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Title: Anomaly detection for high-dimensional linear regression models with possible temporal dependence Authors:  Abolfazl Safikhani - University of Florida (United States) [presenting]
Yue Bai - University of Florida (United States)
Abstract: Detecting structural breaks in high-dimensional linear regression models is a challenging task due to the existence of an unknown number of such breaks, unknown location of breaks, and unknown high-dimensional model parameters. A general methodology for handling this problem will be presented which can cover a wide range of statistical models including mean shift models, Vector Auto-Regressive Models (VARs), and Gaussian graphical models. The proposed algorithm consists of (1) applying blocked fused lasso to identify potential locations of breaks; (2) evaluate the magnitude of changes and apply thresholding to keep only the large enough jumps; (3) apply k-means clustering to the location of large jumps to select clusters around true breaks; (4) exhaustive search within each selected cluster to locate the breaks. Consistency for estimating the number of breaks, their locations and model parameters is verified under mild conditions satisficed in many well-known high-dimensional statistical models. The proposed method performs well in synthetic and real data applications while outperforming some competing methods in the literature.