A Confidence Machine for Sparse High-Order Interaction Model

TL;DR

This paper introduces a new conformal prediction method for sparse high-order interaction models, enabling reliable confidence sets for complex predictors like neural networks and random forests without sacrificing accuracy.

Contribution

It develops a full conformal prediction approach for SHIM, overcoming computational challenges with homotopy mining, and achieves accuracy comparable to complex models.

Findings

SHIM matches RF and NN accuracy

Full-CP provides reliable confidence sets

Homotopy mining reduces computational complexity

Abstract

In predictive modeling for high-stake decision-making, predictors must be not only accurate but also reliable. Conformal prediction (CP) is a promising approach for obtaining the confidence of prediction results with fewer theoretical assumptions. To obtain the confidence 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 to compute the confidence set. Unfortunately, because of the reduced sample size, split-CP is inferior to full-CP both in fitting as well as confidence 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.