Iterative learning algorithms for linear Gaussian observation models

In this paper, we consider a signal/parameter estimation problem that is based on a linear model structure and a given setting of statistical models with unknown hyperparameters. We consider several combinations of Gaussian and Laplacian models. We develop iterative algorithms based on two typical machine learning methods - the evidence-based method and the integration-based method - to deal with the hyperparameters. We have applied the proposed algorithms to adaptive prediction and wavelet denoising. In linear prediction, we show that the proposed algorithms are efficient tools for tackling a difficult problem of adapting simultaneously the order and the coefficients of the predictor. In wavelet denoising, we show that by using the proposed algorithms, the noisy wavelet coefficients are subject to shrinkage and thresholding.