Kernel-based Approach for Learning Causal Graphs from Mixed Data

A causal graph can be generated from a dataset using a particular causal algorithm, for instance, the PC algorithm or Fast Causal Inference (FCI). This paper provides two contributions in learning causal graphs: an easy way to handle mixed data so that it can be used to learn causal graphs using the PC algorithm/FCI and a method to evaluate the learned graph structure when the true graph is unknown. This research proposes using kernel functions and Kernel Alignment to handle mixed data. The two main steps of this approach are computing a kernel matrix for each variable and calculating a pseudo-correlation matrix using Kernel Alignment. The Kernel Alignment matrix is used as a substitute for the correlation matrix that is the main component used in computing a partial correlation for the conditional independence test for Gaussian data in the PC Algorithm and FCI. The advantage of this idea is that is possible to handle more data types when there is a suitable kernel function to compute a kernel matrix for an observed variable. The proposed method is successfully applied to learn a causal graph from mixed data containing categorical, binary, ordinal, and continuous variables. We also introduce the Modal Value of Edges Existence (MVEE) method, a new method to evaluate the structure of learned graphs represented by Partial Ancestral Graph (PAG) when the true graph is unknown. MVEE produces an agreement graph as a proxy to the true graph to evaluate the structure of the learned graph. MVEE is successfully used to choose the best-learned graph when the true graph is unknown.