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In this paper, a data-driven method is proposed for fast cascading outage screening in power systems. The proposed method combines a deep convolutional neural network (deep CNN) and a depth-first search (DFS) algorithm. First, a deep CNN is constructed as a security assessment tool to evaluate system security status based on observable information.With its automatic feature extraction ability and the high generalization, a well-trained deep CNN can produce estimated AC optimal power flow (ACOPF) results for various uncertain operation scenarios, i.e., fluctuated load and system topology change, in a nearly computation-free manner. Second, a scenario tree is built to represent the potential operation scenarios and the associated cascading outages. The DFS algorithm is developed as a fast screening tool to calculate the expected security index value for each cascading outage path along the entire tree, which can be a reference for system operators to take predictive measures against system collapse. The simulation results of applying the proposed deep CNN and the DFS algorithm on standard test cases verify their accuracy, and the computational efficiency is thousands of times faster than the model-based traditional approach, which implies the great potential of the proposed algorithm for online applications.