论文标题
稀疏高阶互动模型的置信机
A Confidence Machine for Sparse High-Order Interaction Model
论文作者
论文摘要
在高风险决策制定的预测建模中，预测因素不仅必须准确而且可靠。共形预测（CP）是一种有前途的方法，用于以更少的理论假设获得预测结果的置信度。为了获得由所谓的Full-CP设定的置信度，我们需要为预测结果的所有可能值重新考虑预测因子，这仅适用于简单的预测因子。对于复杂的预测因素，例如随机森林（RFS）或神经网络（NNS），经常采用拆分CP，其中数据分为两个部分：一个部分：一个拟合的部分，另一部分用于计算置信度集。不幸的是，由于样本量的减少，分裂CP在拟合和置信度设置计算方面均低于Full-CP。在本文中，我们开发了一个稀疏的高阶相互作用模型（SHIM）的完整CP，该模型足够灵活，因为它可以考虑到变量之间的高阶相互作用。我们通过引入一种称为同质挖掘的新方法来解决全CP的计算挑战。通过数值实验，我们证明SHIM与RF和NN等复杂预测因子一样准确，并且具有全CP的出色统计能力。
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.
