In order to reduce DPPM (defect parts per million), IDDQ testing methodology can be exploited for identifying "outliers" which are potentially defective but not detected by signoff functional and parametric tests. Conventional IDDQ testing paradigms depending on a simple statistical 6σ rule or engineers' experience are usually too conservative to effectively identify non-trivial outliers, especially when spatial correlations are of great concern/influence. In this paper, by employing a stochastic regression model, the mean as well as the variance of the IDDQ of a die under test (DUT) can be predicted. According to the predicted mean and variance, we derive an expected IDDQ range and identify the DUT as an outlier if its actual IDDQ measurement is beyond the expected range. The proposed stochastic regression model is obtained by training a convolutional neural network (CNN) and, based on its primitive property of convolutional kernel mapping with large volume of industrial data, spatial correlations (due to spatially-correlated process variations, etc) can be considered/captured. The trained data-driven CNN is highly accurate in terms of R-square (0.958) and RMSE (0.783), and the percentage of identified outliers (0.047%) is very close to the theoretical reference (0.050%), which validates the efficacy of our proposed methodology.