Non-linear Least Mean Squares Prediction Based on Non-Gaussian Mixtures

Independent Component Analyzers Mixture Models (ICAMM) are versatile and general models for a large variety of probability density functions. In this paper, we assume ICAMM to derive a closed-form solution to the optimal Least Mean Squared Error predictor, which we have named E-ICAMM. The new predictor is compared with four classical alternatives (Kriging, Wiener, Matrix Completion, and Splines) which are representative of the large amount of existing approaches. The prediction performance of the considered methods was estimated using four performance indicators on simulated and real data. The experiment on real data consisted in the recovering of missing seismic traces in a real seismology survey. E-ICAMM outperformed the other methods in all cases, displaying the potential of the derived predictor.