用近似消息传递加速高维回归的置信区间计算
Building Conformal Prediction Intervals with Approximate Message Passing
- 基于近似消息传递算法近似计算置信度得分
- 在高维场景下速度提升数个数量级，结果接近基准方法
- 理论证明在极限条件下逼近精确解，适合高维不确定性量化研究
分位数预测已成为一种强大的工具，可在无需分布假设的情况下构建有效的预测区间。然而，在高维设置下（维度与样本量均较大且量级相当），其评估可能计算成本高昂。针对广义线性回归场景，我们提出一种基于近似消息传递（AMP）的新算法，通过近似计算符合度得分来加速完整分位数预测的预测区间计算。本工作弥合了现代不确定性量化技术与高维问题中AMP算法之间的鸿沟。我们在合成数据和真实数据上评估该方法，结果显示其预测区间与基准方法接近，同时速度提升数个数量级。此外，在高维极限下并基于数据分布假设，由AMP计算的符合度得分收敛到精确值，从而为高维分位数方法的理论研究与基准测试提供了可能。
原文摘要 · Abstract (English)
Conformal prediction has emerged as a powerful tool for building prediction intervals that are valid in a distribution-free way. However, its evaluation may be computationally costly, especially in the high-dimensional setting where the dimensionality and sample sizes are both large and of comparable magnitudes. To address this challenge in the context of generalized linear regression, we propose a novel algorithm based on Approximate Message Passing (AMP) to accelerate the computation of prediction intervals using full conformal prediction, by approximating the computation of conformity scores. Our work bridges a gap between modern uncertainty quantification techniques and tools for high-dimensional problems involving the AMP algorithm. We evaluate our method on both synthetic and real data, and show that it produces prediction intervals that are close to the baseline methods, while being orders of magnitude faster. Additionally, in the high-dimensional limit and under assumptions on the data distribution, the conformity scores computed by AMP converge to the one computed exactly, which allows theoretical study and benchmarking of conformal methods in high dimensions.
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