Effective Bayesian Causal Inference via Structural Marginalisation and Autoregressive Orders
TL;DR: We propose ARCO-GP, combining an autoregressive model over causal orders with Gaussian Processes into an effective method for Bayesian causal inference, incorpoating epistemic uncertainty into causal estimates.
Abstract: 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.
Submission Number: 1591
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