Bipartite graphical causal models: beyond causal Bayesian networks and structural causal models

          @misc{ pirsa_PIRSA:24090085,
            doi = {10.48660/24090085},
            url = {https://pirsa.org/24090085},
            author = {},
            keywords = {Quantum Foundations, Quantum Information},
            language = {en},
            title = {Bipartite graphical causal models: beyond causal Bayesian networks and structural causal models},
            publisher = {Perimeter Institute},
            year = {2024},
            month = {sep},
            note = {PIRSA:24090085 see, \url{https://pirsa.org}}
          }
          

Abstract

Based on the immense popularity of causal Bayesian networks and structural causal models, one might expect that these representations are appropriate to describe the causal semantics of any real-world system, at least in principle. In this talk, I will argue that this is not the case, and motivate the study of more general causal modeling frameworks. In particular, I will discuss bipartite graphical causal models. Real-world complex systems are often modelled by systems of equations with endogenous and independent exogenous random variables. Such models have a long tradition in physics and engineering. The structure of such systems of equations can be encoded by a bipartite graph, with variable and equation nodes that are adjacent if a variable appears in an equation. I will show how one can use Simon’s causal ordering algorithm and the Dulmage-Mendelsohn decomposition to derive a Markov property that states the conditional independence for (distributions of) solutions of the equations in terms of the bipartite graph. I will then show how this Markov property gives rise to a do-calculus for bipartite graphical causal models, providing these with a refined causal interpretation.