Conformal inference is a statistical method used to construct prediction sets for point predictors, providing reliable uncertainty quantification with probability guarantees. This method utilizes historical labeled data to estimate the conformity or nonconformity between predictions and true labels. However, conducting conformal inference for hidden states under hidden Markov models (HMMs) presents a significant challenge, as the hidden state data is unavailable, resulting in the absence of a true label set to serve as a conformal calibration set. This paper proposes an adaptive conformal inference framework that leverages a particle filtering approach to address this issue. Rather than directly focusing on the unobservable hidden state, we innovatively use weighted particles as an approximation of the actual posterior distribution of the hidden state. Our goal is to produce prediction sets that encompass these particles to achieve a specific aggregate weight sum, referred to as the aggregated coverage level. The proposed framework can adapt online to the time-varying distribution of data and achieve the defined marginal aggregated coverage level in both one-step and multi-step inference over the long term. We verify the effectiveness of this approach through a real-time target localization simulation study.

翻译：共形推断是一种用于为点预测器构建预测集的统计方法，能够在概率保证下提供可靠的不确定性量化。该方法利用历史标注数据来估计预测值与真实标签之间的符合性或非符合性。然而，在隐马尔可夫模型下对隐状态进行共形推断面临重大挑战，因为隐状态数据不可获取，导致缺乏真实的标签集作为共形校准集。本文提出了一种自适应共形推断框架，利用粒子滤波方法来解决这一问题。我们并未直接关注不可观测的隐状态，而是创新性地使用加权粒子来近似隐状态的真实后验分布。我们的目标是生成包含这些粒子的预测集，以达到特定的聚合权重和，即聚合覆盖水平。所提出的框架能够在线适应数据的时变分布，并在长期的一步和多步推断中实现定义的边际聚合覆盖水平。我们通过一个实时目标定位仿真研究验证了该方法的有效性。