Online conformal prediction methods such as Adaptive Conformal Inference (ACI) and Fully Adaptive Conformal Inference (FACI) adjust prediction intervals under distribution shift, but their calibration is based on a common stream of recent nonconformity scores. We introduce Population-based Adaptive Conformal Ensembles (PACE), a heuristic method that maintains online conformal quantile calibrators with different window sizes, decay rates, and quantile scales. PACE combines the best-calibrated members through fitness-weighted top-K averaging and periodically refreshes the population using clonal selection. For context, Strongly Adaptive Online Conformal Prediction (SAOCP) is a benchmark method that combines online calibration experts operating over different time intervals and provides a formal strongly adaptive regret guarantee. PACE is heuristic and does not provide an analogous regret or coverage guarantee. We evaluate the method on two synthetic datasets and three real-world time series. Against five adaptive conformal baselines, PACE achieves higher empirical coverage during extreme regimes. Compared with SAOCP, it generally obtains higher coverage by producing wider intervals, resulting in less favorable interval scores on most datasets.
Marzieh Amiri Shahbazi, Ali Baheri· Forecasting· 0 citations
Contraction theory guaranties exponential convergence between trajectories of a stable nonlinear system. When initial conditions are uncertain and represented as probability distributions, as in ensemble control, Bayesian estimation, and generative modeling, this guaranty extends to the distributional level via Wasserstein distance. However, the classical distributional bound is tight only for linear systems; for nonlinear dynamics, it can be significantly conservative because it collapses the spatially varying local contraction rate to a single worst-case constant, discarding distributional information entirely. We address three concrete consequences of this conservatism. First, we derive a tighter Wasserstein bound by replacing the worst-case rate with a displacement-weighted distributional average of the local contraction rate, which strictly improves upon the classical bound for every nonlinear contracting system. Second, we provide the first theoretical characterization of the self-correcting Euler discretization error under contraction: the error profile is non-monotone, peaks at a universal time that depends only on the contraction rate, and then decays exponentially, a behavior absent in non-contracting dynamics. Third, we prove that nonlinear contracting drifts always achieve strictly smaller stationary variance than a linear system sharing the same worst-case contraction rate, formally establishing the noise-rejection advantage of nonlinear controllers. All results are validated on a representative suite of one- and two-dimensional vector fields.