CDS&E-MSS: Causal learning and inference on complex observational data

从给定的数据中学习一组变量之间的因果关系是科学研究和工程中的一个基本问题。有向无环图（DAG）是一类流行的因果网络数学模型，其中有向链接编码两个变量之间的因果关系。虽然实验干预提供了一个直接的手段，因果推理，这样的实验往往是不可用或限制在许多领域。因此，从观测数据中进行因果网络的结构学习是统计学和数据科学中一个重要而活跃的研究领域。该项目针对从观测数据中学习因果网络的几个众所周知的困难，即数据的高维性，非线性和潜在的依赖性。新的统计方法和因果结构学习和因果推理的理论将被开发，以克服这些困难。将发布软件包，以提供方法和算法的有效实施。 为了处理高维问题，PI将开发一套用于局部结构学习的方法，而不是估计完整DAG的结构，该方法识别目标变量的因果父变量，然后在给定估计父变量集的情况下进行因果效应估计。利用最近的非线性和非高斯DAG的可识别性结果，将开发一种序贯蒙特卡罗方法来对因果顺序进行采样，并估计一组变量的联合干预效应。为了适应个体之间的数据依赖性，DAG模型将通过图形模型的克罗内克积推广到网络数据。将开发一种算法来估计参数和DAG结构在这个新的模型，它迭代之间的去相关步骤，以消除数据的依赖性和DAG学习步骤的标准方法。将建立局部结构和因果顺序估计方法的理论结果，并证明去相关方法。该项目将图形模型的结构学习、蒙特卡罗方法、非凸优化、非参数回归和条件独立性检验集成到观测数据的因果发现和推断中。此外，该项目中的许多组成部分都受到了最近单细胞RNA测序数据和基因调控因果网络构建的良好激励。将这些方法应用于快速积累的单细胞RNA测序数据，将对基因表达的因果关系产生可靠和准确的推断，这是分子生物学中的一个基本问题。该奖项反映了NSF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。

Learning the causal relations among a set of variables from given data is a fundamental problem in scientific research and engineering. Directed acyclic graphs (DAGs) are a popular class of mathematical models for causal networks, in which a directed link encodes a cause-effect relation between two variables. Although experimental intervention provides a direct means to causal inference, such experiments are often not available or limited in many domains. Consequently, structure learning of causal networks from observational data is an important and active research area in statistics and data science. This project targets a few notorious difficulties in causal network learning from observational data, namely the high-dimensionality, nonlinearity and potential dependence in the data. Novel statistical methods and theory for causal structure learning and causal inference will be developed to overcome these difficulties. Software packages will be released to provide efficient implementation of the methods and algorithms. To handle high-dimensionality, instead of estimating the structure of a full DAG, the PI will develop a set of methods for local structure learning that identifies the causal parents of target variables, followed by causal effect estimation given the estimated parent sets. Leveraging recent identifiability results for nonlinear and non-Gaussian DAGs, a sequential Monte Carlo method will be developed to sample causal orders and to estimate the joint intervention effects of a set of variables given a partial causal ordering. To accommodate data dependence among individuals, the DAG model will be generalized to network data via the Kronecker product of graphical models. An algorithm will be developed to estimate parameters and DAG structure under this new model, which iterates between a de-correlation step to remove data dependence and a DAG learning step by a standard method. Theoretical results will be established for the local structure and causal order estimation methods and to justify the de-correlation approach. The project integrates structure learning of graphical models, Monte Carlo methods, nonconvex optimization, nonparametric regression, and conditional independence test into causal discovery and inference on observational data. Moreover, many components in this project are well-motivated by recent single-cell RNA-sequencing data and the construction of causal networks for gene regulation. Application of the methods to the fast accumulating single-cell RNA-sequencing data will produce reliable and accurate inference for the causality of gene expression, which is a fundamental problem in molecular biology.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.