Estimating Causal Bounds from Observational Data With Neural Generative Models

We introduce DeDiCa, a practical framework for efficient causal inference with discrete variables and hidden confounding that revisits classical probabilistic modeling through a tensorized parameterization of causal Bayesian networks, enabling tractable inference. Given a causal graph, DeDiCa is trained once on observational data by maximum likelihood, exactly marginalizing over hidden confounders, and can then estimate any (proxy-)identifiable interventional query. Despite this deliberately simple parameterization, DeDiCa matches state-of-the-art neural causal generative models in ATE estimation, while supporting memory-efficient CPU training and exact interventional inference in milliseconds. Compared with causal foundation models, DeDiCa scales more effectively with additional observational samples and achieves competitive accuracy at substantially lower inference time and memory. DeDiCa provides a tractable, accurate, and scalable approach to causal inference in discrete settings with hidden confounding.

Causal inference from observational data can provide strong evidence for finding the best action in a decision-making scenario without having to perform expensive randomized trials. The causal effect of an action is often not pointwise identifiable even with infinite data due to unobserved confounding factors. Furthermore, having only finitely many samples adds another layer of uncertainty to causal effect estimation. Several existing methods can be used to obtain upper and lower bounds to the causal effect, ranging from symbolic methods to the more recent neural network-based approaches, which implicitly incorporate both sources of uncertainty. However, these methods do not inform whether collecting more samples may or may not help identify the best action from observational data, leaving experts in the dark about their data collection strategies. We address this problem with a novel framework that can distinguish the range of causal effect values that might be eliminated by collecting more samples from the range of values that, with high probability, cannot be eliminated with more observational samples. We show that this partitioning can be obtained by solving max-min and min-max optimization problems. We leverage neural causal models to approximately recover this decomposition in practice. We demonstrate via experiments on synthetic and real-world datasets that our algorithm can determine when collecting more samples will not help determine the best action. Our framework can help practitioners decide when to resort to non-observational studies or seek to measure some of the unmeasured confounders for optimal decision-making.

Individual treatment effects are not point-identified from data. The Probability of Necessity and Sufficiency (PNS) circumvents this limitation by characterizing individual-level causality through intersection bounds derived from combined experimental and observational data. In finite samples, however, standard plug-in estimators systematically fail: they violate structural probability constraints and suffer from extremum bias induced by max-min operators, yielding spuriously narrow intervals. We propose a neural framework for finite-sample PNS estimation that resolves both pathologies. We introduce an anchored neural architecture that guarantees structural constraint satisfaction by construction. To correct extremum bias, we employ precision-corrected intersection-bound inference, leveraging Epistemic Neural Networks for scalable, high-dimensional uncertainty quantification. Empirical evaluations confirm that this approach maintains nominal coverage and exact constraint validity in high-dimensional regimes where standard estimators systematically undercover.