We study the performance of risk-controlling prediction sets (RCPS), an empirical risk minimization-based formulation of conformal prediction, with a single trajectory of temporally correlated data from an unknown stochastic dynamical system. First, we use the blocking technique to show that RCPS attains performance guarantees similar to those enjoyed in the iid setting whenever data is generated by asymptotically stationary and contractive dynamics. Next, we use the decoupling technique to characterize the graceful degradation in RCPS guarantees when the data generating process deviates from stationarity and contractivity. We conclude by discussing how these tools could be used toward a unified analysis of online and offline conformal prediction algorithms, which are currently treated with very different tools.

翻译：我们研究了风险控制预测集（RCPS）的性能，这是一种基于经验风险最小化的保形预测方法，应用于来自未知随机动力系统的单条时间相关数据轨迹。首先，我们利用分块技术证明，当数据由渐近平稳且压缩的动态系统生成时，RCPS能够获得与独立同分布（iid）设定下类似的性能保证。其次，我们采用解耦技术刻画了当数据生成过程偏离平稳性和压缩性时，RCPS性能保证的渐进退化特性。最后，我们讨论了如何利用这些工具对在线和离线保形预测算法进行统一分析——目前这两类算法通常采用截然不同的分析工具。