论文标题
随着任意分配变化的在线预测的共形推断
Conformal Inference for Online Prediction with Arbitrary Distribution Shifts
论文作者
论文摘要
我们考虑在在线环境中形成预测集的问题，在线设置中，允许生成数据随着时间而变化。以前解决此问题的方法遭受了过度加权的历史数据，因此可能无法快速对基本动态做出反应。在这里，我们纠正了此问题，并在所有特定宽度的所有本地时间间隔中制定了一个新颖的程序，并以很小的遗憾。我们通过修改Gibbs andCandès（2021）的自适应共形推理（ACI）算法来实现这一目标，以包含一个额外的步骤，其中ACI梯度下降更新的台阶参数会随着时间的推移而调整。至关重要的是，这意味着与ACI不同，ACI需要了解数据生成机制的变化率，我们的新程序对分布变化的大小和类型都具有适应性。我们的方法具有很高的灵活性，可以与任何基线预测算法结合使用，该算法可产生目标的点估计值或估计的目标分位数，而无需分配假设。我们在两个现实世界中的数据集上测试了我们的技术，旨在预测股票市场的波动和COVID-19案例计数，并发现它们对现实世界的分配变化是强大的和适应性的。
We consider the problem of forming prediction sets in an online setting where the distribution generating the data is allowed to vary over time. Previous approaches to this problem suffer from over-weighting historical data and thus may fail to quickly react to the underlying dynamics. Here we correct this issue and develop a novel procedure with provably small regret over all local time intervals of a given width. We achieve this by modifying the adaptive conformal inference (ACI) algorithm of Gibbs and Candès (2021) to contain an additional step in which the step-size parameter of ACI's gradient descent update is tuned over time. Crucially, this means that unlike ACI, which requires knowledge of the rate of change of the data-generating mechanism, our new procedure is adaptive to both the size and type of the distribution shift. Our methods are highly flexible and can be used in combination with any baseline predictive algorithm that produces point estimates or estimated quantiles of the target without the need for distributional assumptions. We test our techniques on two real-world datasets aimed at predicting stock market volatility and COVID-19 case counts and find that they are robust and adaptive to real-world distribution shifts.
