In order to achieve online awareness of the transient stability of power systems, 10 different transient indicators that can be directly obtained or indirectly calculated using WAMS measurement data were chosen as original covariates for regression analysis of stability margins. Furthermore, feature covariates were consequently selected via a method called Nonparametric Independence Screening (NIS) so that the dimension of multivariate regression was reduced. Finally, a Group-Lasso algorithm was adopted to perform multivariate nonparametric regression in order to form a prediction function for transient stability awareness. An IEEE-39 bus case study demonstrated that the prediction function trained by correlation learning not only assessed the stability of the disturbed power system accurately, but also provided the evaluation of stability margin of the fault contingencies.