BYY data smoothing based learning on a small size of samples

Bayesian ying-yang (BYY) data smoothing based learning provides a general framework for parametric learning on a small size of samples by Parzen window nonparametric density estimation, with the best optimal smoothing parameter. This paper not only systematically elaborates the general formulation of BYY data smoothing based learning, but also presents several new results on both implementing smoothed parameter learning and estimating the best smoothing parameter for supervised and unsupervised learning tasks. Moreover, detailed studies have also been made on data smoothing based learning for Gaussian mixture, mixture-of-expert models, and three layer nets