Efficient Approximation of Leverage Scores in Two-Dimensional Autoregressive Models with Application to Image Anomaly Detection
研究了二维自回归模型中的杠杆得分，提出一种利用协变量矩阵结构加速计算的算法，理论证明近似误差有界，在合成数据和图像异常检测任务中均取得高效且准确的结果。
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.