Collaborative Research: Statistical Inference Using Random Forests and Related Methods

该项目旨在开发方法来量化机器学习算法中的不确定性，并将机器学习和统计推断结合起来。机器学习在使用数据进行预测方面取得了巨大的成功;它被用于从手写识别到高频交易到无人驾驶汽车和个性化医疗的广泛应用。然而，虽然机器学习算法可以做出很好的预测，但它们很少告诉人类这些预测是如何得出的：重要的因素是什么？他们是如何影响预测的？他们也没有区分那些有很多关于不同结果概率的信息（即使这些信息覆盖的范围很广）的预测和那些信息很少的预测。例如，机器学习算法可以非常准确地预测一个人是否有可能患糖尿病，但几乎没有提供任何关于该人如何降低其风险的信息。该项目将建立在最初的数学理论基础上，开发方法来解释随机森林如何得出预测以及这些预测在统计上有多可信，并提出将机器学习方法与其他统计模型联系起来的方法。该项目旨在开发方法来量化机器学习算法中的不确定性，并将机器学习和统计推理结合起来。该项目将扩展将随机森林表示为U统计的理论框架，以产生机器学习中统计不确定性量化的实际实现。特别是，它将改进随机森林预测中估计样本变异性的方法，开发用于协变量和相互作用选择的计算效率高的筛选工具，并将集成方法作为部分线性模型中的非参数项，同时通过修改的boosting算法保留统计推断。这些方法将在鸟类学和各种生物医学应用中的公民科学数据库上进行演示。

This project seeks to develop methods to quantify uncertainty in machine learning algorithms and to incorporate machine learning and statistical inference. Machine learning has been enormously successful at using data to make predictions; it is used in an extensive range of applications from handwriting recognition to high frequency trading to driverless cars and personalized medicine. However, while machine learning algorithms make good predictions, they tell humans very little about how those predictions were arrived at: What were the important factors? How did they affect the prediction? They also don't distinguish predictions for which there is a lot of information about the probability of different outcomes (even if that covers a wide range) from those where very little information is available. For example, a machine learning algorithm may very accurately predict whether a person is likely to develop diabetes, but provides little if any information regarding how that person might lower his or her risk. This project will build on initial mathematical theory to develop methods to explain how Random Forests arrive at their predictions and how statistically confident those predictions are, and produce ways to link machine learning methods to other statistical models.This project seeks to develop methods to quantify uncertainty in machine learning algorithms and to incorporate machine learning and statistical inference. The project will extend on a theoretical framework representing Random Forests as U-statistics to produce a practical implementation of statistical uncertainty quantification in machine learning. In particular, it will improve on methods to estimate sample variability in Random Forest predictions, develop computationally efficient screening tools for covariate and interaction selection, and incorporate ensemble methods as non-parametric terms in partially-linear models while retaining statistical inference via a modified boosting algorithm. These methods will be demonstrated on a citizen science data base in ornithology and in various biomedical applications.