Effective Bayesian Causal Inference via Structural Marginalisation and Autoregressive Orders
This work addresses computational bottlenecks in Bayesian causal inference for researchers and practitioners, though it is incremental as it builds on existing marginalisation techniques with specific improvements.
The paper tackled the computational challenge of Bayesian causal inference by decomposing structure marginalisation into orders and DAGs, using a novel auto-regressive distribution for orders and closed-form marginalisation for DAGs. It outperformed state-of-the-art methods on simulated benchmarks and achieved competitive results on real-world data, with accurate inference of interventional distributions and causal effects.
The traditional two-stage approach to causal inference first identifies a single causal model (or equivalence class of models), which is then used to answer causal queries. However, this neglects any epistemic model uncertainty. In contrast, Bayesian causal inference does incorporate epistemic uncertainty into query estimates via Bayesian marginalisation (posterior averaging) over all causal models. While principled, this marginalisation over entire causal models, i.e., both causal structures (graphs) and mechanisms, poses a tremendous computational challenge. In this work, we address this challenge by decomposing structure marginalisation into the marginalisation over (i) causal orders and (ii) directed acyclic graphs (DAGs) given an order. We can marginalise the latter in closed form by limiting the number of parents per variable and utilising Gaussian processes to model mechanisms. To marginalise over orders, we use a sampling-based approximation, for which we devise a novel auto-regressive distribution over causal orders (ARCO). Our method outperforms state-of-the-art in structure learning on simulated non-linear additive noise benchmarks, and yields competitive results on real-world data. Furthermore, we can accurately infer interventional distributions and average causal effects.