Shapley-PC: Constraint-based Causal Structure Learning with Shapley Values

Causal Structure Learning (CSL), amounting to extracting causal relations among the variables in a dataset, is widely perceived as an important step towards robust and transparent models. Constraint-based CSL leverages conditional independence tests to perform causal discovery. We propose Shapley-PC, a novel method to improve constraint-based CSL algorithms by using Shapley values over the possible conditioning sets to decide which variables are responsible for the observed conditional (in)dependences. We prove soundness and asymptotic consistency and demonstrate that it can outperform state-of-the-art constraint-based, search-based and functional causal model-based methods, according to standard metrics in CSL.

Causal Discovery and Injection for Feed-Forward Neural Networks

Neural networks have proven to be effective at solving a wide range of problems but it is often unclear whether they learn any meaningful causal relationship: this poses a problem for the robustness of neural network models and their use for high-stakes decisions. We propose a novel method overcoming this issue by injecting knowledge in the form of (possibly partial) causal graphs into feed-forward neural networks, so that the learnt model is guaranteed to conform to the graph, hence adhering to expert knowledge. This knowledge may be given up-front or during the learning process, to improve the model through human-AI collaboration. We apply our method to synthetic and real (tabular) data showing that it is robust against noise and can improve causal discovery and prediction performance in low data regimes.