Hristo Petkov

Hristo Petkov, Colin Hanley, Feng Dong

The combinatorial search space presents a significant challenge to learning causality from data. Recently, the problem has been formulated into a continuous optimization framework with an acyclicity constraint, allowing for the exploration of deep generative models to better capture data sample distributions and support the discovery of Directed Acyclic Graphs (DAGs) that faithfully represent the underlying data distribution. However, so far no study has investigated the use of Wasserstein distance for causal structure learning via generative models. This paper proposes a new model named DAG-WGAN, which combines the Wasserstein-based adversarial loss, an auto-encoder architecture together with an acyclicity constraint. DAG-WGAN simultaneously learns causal structures and improves its data generation capability by leveraging the strength from the Wasserstein distance metric. Compared with other models, it scales well and handles both continuous and discrete data. Our experiments have evaluated DAG-WGAN against the state-of-the-art and demonstrated its good performance.

Hristo Petkov, Colin Hanley, Feng Dong

Conventional methods for causal structure learning from data face significant challenges due to combinatorial search space. Recently, the problem has been formulated into a continuous optimization framework with an acyclicity constraint to learn Directed Acyclic Graphs (DAGs). Such a framework allows the utilization of deep generative models for causal structure learning to better capture the relations between data sample distributions and DAGs. However, so far no study has experimented with the use of Wasserstein distance in the context of causal structure learning. Our model named DAG-WGAN combines the Wasserstein-based adversarial loss with an acyclicity constraint in an auto-encoder architecture. It simultaneously learns causal structures while improving its data generation capability. We compare the performance of DAG-WGAN with other models that do not involve the Wasserstein metric in order to identify its contribution to causal structure learning. Our model performs better with high cardinality data according to our experiments.

Hristo Petkov, Calum MacLellan, Feng Dong

Understanding the causal relationships between data variables can provide crucial insights into the construction of tabular datasets. Most existing causality learning methods typically focus on applying a single identifiable causal model, such as the Additive Noise Model (ANM) or the Linear non-Gaussian Acyclic Model (LiNGAM), to discover the dependencies exhibited in observational data. We improve on this approach by introducing a novel dual-step framework capable of performing both causal structure learning and tabular data synthesis under multiple causal model assumptions. Our approach uses Directed Acyclic Graphs (DAG) to represent causal relationships among data variables. By applying various functional causal models including ANM, LiNGAM and the Post-Nonlinear model (PNL), we implicitly learn the contents of DAG to simulate the generative process of observational data, effectively replicating the real data distribution. This is supported by a theoretical analysis to explain the multiple loss terms comprising the objective function of the framework. Experimental results demonstrate that DAGAF outperforms many existing methods in structure learning, achieving significantly lower Structural Hamming Distance (SHD) scores across both real-world and benchmark datasets (Sachs: 47%, Child: 11%, Hailfinder: 5%, Pathfinder: 7% improvement compared to state-of-the-art), while being able to produce diverse, high-quality samples.