Constraint-based causal discovery is widely used for learning causal structures, but heavy reliance on conditional independence (CI) testing makes it computationally expensive in high-dimensional settings. To mitigate this limitation, many divide-and-conquer frameworks have been proposed, but most assume causal sufficiency, i.e., no latent variables. In this paper, we show that divide-and-conquer strategies can be theoretically generalized beyond causal sufficiency to settings with latent variables. Specifically, we propose a recursive decomposition framework, termed DiCoLa, that enables divide-and-conquer causal discovery in the presence of latent variables. It recursively decomposes the global learning task into smaller subproblems and integrates their solutions through a principled reconstruction step to recover the global structure. We theoretically establish the soundness and completeness of the proposed framework. Extensive experiments on synthetic data demonstrate that our approach significantly improves computational efficiency across a range of causal discovery algorithms, while experiments on a real-world dataset further illustrate its practical effectiveness.

Graph property prediction tasks are important and numerous.

Graph Neural Networks (GNNs) often suffer from weak-generalization due to sparsely labeled data despite their promising results on various graph-based tasks. Data augmentation is a prevalent remedy to improve the generalization ability of models in many domains. However, due to the non-Euclidean nature of data space and the dependencies between samples, designing effective augmentation on graphs is challenging. In this paper, we propose a novel framework Metropolis-Hastings Data Augmentation (MH-Aug) that draws augmented graphs from an explicit target distribution for semi-supervised learning. MH-Aug produces a sequence of augmented graphs from the target distribution enables flexible control of the strength and diversity of augmentation. Since the direct sampling from the complex target distribution is challenging, we adopt the Metropolis-Hastings algorithm to obtain the augmented samples. We also propose a simple and effective semi-supervised learning strategy with generated samples from MH-Aug. Our extensive experiments demonstrate that MH-Aug can generate a sequence of samples according to the target distribution to significantly improve the performance of GNNs.

Extensive experiments across six real-world scenarios demonstrate our method's

We propose a novel framework for structured node classification called DPM-SNC.

Graph property prediction tasks are important and numerous.