Current causal discovery approaches require restrictive model assumptions or assume access to interventional data to ensure structure identifiability. These assumptions often do not hold in real-world applications leading to a loss of guarantees and poor accuracy in practice. Recent work has shown that, in the bivariate case, Bayesian model selection can greatly improve accuracy by exchanging restrictive modelling for more flexible assumptions, at the cost of a small probability of error. We extend the Bayesian model selection approach to the important multivariate setting by making the large discrete selection problem scalable through a continuous relaxation. We demonstrate how for our choice of Bayesian non-parametric model, the Causal Gaussian Process Conditional Density Estimator (CGP-CDE), an adjacency matrix can be constructed from the model hyperparameters. This adjacency matrix is then optimised using the marginal likelihood and an acyclicity regulariser, outputting the maximum a posteriori causal graph. We demonstrate the competitiveness of our approach on both synthetic and real-world datasets, showing it is possible to perform multivariate causal discovery without infeasible assumptions using Bayesian model selection.

翻译：现有因果发现方法通常需要严格的模型假设或依赖干预数据以确保结构可识别性。这些假设在现实应用中往往难以满足，导致理论保证失效与实践准确性下降。近期研究表明，在双变量场景下，贝叶斯模型选择能够通过以柔性假设替代严格建模来显著提升准确性，仅需承受较小的错误概率代价。本研究将贝叶斯模型选择方法拓展至关键的多变量场景，通过连续松弛技术实现大规模离散选择问题的可扩展求解。我们证明，对于选定的贝叶斯非参数模型——因果高斯过程条件密度估计器（CGP-CDE），其模型超参数可构建出邻接矩阵。该邻接矩阵随后通过边缘似然与无环正则化器进行优化，最终输出最大后验因果图。通过在合成数据集与真实数据集上的实验验证，本方法展现出卓越的竞争力，证明基于贝叶斯模型选择可实现无需苛刻假设的多元因果发现。