We introduce Longitudinal Predictive Conformal Inference (LPCI), a novel distribution-free conformal prediction algorithm for longitudinal data. Current conformal prediction approaches for time series data predominantly focus on the univariate setting, and thus lack cross-sectional coverage when applied individually to each time series in a longitudinal dataset. The current state-of-the-art for longitudinal data relies on creating infinitely-wide prediction intervals to guarantee both cross-sectional and asymptotic longitudinal coverage. The proposed LPCI method addresses this by ensuring that both longitudinal and cross-sectional coverages are guaranteed without resorting to infinitely wide intervals. In our approach, we model the residual data as a quantile fixed-effects regression problem, constructing prediction intervals with a trained quantile regressor. Our extensive experiments demonstrate that LPCI achieves valid cross-sectional coverage and outperforms existing benchmarks in terms of longitudinal coverage rates. Theoretically, we establish LPCI's asymptotic coverage guarantees for both dimensions, with finite-width intervals. The robust performance of LPCI in generating reliable prediction intervals for longitudinal data underscores its potential for broad applications, including in medicine, finance, and supply chain management.

翻译：我们提出了纵向预测保形推断（LPCI），一种适用于纵向数据的新型无分布保形预测算法。当前用于时间序列数据的保形预测方法主要关注单变量场景，因此当单独应用于纵向数据集中的每个时间序列时，缺乏横截面覆盖能力。现有纵向数据的最先进方法依赖构建无限宽的预测区间来保证横截面和渐近纵向覆盖。所提出的LPCI方法通过在不依赖无限宽区间的前提下同时保证纵向和横截面覆盖解决了这一问题。在我们的方法中，我们将残差数据建模为分位数固定效应回归问题，利用训练后的分位数回归器构建预测区间。大量实验表明，LPCI实现了有效的横截面覆盖，并在纵向覆盖率方面优于现有基准。理论上，我们建立了LCPI在有限宽度区间下两个维度的渐近覆盖保证。LPCI在生成纵向数据可靠预测区间方面的稳健性能凸显了其在医学、金融和供应链管理等领域的广泛应用潜力。