Supervised Neural Network Training using the Minimum Error Entropy Criterion with Variable-Size and Finite-Support Kernel Estimates

The insufficiency of mere second-order statistics in many application areas have been discovered and more advanced concepts including higher-order statistics, especially those stemming from information theory like error entropy minimization are now being studied and applied in many contexts by researchers in machine learning and signal processing. The main drawback of using minimization of output error entropy for adaptive system training is the computational load when fixed-size kernel estimates are employed. Entropy estimators based on sample spacing, on the other hand, have lower computational cost, however they are not differentiable, which makes them unsuitable for adaptive learning. In this paper, a nonparametric entropy estimator that blends the desirable properties of both techniques in a variable-size finite-support kernel estimation methodology is presented. This yields an estimator suitable for adaptation, yet has computational complexity similar to sample spacing techniques. The estimator is illustrated in supervised adaptive system training using the minimum error entropy criterion