在隐马尔可夫模型中，用粒子滤波实现动态预测集构造。
Adaptive Conformal Inference by Particle Filtering under Hidden Markov Models
- 用加权粒子逼近隐藏状态后验分布，替代不可观测的真实标签。
- 在线适应数据分布变化，长期保持预定的覆盖权重和水平。
- 适用于需要可靠不确定性量化的时间序列推断任务。
置信推断是一种用于点预测器构建预测集的统计方法，可提供具有概率保证的不确定性量化。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（HMM）下对隐藏状态进行置信推断面临重大挑战，因为隐藏状态数据不可观测，导致缺乏可用于置信校准的真实标签集合。本文提出一种自适应置信推断框架，采用粒子滤波方法解决此问题。我们创新性地不直接针对不可观测的隐藏状态，而是利用加权粒子作为隐藏状态后验分布的近似。目标是生成包含这些粒子并达到特定聚合权重和的预测集，称为聚合覆盖率。所提框架能够在线适应数据的时变分布，在一阶和多步推断中长期实现定义的边际聚合覆盖率。通过实时目标定位仿真研究验证了该方法的有效性。
原文摘要 · Abstract (English)
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.
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