A confidence machine for sparse high-order interaction model

In predictive modelling for high-stake decision-making, predictors must be not only accurate but also reliable. Conformal prediction (CP) is a promising approach for obtaining the coverage of prediction results with fewer theoretical assumptions. To obtain the prediction set by so-called full-CP, we need to refit the predictor for all possible values of prediction results, which is only possible for simple predictors. For complex predictors such as random forests (RFs) or neural networks (NNs), split-CP is often employed where the data is split into two parts: one part for fitting and another for computing the prediction set. Unfortunately, because of the reduced sample size, split-CP is inferior to full-CP both in fitting as well as prediction set computation. In this paper, we develop a full-CP of sparse high-order interaction model (SHIM), which is sufficiently flexible as it can take into account high-order interactions among variables. We resolve the computational challenge for full-CP of SHIM by introducing a novel approach called homotopy mining. Through numerical experiments, we demonstrate that SHIM is as accurate as complex predictors such as RF and NN and enjoys the superior statistical power of full-CP.