This paper presents a new conformal method for generating simultaneous
forecasting bands guaranteed to cover the entire path of a new random
trajectory with sufficiently high probability. Prompted by the need for
dependable uncertainty estimates in motion planning applications where the
behavior of diverse objects may be more or less unpredictable, we blend
different techniques from online conformal prediction of single and multiple
time series, as well as ideas for addressing heteroscedasticity in regression.
This solution is both principled, providing precise finite-sample guarantees,
and effective, often leading to more informative predictions than prior
methods.

本文介绍了一种新的符合方法，用于生成能够以足够高的概率覆盖新的随机轨迹整个路径的同时预测带。在需要可靠的不确定性估计的运动规划应用中，我们结合了在线符合单个和多个时间序列的不同技术，以及解决回归异方差性的思想。这种解决方案既是有原则的，提供了精确的有限样本保证，又是有效的，通常比先前方法提供更多信息的预测。

异质轨迹的合拟可调预测

Conformalized Adaptive Forecasting of Heterogeneous Trajectories

This paper develops a conformal method to compute prediction intervals for
non-parametric regression that can automatically adapt to skewed data.
Leveraging black-box machine learning algorithms to estimate the conditional
distribution of the outcome using histograms, it translates their output into
the shortest prediction intervals with approximate conditional coverage. The
resulting prediction intervals provably have marginal coverage in finite
samples, while asymptotically achieving conditional coverage and optimal length
if the black-box model is consistent. Numerical experiments with simulated and
real data demonstrate improved performance compared to state-of-the-art
alternatives, including conformalized quantile regression and other
distributional conformal prediction approaches.

本文开发了一种符合性方法，用于计算自适应于倾斜数据的非参数回归预测区间，利用黑盒机器学习算法用直方图估计结果的条件分布，将它们转化为具有近似条件覆盖的最短预测区间，数值实验表明，与最先进的相关方法相比，这些结果在有限样本情况下可以得到较好的表现，并且如果黑盒模型一致，则渐近达到条件覆盖和最优长度。