Amortized Conditional Independence Testing

Testing for the conditional independence structure in data is a fundamental and critical task in statistics and machine learning, which finds natural applications in causal discovery - a highly relevant problem to many scientific disciplines. Existing methods seek to design explicit test statistics that quantify the degree of conditional dependence, which is highly challenging yet cannot capture nor utilize prior knowledge in a data-driven manner. In this study, an entirely new approach is introduced, where we instead propose to amortize conditional independence testing and devise ACID - a novel transformer-based neural network architecture that learns to test for conditional independence. ACID can be trained on synthetic data in a supervised learning fashion, and the learned model can then be applied to any dataset of similar natures or adapted to new domains by fine-tuning with a negligible computational cost. Our extensive empirical evaluations on both synthetic and real data reveal that ACID consistently achieves state-of-the-art performance against existing baselines under multiple metrics, and is able to generalize robustly to unseen sample sizes, dimensionalities, as well as non-linearities with a remarkably low inference time.

Enabling Causal Discovery in Post-Nonlinear Models with Normalizing Flows

Post-nonlinear (PNL) causal models stand out as a versatile and adaptable framework for modeling intricate causal relationships. However, accurately capturing the invertibility constraint required in PNL models remains challenging in existing studies. To address this problem, we introduce CAF-PoNo (Causal discovery via Normalizing Flows for Post-Nonlinear models), harnessing the power of the normalizing flows architecture to enforce the crucial invertibility constraint in PNL models. Through normalizing flows, our method precisely reconstructs the hidden noise, which plays a vital role in cause-effect identification through statistical independence testing. Furthermore, the proposed approach exhibits remarkable extensibility, as it can be seamlessly expanded to facilitate multivariate causal discovery via causal order identification, empowering us to efficiently unravel complex causal relationships. Extensive experimental evaluations on both simulated and real datasets consistently demonstrate that the proposed method outperforms several state-of-the-art approaches in both bivariate and multivariate causal discovery tasks.

Scalable Variational Causal Discovery Unconstrained by Acyclicity

Bayesian causal discovery offers the power to quantify epistemic uncertainties among a broad range of structurally diverse causal theories potentially explaining the data, represented in forms of directed acyclic graphs (DAGs). However, existing methods struggle with efficient DAG sampling due to the complex acyclicity constraint. In this study, we propose a scalable Bayesian approach to effectively learn the posterior distribution over causal graphs given observational data thanks to the ability to generate DAGs without explicitly enforcing acyclicity. Specifically, we introduce a novel differentiable DAG sampling method that can generate a valid acyclic causal graph by mapping an unconstrained distribution of implicit topological orders to a distribution over DAGs. Given this efficient DAG sampling scheme, we are able to model the posterior distribution over causal graphs using a simple variational distribution over a continuous domain, which can be learned via the variational inference framework. Extensive empirical experiments on both simulated and real datasets demonstrate the superior performance of the proposed model compared to several state-of-the-art baselines.