Bayesian Non-Parametric Test for Conditional Independence

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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.