Conformal Prediction for Hierarchical Data
This work addresses the challenge of improving prediction efficiency for hierarchical data in statistical learning, representing an incremental advance by combining existing methods from conformal prediction and forecast reconciliation.
The paper tackles the problem of constructing prediction regions for hierarchical data, where some components are linear combinations of others, by incorporating a projection step into split conformal prediction to leverage the hierarchical structure. The result is globally smaller prediction regions while maintaining coverage, demonstrated under both joint and component-wise coverage objectives.
We consider conformal prediction for multivariate data and focus on hierarchical data, where some components are linear combinations of others. Intuitively, the hierarchical structure can be leveraged to reduce the size of prediction regions for the same coverage level. We implement this intuition by including a projection step (also called a reconciliation step) in the split conformal prediction [SCP] procedure, and prove that the resulting prediction regions are indeed globally smaller. We do so both under the classic objective of joint coverage and under a new and challenging task: component-wise coverage, for which efficiency results are more difficult to obtain. The associated strategies and their analyses are based both on the literature of SCP and of forecast reconciliation, which we connect. We also illustrate the theoretical findings, for different scales of hierarchies on simulated data.