Causal Graph Learning via Distributional Invariance of Cause-Effect Relationship
Nang Hung Nguyen, Phi Le Nguyen, Thao Nguyen Truong, Trong Nghia Hoang, Masashi Sugiyama
TL;DR
The paper tackles causal graph discovery from observational data by exploiting the invariance of the effect–causal conditional $P(X\mid \mathrm{Pa}[X])$ to changes in the source-prior $P(\boldsymbol{B})$. It introduces GLIDE, a scalable framework that tests causality via variance of $P_i(X\mid Z)$ across multiple downsampled environments $D_i$, while efficiently enumerating plausible parent sets through Markov-blanket-based pruning and maximal-clique discovery in an augmented graph. Key contributions include a formal invariance test, a basis-based method to identify source variables, a principled downsampling scheme to generate augmented datasets, and a practical DFS-based search yielding $O(d^2)$ per-graph complexity. Extensive experiments on synthetic and real-world data show that GLIDE achieves comparable or better causal accuracy than state-of-the-art methods while significantly improving scalability and reducing spurious relations, including on large graphs with over a thousand variables. The approach offers a robust, model-agnostic route to scalable causal discovery with potential extensions to federated and distributed settings.
Abstract
This paper introduces a new framework for recovering causal graphs from observational data, leveraging the observation that the distribution of an effect, conditioned on its causes, remains invariant to changes in the prior distribution of those causes. This insight enables a direct test for potential causal relationships by checking the variance of their corresponding effect-cause conditional distributions across multiple downsampled subsets of the data. These subsets are selected to reflect different prior cause distributions, while preserving the effect-cause conditional relationships. Using this invariance test and exploiting an (empirical) sparsity of most causal graphs, we develop an algorithm that efficiently uncovers causal relationships with quadratic complexity in the number of observational variables, reducing the processing time by up to 25x compared to state-of-the-art methods. Our empirical experiments on a varied benchmark of large-scale datasets show superior or equivalent performance compared to existing works, while achieving enhanced scalability.