High-Dimensional Interaction Detection and Nonparametric Inference

理解变量之间如何相互作用对于许多科学发现和当代应用来说是至关重要的，特别是在社会网络、市场营销、医学、遗传学和癌症研究等领域。识别重要的相互作用也有助于提高模型的可解释性和预测能力。然而，高维数据的相互作用检测面临着巨大的挑战，因为成对相互作用的数量随着协变量的数量呈二次增长，而高阶相互作用的增长速度更快。尽管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。构建交互检测和非参数推理的健壮统计基础，并为选择重要交互提供可重复和可扩展的算法，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发展高维交互检测和非参数推理的统计方法和理论，具有统计保证和改进的可重复性和可解释性。该项目有三个相互关联的目标，即对高维相互作用检测和非参数推理进行及时的理论和方法研究。第一个目标是为超高维回归模型中交互检测的预测和假符号率控制建立理论基础。第二个目标建立在模型x仿制品的最新发展基础上，并提出了具有错误发现率控制和吸引力的高维交互检测的新方法。第三个目标是进一步研究一对高维随机向量之间的非线性相互作用，并通过距离相关透镜开发一种新的高维非参数推理测试程序。基于上述三个目标的系统研究计划将有助于为高维数据分析建立严格的理论和方法统计基础，从而指导实践者和研究人员。研究人员还计划系统地开发易于处理和高效的计算算法，通过免费软件包（如R和Python）实现所提出的方法，然后使它们随时可用，并在所有相关领域进行宣传。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.