Bayesian Non-Parametric Test for Conditional Independence

条件独立性测试是现代因果发现的核心，它本身在整个科学和机器学习中至关重要。特别是，因果关系的发现是公共卫生和流行病学、生命和地球科学、社会学研究和计量经济学的基础。在一些最重要的应用中，这种基于随机试验的因果关系发现的传统方法是不可能的，甚至是不道德的。例如，调查吸烟或接触特定化学品等环境因素对患者健康的影响，不能通过将患者随机分配到将接触可能非常有害因素的一组来进行研究。在这种情况下，在大量变量中确定因果关系的唯一方法是利用日益丰富的观察性研究。从观测数据进行因果推理的大多数算法方法依赖于变量之间独立性和条件独立性的统计检验。在因果发现中使用最广泛的独立性和条件独立性检验，如Pearson相关和偏相关，只能检验线性依赖关系。虽然如果关系确实是线性的，这些方法是非常有效的，但是它们对最具挑战性的应用程序中存在的复杂关系类型视而不见，这些应用程序中的依赖关系实际上是高度非线性的。为了正确地检测这些关系，人们不仅需要超越线性假设，而且还需要使用对变量之间的依赖形式不做假设的非参数方法。该项目涉及开发一种非参数统计方法来测试贝叶斯框架中的条件独立性。贝叶斯设置将提供严格的统计基础，而所提议的方法的非参数方面将允许更大的鲁棒性和灵敏度。这种新方法将有利于科学家、流行病学家和计量经济学家，因为它有助于发现变量之间以前未知的关系。为了确保该方法可以被最广泛的研究人员使用，它的实现将在R统计编程平台中以公开可用的软件包发布。一个网站将专门介绍该方法及其实际应用，包括说明R包使用的简单示例。

Conditional independence testing is at the core of modern causal discovery, which is itself of paramount importance throughout the sciences and in Machine Learning. In particular, the discovery of causal relationships is fundamental in public health and epidemiology, in life and earth sciences, in sociological studies and in econometrics. The traditional approach for such causal discovery based on randomised trials is impossible and even unethical in some of the most important applications. For example the investigation of the impact of environmental factors, such as smoking or exposure to specific chemicals, on patient health cannot be studied by randomly allocating patients to a group that would be exposed to a potentially very harmful factor. In such cases, the only way to identify causal links among a large set of variables is to exploit the growing abundance of observational studies. Most of the algorithmic approaches to causal inference from observational data rely on statistical tests of independence and conditional independence between variables. The most widely used existing independence and conditional independence tests in causal discovery, such as Pearson correlation and partial correlation, can only test for linear dependencies. While these approaches are very efficient if the relationships are indeed linear, they are blind to the type of intricate relationships present in the most challenging applications where dependencies are in fact highly non-linear. To correctly detect these relationships one needs to not only go beyond linearity assumptions, but also to use non-parametric approaches that make no assumption on the form of dependence between the variables.The project is concerned with developing a non-parametric statistical method to test for conditional independence in a Bayesian framework. The Bayesian setting will provide a rigorous statistical grounding and the non-parametric aspect of the proposed approach will allow greater robustness and sensitivity. This new approach will be beneficial for scientists, epidemiologists and econometricians by facilitating the detection of previously unknown relationships between variables.To ensure that the method can be used by the widest audience of researchers, its implementation will be distributed in an openly available software package in the R statistical programming platform. A website will be dedicated to the method and its practical applications, including simple examples illustrating the use of the R package.