Incipient faults in high-speed railway have been rarely considered before developing into faults or failures. In this paper, a new data-driven incipient fault estimate (FE) methodology is proposed under multivariate statistics frame, which incorporates with Kullback-Leibler divergence (KLD) in information domain and neural network approximation in machine learning. By defining one sensitive fault indicator (SFI), the incipient fault amplitude can be precisely estimated. According to the experimental platform of China Railway High-speed 2 (CRH2), the proposed incipient FE algorithm is examined, and the more sensitivity and accuracy to tiny abnormality are demonstrated. Followed by the incipient FE results, several factors on FE performance are further analyzed.