Bayesian causal inference, i.e., inferring a posterior over causal models for
the use in downstream causal reasoning tasks, poses a hard computational
inference problem that is little explored in literature. In this work, we
combine techniques from order-based MCMC structure learning with recent
advances in gradient-based graph learning into an effective Bayesian causal
inference framework. Specifically, we decompose the problem of inferring the
causal structure into (i) inferring a topological order over variables and (ii)
inferring the parent sets for each variable. When limiting the number of
parents per variable, we can exactly marginalise over the parent sets in
polynomial time. We further use Gaussian processes to model the unknown causal
mechanisms, which also allows their exact marginalisation. This introduces a
Rao-Blackwellization scheme, where all components are eliminated from the
model, except for the causal order, for which we learn a distribution via
gradient-based optimisation. The combination of Rao-Blackwellization with our
sequential inference procedure for causal orders yields state-of-the-art on
linear and non-linear additive noise benchmarks with scale-free and Erdos-Renyi
graph structures.

贝叶斯因果推断结合基于序的 MCMC 结构学习和基于梯度的图学习技术，提出了一个有效的因果推断框架，可以推断变量的拓扑次序和父集，限制每个变量的父集数量，可以在多项式时间内精确计算边缘化。使用高斯过程对未知因果机制进行建模，引入 Rao-Blackwell 化方案，通过基于梯度的优化学习因果次序分布，采用顺序推断并结合 Rao-Blackwell 化，能够在具有无标度和 Erdos-Renyi 图结构的线性和非线性加性噪声基准测试中达到最先进的效果。