Dynamic Conformal Prediction for Multi-Target Regression: Optimising Informational Efficiency under Joint Validity

Inductive conformal prediction equips point regressors with finite-sample prediction sets that provably contain the unknown label with prescribed probability. For multi-target regression, joint coverage across all output dimensions can be guaranteed by combining one-dimensional conformal predictors, one for each output dimension, resulting in an axis-aligned hyperrectangular prediction region. The validity and informational efficiency of these hyperrectangular prediction regions depend on the choice of the targeted error rate for the individual one-dimensional conformal predictors. We cast this choice as an error-budget allocation problem and introduce Dynamic Conformal Prediction for Multi-Target Regression (DCP-MT), a method that finds the budget allocation which minimises the hyperrectangles’ volumes while retaining joint coverage under exchangeability. Experiments on synthetic and real-world data sets demonstrate that DCP-MT reduces hyperrectangle volumes compared to state-of-the-art methods when nonconformity scores’ correlations across target dimensions are weak or heterogeneous, while maintaining the nominal coverage. The proposed method thus offers a simple, drop-in solution for existing multi-target regression pipelines.