Hybrid Global Causal Discovery with Local Search

Learning the unique directed acyclic graph corresponding to an unknown causal model is a challenging task. Methods based on functional causal models can identify a unique graph, but either suffer from the curse of dimensionality or impose strong parametric assumptions. To address these challenges, we propose a novel hybrid approach for global causal discovery in observational data that leverages local causal substructures. We first present a topological sorting algorithm that leverages ancestral relationships in linear structural equation models to establish a compact top-down hierarchical ordering, encoding more causal information than linear orderings produced by existing methods. We demonstrate that this approach generalizes to nonlinear settings with arbitrary noise. We then introduce a nonparametric constraint-based algorithm that prunes spurious edges by searching for local conditioning sets, achieving greater accuracy than current methods. We provide theoretical guarantees for correctness and worst-case polynomial time complexities, with empirical validation on synthetic data.

Regularized Data Programming with Bayesian Priors

The cost of manual data labeling can be a significant obstacle in supervised learning. Data programming (DP) offers a weakly supervised solution for training dataset creation, wherein the outputs of user-defined programmatic labeling functions (LFs) are reconciled through unsupervised learning. However, DP can fail to outperform an unweighted majority vote in some scenarios, including low-data contexts. This work introduces a Bayesian extension of classical DP that mitigates failures of unsupervised learning by augmenting the DP objective with regularization terms. Regularized learning is achieved through maximum a posteriori estimation in the Bayesian model. Results suggest that regularized DP improves performance relative to maximum likelihood and majority voting, confers greater interpretability, and bolsters performance in low-data regimes.