This paper introduces GRAD, a real-time anomaly detection method for autonomous vehicle sensors that integrates statistical analysis and deep learning to ensure the reliability of sensor data. The proposed approach combines the Reinforced Exponential Moving Average (REMA), which adapts smoothing factors and thresholding for outlier detection, with the Multi-Stage Sliding Window (MS-SW) technique for capturing both short- and long-term patterns. These features are processed using a lightweight Gated Recurrent Unit (GRU) model, which detects and classifies anomalies based on bias types, while a recovery module restores damaged sensor data to ensure continuous system operation. GRAD has a lightweight architecture consisting of two layers of GRU with a limited number of neurons that make it appropriate for real-time applications while maintaining high detection accuracy. The GRAD framework achieved remarkable performance in anomaly detection and classification. The model demonstrated an overall F1-score of 97.6% for abnormal data and 99.4% for normal data, signifying its high accuracy in distinguishing between normal and anomalous sensor data. Regarding the anomaly classification, GRAD successfully categorized different anomaly types with high precision, enabling the recovery module to accurately restore damaged sensor data. Relative to analogous studies, GRAD surpasses current models by attaining a balance between elevated detection accuracy and diminished computational expense. These results demonstrate GRAD's potential as a reliable and efficient solution for real-time anomaly detection in autonomous vehicle systems, guaranteeing safe vehicle operation with minimal computational overhead.

We introduce an online tensor decomposition based approach for two latent variable modeling problems namely, (1) community detection, in which we learn the latent communities that the social actors in social networks belong to, and (2) topic modeling, in which we infer hidden topics of text articles. We consider decomposition of moment tensors using stochastic gradient descent. We conduct optimization of multilinear operations in SGD and avoid directly forming the tensors, to save computational and storage costs. We present optimized algorithm in two platforms. Our GPU-based implementation exploits the parallelism of SIMD architectures to allow for maximum speed-up by a careful optimization of storage and data transfer, whereas our CPU-based implementation uses efficient sparse matrix computations and is suitable for large sparse datasets. For the community detection problem, we demonstrate accuracy and computational efficiency on Facebook, Yelp and DBLP datasets, and for the topic modeling problem, we also demonstrate good performance on the New York Times dataset. We compare our results to the state-of-the-art algorithms such as the variational method, and report a gain of accuracy and a gain of several orders of magnitude in the execution time.