Learning causal theories with non-reversible MCMC methods

Causal laws are defined in terms of concepts and the causal relations between them. Following Kemp et al. (2010), we investigate the performance of the hierarchical Bayesian model, in which causal systems are represented by directed acyclic graphs (DAGs) with nodes divided into distinct categories. This paper presents two non-reversible search and score algorithms (Q₁ and Q₂) and their application to the causal learning system. The algorithms run through the pairs of class-assignment vectors and graph structures and choose the one which maximizes the probability of given observations. The model discovers latent classes in relational data and the number of these classes and predicts relations between objects belonging to them. We evaluate its performance on prediction tasks from the behavioural experiment about human cognition. Within the discussed approach, we solve a simplified prediction problem when object classification is known in advance. Finally, we describe the experimental procedure allowing in-depth analysis of the efficiency and scalability of both search and score algorithms.