Abstract
Interpretability and causality have been acknowledged as key ingredients to the success and evolution of modern machine learning systems. Graphical models, and more specifically directed acyclic graphs (DAGs, also known as Bayesian networks), are an established tool for learning and representing interpretable causal models. Unfortunately, estimating the structure of DAGs from data is a notoriously difficult problem, coming with a host of identifiability issues. We will discuss our recent work towards overcoming these challenges in distribution-free and nonparametric models. Starting with the fully observed case, we will discuss how known identifiability results in the linear Gaussian case can be generalized to nonparametric models. We will then discuss more difficult problems involving latent variables, and show how to identify latent causal graphs without linear or parametric assumptions. In both cases, the theory leads to efficient, polynomial time algorithms that are easily implemented in practice.