# Efficient estimation of AUC in a sliding window

## TL;DR

This paper introduces an efficient algorithm for approximating the AUC in a sliding window over data streams, significantly reducing computation time while maintaining high accuracy, which is crucial for real-time system monitoring.

## Contribution

The paper presents a novel grouping-based algorithm for approximate AUC estimation in sliding windows, achieving faster updates with controlled error margins.

## Key findings

- The proposed method reduces update time from O(k) to O((log k)/ε).
- Experimental results show the approximation error is often much smaller than the theoretical bound.
- Significant speed-ups are achieved with only a modest decrease in accuracy.

## Abstract

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 $\epsilon$, estimates AUC within $\epsilon / 2$, and can maintain this estimate in $O((\log k) / \epsilon)$ 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 $\epsilon / 2$, and that we can achieve significant speed-ups with only a modest sacrifice in accuracy.