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。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性。然而，高维数据的交互检测带来了巨大的挑战，因为成对交互的数量随着协变量的数量呈二次方增长，高阶交互的增长甚至更快。虽然有越来越多的文献相互作用检测，有一个有限的工作量的错误率控制和推理方面。建立交互检测和非参数推断的强大统计基础，并提供用于选择重要交互的可再现和可扩展算法，可以极大地促进这些急需的工具在真实的应用中的使用。整个项目的共同主题是发展具有统计保证和改进的可重复性和可解释性的高维交互检测和非参数推断的统计方法和理论。本项目有三个相互关联的目标，即及时对高维交互检测和非参数推断进行理论和方法研究。第一个目标是为超高维回归模型中交互检测的预测和虚警率控制奠定理论基础。第二个目标是建立在最近的发展模型X的仿制品，并提出了新的方法，高维互动检测与错误发现率控制和吸引力。第三个目的是进一步研究了高维随机向量间的非线性相互作用，并通过距离相关的透镜，发展了一种新的高维非参数推断检验方法。基于以上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统计理论和方法基础，以指导实践者和研究者。研究人员还计划通过R和Python等免费软件包系统地开发易于处理的高效计算算法，以实现所提出的方法，然后将其随时可用并在所有相关领域进行宣传。该奖项反映了NSF的法定使命，并通过使用基金会的智力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.