Efficient Approximation of Leverage Scores in Two-dimensional Autoregressive Models with Application to Image Anomaly Detection

Leverage scores quantify the influence of individual data points within a dataset and are widely used in subsampling methods to obtain a representative subsample. Numerous algorithms have been proposed to efficiently approximate leverage scores, thereby reducing the time complexity in model parameter estimation. In this paper, we study leverage scores in two-dimensional autoregressive models. We develop an efficient algorithm that accelerates the calculation of leverage scores by exploiting the unique structure of the covariate matrix specific to this model. Theoretically, we show that leverage scores can be approximated quickly and accurately by deriving an error bound between the approximated and true values. Numerical studies on synthetic datasets demonstrate the superior performance of the proposed algorithm. Additionally, when applying leverage scores in the two-dimensional autoregressive model to anomaly detection tasks, we achieve competitive detection results compared to state-of-the-art methods, with significantly reduced computational time. Furthermore, the efficient approximation of the leverage scores further reduces the time cost without loss of detection accuracy.