Building Conformal Prediction Intervals with Approximate Message Passing
Lucas Clarté, Lenka Zdeborová
构图预测已成为构建预测间隔的有力工具,该预测间隔以无分布方式有效。 然而,其评估可能具有计算成本,特别是在高维设置中,尺寸和样本大小都很大且具有可比的幅度。 为了在广义线性回归的背景下应对这一挑战,我们提出了一种基于近似消息传递(AMP)的新算法,通过近似合格分数的计算,使用完整的构象预测加速预测间隔的计算。 我们的工作弥合了现代不确定性量化技术和涉及AMP算法的高维问题工具之间的差距。 我们在合成和真实数据上评估我们的方法,并表明它产生的预测间隔接近基线方法,同时速度要快一些。 此外,在高维极限和数据分布假设下,AMP计算的合格分数收敛到精确计算的合格分数,从而允许在高维度上对构象方法进行理论研究和基准测试。
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 predic...