Deep conditional independence tests with application to imaging genetics

深度学习是生物医学数据分析的主力，因为它能够利用高度非线性关联来训练准确的预测模型，特别是对于图像或序列等结构化数据。然而，仅仅预测质量--可能受到混淆的影响--是不够的，以便从数据转向理解潜在的生物学。对潜在混杂影响进行调整的独立性统计检验，对生物变量之间在总体水平上的相关性做出了合理的陈述。然而，当前的统计测试并不是针对结构化数据的应用程序量身定做的。在这个项目中，我们开发了连续标量响应Y和输入/协变量X之间的统计相关性的条件独立性检验，同时条件变量Z可能由于与X和Y的相关性而混淆了相关性。具体地说，我们考虑了X和Z中的一个或两个是结构化的情况(特别是图像)。我们的方法使用深度学习将结构化数据X和/或Z映射到连续嵌入上，例如，这可能来自转移学习。然后，我们在嵌入变量的线性化混合效应模型中使用测试，其中随机效应允许在高维中进行简约建模。我们将研究所有开发的测试的理论性质，并提供高效的算法和实现。我们还特别关注了有限样本中良好的功率特性，并推导了样本量和功率计算。所开发的方法受到成像遗传学应用的推动，其中条件独立性检验被用于将图像中的可遗传表型映射到遗传位点，通过条件条件来校正种群结构和关联性的混杂。基于群体的成像可以有效地量化表型，包括疾病生物标记物。虽然目前的全基因组关联研究分析了已知的先验标量生物标记，如器官大小，但该项目的目标是实现对图像中是否存在任何可遗传的表型变异的无偏见测试，以发现新的生物标记。特别是，我们将使用我们的方法在英国生物库中对2D视网膜眼底图像和3D大脑磁共振图像进行基于基因的关联研究。

Deep learning is a workhorse for biomedical data analysis due to its ability to leverage highly nonlinear associations to train accurate prediction models, in particular for structured data such as images or sequences. However, prediction quality alone - which may be influenced by confounding - is insufficient in order to move from data towards understanding the underlying biology. Statistical tests for independence that adjust for potential confounding influences make sound statements about dependencies between biological variables on the population level. Current statistical tests, however, are not tailored towards applications to structured data. In this project, we develop conditional independence tests for statistical association between a continuous scalar response Y and an input/covariate X, while conditioning on covariates Z that may confound the association due to dependencies with both X and Y. Specifically, we consider the cases where one or both of X and Z are structured (in particular images). Our approach uses deep learning to map structured data X and/or Z onto continuous embeddings, which may for example come from transfer learning. We then use tests in linearized mixed effects models on embedded variables, where random effects allow for parsimonious modeling in high dimensions. We will investigate theoretical properties of all developed tests and provide efficient algorithms and implementations. We focus in particular also on good power properties in finite samples and derive sample size and power calculations.The developed methods are motivated by applications in imaging genetics, where conditional independence testing is used to map heritable phenotypes in images to genetic loci, correcting for confounding by population structure and relatedness via conditioning. Population-based imaging allows to efficiently quantify phenotypes, including disease biomarkers. While current genome-wide association studies analyze a priori known scalar biomarkers such as organ sizes, the goal of this project is to enable unbiased testing for the presence of any heritable phenotypic variation in images towards the discovery of novel biomarkers. In particular, we will use our methods for gene-based association studies of 2D retinal fundus images and 3D brain magnetic resonance images in the UK Biobank.