Learning Ancestral Polytrees

Causal polytrees are singly connected causal models and they are frequently applied in practice. However, in various applications, many variables remain unobserved and causal polytrees cannot be applied without explicitly including unobserved variables. Our study thus proposes the ancestral polytree model, a novel combination of ancestral graphs and singly connected graphs. Ancestral graphs can model causal and non-causal dependencies, while singly connected models allow for efficient learning and inference. We discuss the basic properties of ancestral polytrees and propose an efficient structure learning algorithm. Experiments on synthetic datasets and biological datasets show that our algorithm is efficient and the applications of ancestral polytrees are promising.