Variational Causal Networks: Approximate Bayesian Inference over Causal Structures

By Yashas Annadani, Jonas Rothfuss, Alexandre Lacoste, Nino Scherrer, Anirudh Goyal, Yoshua Bengio, Stefan Bauer. 2021

61 citations recorded by the source corpus.

Learning the causal structure that underlies data is a crucial step towards robust real-world decision making. The majority of existing work in causal inference focuses on determining a single directed acyclic graph (DAG) or a Markov equivalence class thereof. However, a crucial aspect to acting intelligently upon the knowledge about causal structure which has been inferred from finite data demands reasoning about its uncertainty. For instance, planning interventions to find out more about the causal mechanisms that govern our data requires quantifying epistemic uncertainty over DAGs. While Bayesian causal inference allows to do so, the posterior over DAGs becomes intractable even for a small number of variables. Aiming to overcome this issue, we propose a form of variational inference over the graphs of Structural Causal Models (SCMs). To this end, we introduce a parametric variational family modelled by an autoregressive distribution over the space of discrete DAGs. Its number of parameters does not grow exponentially with the number of variables and can be tractably learned by maximising an Evidence Lower Bound (ELBO). In our experiments, we demonstrate that the proposed variational posterior is able to provide a good approximation of the true posterior.

Subfields: Artificial Intelligence, Statistics and Probability, Probabilistic & Bayesian Methods

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Citations in the corpus

Bayesian Structure Learning with Generative Flow Networks (2022, methodology): “We call our method DAG-Accepted GFlowNet , to emphasize that the support of the distribution induced by the GFlowNet is exactly the space of DAGs, unlike some variational approaches that may sample cyclic graphs (Annadani et al., 2021; Lorch et al., 2021).”
TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Second (2022, background): “While [1] extend this representation to the space of discrete DAGs, this work is limited to a few subfamilies of SCMs while the computational complexity is high.”