In many applications, monitoring area under the ROC curve (AUC) in a sliding window over a data stream is a natural way of detecting changes in the system. The drawback is that computing AUC in a sliding window is expensive, especially if the window size is large and the data flow is significant.
In this paper we propose a scheme for maintaining an approximate AUC in a sliding window of length $k$. More specifically, we propose an algorithm that, given $ε$, estimates AUC within $ε/ 2$, and can maintain this estimate in $O((\log k) / ε)$ time, per update, as the window slides. This provides a speed-up over the exact computation of AUC, which requires $O(k)$ time, per update. The speed-up becomes more significant as the size of the window increases. Our estimate is based on grouping the data points together, and using these groups to calculate AUC. The grouping is designed carefully such that ($i$) the groups are small enough, so that the error stays small, ($ii$) the number of groups is small, so that enumerating them is not expensive, and ($iii$) the definition is flexible enough so that we can maintain the groups efficiently.
Our experimental evaluation demonstrates that the average approximation error in practice is much smaller than the approximation guarantee $ε/ 2$, and that we can achieve significant speed-ups with only a modest sacrifice in accuracy.
Department of Mathematics, The Ohio State University（俄亥俄州立大学数学系）；Translational Data Analytics Institute, The Ohio State University（俄亥俄州立大学转化数据分析研究所）；Department of Mathematics and Statistics, San José State University（圣何塞州立大学数学与统计系）
Designing Adaptive Algorithms Based on Reinforcement Learning for Dynamic Optimization of Sliding Window Size in Multi-Dimensional Data Streams
Department of Computer Engineering, Ferdowsi University of Mashhad（法尔多西大学马什哈德分校计算机工程系）；Department of Computer Engineering, University of Tehran（德黑兰大学计算机工程系）
Sliding-Window Reordering with Overlap Averaging: A Simple Time-Domain Augmentation for Multivariate Forecasting
Data Science Group, University of Hildesheim（希尔德斯海姆大学数据科学组）；Information Systems and Machine Learning Lab (ISMLL), University of Hildesheim（希尔德斯海姆大学信息系统与机器学习实验室）
Renmin University of China（中国人民大学）；Gaoling School of Artificial Intelligence（高瓴人工智能学院）；Pazhou Laboratory (Huangpu)（琶洲实验室（黄埔））；Fudan University（复旦大学）；Alibaba Group（阿里巴巴集团）
