Robust ridge regression based on self-paced learning for multivariate calibration

In this paper, we propose a robust ridge regression model based on self-paced learning (RR-SPL) for the high-dimensional spectroscopic data. The proposed RR-SPL model consists of a weighted least-squares loss term on all training samples, a self-paced regularizer on sample weights, and a smoothness penalty on the model parameter. Designating an explicit form of the self-paced regularizer, the weights that indicate the importance of training samples can be automatically optimized in an augmented ridge regression framework. By increasing the model age, more and more training samples from easy to hard are added into the training set to learn a mature model. As a result, the RR-SPL model can weaken the effect of outliers and obtain an accurate spectra-concentrate relation. Experimental results on simulated data sets and four real near-infrared (NIR) spectra data sets show the effectiveness of the proposed RR-SPL method in a wide range of specific prediction tasks with or without outliers.