  When building either prediction intervals for regression (with real-valued
response) or prediction sets for classification (with categorical responses),
uncertainty quantification is essential to studying complex machine learning
methods. In this paper, we develop Ensemble Regularized Adaptive Prediction Set
(ERAPS) to construct prediction sets for time-series (with categorical
responses), based on the prior work of [Xu and Xie, 2021]. In particular, we
allow unknown dependencies to exist within features and responses that arrive
in sequence. Method-wise, ERAPS is a distribution-free and ensemble-based
framework that is applicable for arbitrary classifiers. Theoretically, we bound
the coverage gap without assuming data exchangeability and show asymptotic set
convergence. Empirically, we demonstrate valid marginal and conditional
coverage by ERAPS, which also tends to yield smaller prediction sets than
competing methods.
