Orthogonalized Kernel Debiased Machine Learning for Multimodal Data Analysis

ABSTRACT Multimodal imaging has transformed neuroscience research. While it presents unprecedented opportunities, it also imposes serious challenges. Particularly, it is difficult to combine the merits of the interpretability attributed to a simple association model with the flexibility achieved by a highly adaptive nonlinear model. In this article, we propose an orthogonalized kernel debiased machine learning approach, which is built upon the Neyman orthogonality and a form of decomposition orthogonality, for multimodal data analysis. We target the setting that naturally arises in almost all multimodal studies, where there is a primary modality of interest, plus additional auxiliary modalities. We establish the root-N-consistency and asymptotic normality of the estimated primary parameter, the semi-parametric estimation efficiency, and the asymptotic validity of the confidence band of the predicted primary modality effect. Our proposal enjoys, to a good extent, both model interpretability and model flexibility. It is also considerably different from the existing statistical methods for multimodal data integration, as well as the orthogonality-based methods for high-dimensional inferences. We demonstrate the efficacy of our method through both simulations and an application to a multimodal neuroimaging study of Alzheimer’s disease. Supplementary materials for this article are available online.

**摘要** 多模态成像已经改变了神经科学研究。虽然它带来了前所未有的机遇，但也带来了严峻的挑战。特别是，很难将简单关联模型所具有的可解释性优点与高度自适应非线性模型所实现的灵活性相结合。在本文中，我们提出了一种正交化核去偏机器学习方法，它基于奈曼正交性和一种分解正交性形式，用于多模态数据分析。我们针对几乎所有多模态研究中自然出现的情况，即存在一个主要关注的模态以及额外的辅助模态。我们确立了估计的主要参数的$\sqrt{N}$一致性和渐近正态性、半参数估计效率以及预测的主要模态效应的置信带的渐近有效性。我们的方法在很大程度上兼具模型可解释性和模型灵活性。它也与现有的多模态数据整合统计方法以及基于正交性的高维推断方法有很大不同。我们通过模拟以及在阿尔茨海默病多模态神经成像研究中的应用证明了我们方法的有效性。本文的补充材料可在线获取。