Adaptive Filtering for Desired Error Distribution under Minimum Information Divergence Criterion

Conventional cost functions of adaptive filtering are usually related to the error's dispersion, such as error's moments or error's entropy, but neglect the shape aspects (peaks, kurtosis, tails, etc.) of the error distribution. In this work, we propose a new notion of filtering (or estimation) in which the error's probability density function (PDF) is shaped into a desired one. As PDFs contain all the probabilistic information, the proposed method can be used to achieve the desired error variance or error entropy, and is expected to be useful in the complex signal processing and learning systems. In our approach, the information divergence between the actual errors and the desired errors is used as the cost function. By kernel density estimation, we derive the associated stochastic gradient algorithm for the finite impulse response (FIR) filter. Simulation results emphasize the effectiveness of this new algorithm in adaptive system training.