High-Dimensional Interaction Detection and Nonparametric Inference

了解变量如何相互作用在许多科学发现和当代应用中至关重要，特别是在社交网络、营销、医学、遗传学和癌症研究等领域。确定重要的交互作用还有助于提高模型的可解释性和预测性。然而，高维数据的交互作用检测带来了巨大的挑战，因为成对交互作用的数量随着协变量的数量呈二次曲线增长，而高阶交互作用的增长甚至更快。虽然关于交互检测的文献越来越多，但在错误率控制和推理方面的工作有限。建立强大的交互检测和非参数推理的统计基础，并提供可重复和可扩展的选择重要交互的算法，可以极大地促进这些急需的工具在实际应用中的使用。整个项目的共同主题是开发关于高维相互作用检测和非参数推理的统计方法和理论，并提供统计保证和改进的重现性和可解释性。该项目有三个相互关联的目标，即及时对高维相互作用检测和非参数推理进行理论和方法论研究。第一个目的是为超高维回归模型中交互检测的预测和假符率控制奠定理论基础。第二个目标是基于Model-X仿冒品的最新发展，提出具有错误发现率控制和吸引力的高维交互检测的新方法。第三个目标进一步研究了高维随机向量之间的非线性相互作用，并发展了一种通过距离相关透镜进行高维非参数推断的新的检验方法。在上述三个目标下开发的系统研究计划将有助于为高维数据分析建立严密的统计理论和方法基础，以指导从业者和研究人员。调查人员还计划系统地开发易处理和高效的计算算法，通过R和PYTHON等自由软件包来实施所提出的方法，然后使它们随时可用，并在所有相关领域宣传它们。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Understanding how variables interact with each other is fundamentally important in many scientific discoveries and contemporary applications, especially in areas such as social networks, marketing, medicine, genetics, and cancer studies. Identifying important interactions can also help improve model interpretability and prediction. Yet interaction detection with high-dimensional data poses great challenges since the number of pairwise interactions increases quadratically with the number of covariates and that of higher-order interactions grows even faster. Although there is a growing literature on interaction detection, there is a limited amount of work on the error rate control and inference aspects. Building robust statistical foundations of interaction detection and nonparametric inference, and offering reproducible and scalable algorithms for selecting important interactions can greatly facilitate the use of these much-needed tools in real applications. The common theme underlying this entire project is that of developing statistical methodologies and theories on high-dimensional interaction detection and nonparametric inference with statistical guarantees and improved reproducibility and interpretability.This project has three interrelated aims of timely theoretical and methodological studies on high-dimensional interaction detection and nonparametric inference. The first aim establishes the theoretical foundation of prediction and false sign rate control for interaction detection in ultra-high dimensional regression models. The second aim builds on the recent development of model-X knockoffs and proposes new methods for high-dimensional interaction detection with false discovery rate control and appealing power. The third aim further investigates the nonlinear interactions between a pair of high-dimensional random vectors and develops a new testing procedure for high-dimensional nonparametric inference through the lens of distance correlation. The systematic research program developed in three aims above will help build rigorous statistical foundations of theory and methodologies for high-dimensional data analysis that can guide practitioners and researchers. The investigators also plan to systematically develop tractable and efficient computation algorithms to implement the proposed methods through free software packages, like R and Python, and then make them readily available and publicize them in all relevant fields.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.