural basis of abstract concept learning. By including a neural adaptation mechanism to a discriminator model formerly introduced in the literature, selective clusters of neurons fire depending on whether or not the stimuli compared are the same or not. These selective neurons are consistent with experimental findings in the literature. Moreover, reward and attention can modulate the relative strength of each attribute/feature of the stimulus, so more complex abstract discriminations can be achieved using the proposed model as a building block. As a formal model, it can be easily incorporated into several applications in robotics and intelligent machines.