Conformal Predictions for Longitudinal Data
Devesh Batra Salvatore Mercuri Raad Khraishi
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.