标题： 用于可靠统计推断的预测增强树 显示英文标题

标题： Prediction-Augmented Trees for Reliable Statistical Inference

摘要： 机器学习（ML）在预测任务中的显著成功促使科学家将ML预测作为科学发现流程的核心组成部分。 这由AlphaFold（Jumper等，2021年）的里程碑式成就所体现。 在本文中，我们研究如何在统计分析数据以促进科学发现时安全地使用ML预测。 特别是，我们遵循Angelopoulos等（2023年）引入的框架。 在这个框架中，我们假设可以访问一小部分$n$黄金标准标记样本，一个数量大得多的$N$未标记样本集，以及一个可用于填补未标记数据点标签的ML模型。 我们引入了两种新的增强学习估计器：（1）预测增强残差树（PART），以及（2）预测增强求积（PAQ）。 这两种估计器相比Angelopoulos等（2023年）和Angelopoulos等（2024年）分别引入的PPI和PPI++现有估计器具有显著优势。 PART是一种基于决策树的估计器，使用贪心准则构建。 我们首先描述PART的渐近分布，并展示如何构建有效的置信区间。 然后我们证明PART在生态学、天文学和人口普查报告等领域的实际数据集中优于现有方法。 这导致了更具信心的估计器，这是由于同时使用了黄金标准样本和机器学习预测。 最后，我们通过探索PAQ来正式证明PART的优势，PAQ是一种在考虑PART的树深度趋于无穷时的极限情况下出现的估计方法。 在输入数据的适当假设下，我们证明PAQ的方差以$O(N^{-1} + n^{-4})$的速度缩小，显著优于现有方法的$O(N^{-1}+n^{-1})$速度。 显示英文摘要

摘要： The remarkable success of machine learning (ML) in predictive tasks has led scientists to incorporate ML predictions as a core component of the scientific discovery pipeline. This was exemplified by the landmark achievement of AlphaFold (Jumper et al. (2021)). In this paper, we study how ML predictions can be safely used in statistical analysis of data towards scientific discovery. In particular, we follow the framework introduced by Angelopoulos et al. (2023). In this framework, we assume access to a small set of $n$ gold-standard labeled samples, a much larger set of $N$ unlabeled samples, and a ML model that can be used to impute the labels of the unlabeled data points. We introduce two new learning-augmented estimators: (1) Prediction-Augmented Residual Tree (PART), and (2) Prediction-Augmented Quadrature (PAQ). Both estimators have significant advantages over existing estimators like PPI and PPI++ introduced by Angelopoulos et al. (2023) and Angelopoulos et al. (2024), respectively. PART is a decision-tree based estimator built using a greedy criterion. We first characterize PART's asymptotic distribution and demonstrate how to construct valid confidence intervals. Then we show that PART outperforms existing methods in real-world datasets from ecology, astronomy, and census reports, among other domains. This leads to estimators with higher confidence, which is the result of using both the gold-standard samples and the machine learning predictions. Finally, we provide a formal proof of the advantage of PART by exploring PAQ, an estimation that arises when considering the limit of PART when the depth its tree grows to infinity. Under appropriate assumptions in the input data we show that the variance of PAQ shrinks at rate of $O(N^{-1} + n^{-4})$, improving significantly on the $O(N^{-1}+n^{-1})$ rate of existing methods.