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In this paper, we propose a weakly supervised deep temporal encoding-decoding solution for anomaly detection in surveillance videos using multiple instance learning. The proposed approach uses both abnormal and normal video clips during the training phase which is developed in the multiple instance framework where we treat video as a bag and video clips as instances in the bag. Our main contribution lies in the proposed novel approach to consider temporal relations between video instances. We deal with video instances (clips) as a sequential visual data rather than independent instances. We employ a deep temporal and encoder network that is designed to capture spatial-temporal evolution of video instances over time. We also propose a new loss function that is smoother than similar loss functions recently presented in the computer vision literature, and therefore; enjoys faster convergence and improved tolerance to local minima during the training phase. The proposed temporal encoding-decoding approach with modified loss is benchmarked against the state-of-the-art in simulation studies. The results show that the proposed method performs similar to or better than the state-of-the-art solutions for anomaly detection in video surveillance applications.