A Computationally Feasible Framework for Causal Probabilistic Explanation

Explaining why a specific outcome occurred, and which inputs deserve the blame or credit, is central to philosophical, scientific, and policy analysis. Existing tools split into two camps. The theory of actual causality (AC) gives principled verdicts, but only for toy-sized models, because computing them requires enumerating counterfactual scenarios. Scalable attribution methods like SHAP (or even causal SHAP) at least partially ignore the causal structure that generated the data, and can give answers that conflict with a careful causal analysis. We close this gap with Probabilistic Causal Impact (PCI). PCI builds on actual causality and on Pearl's notions of probability of necessity and sufficiency, but recasts the question of explainability as an estimation problem on a probabilistic causal model that is easily approximated via Monte Carlo. By specifying a distribution over "candidate explanations," a distribution over counterfactual values, and a scoring function, PCI provides tractable, causally grounded, graded explanations, generalizing AC and Pearl's probability of causation as degenerate cases. We evaluate PCI in synthetic and real-world examples, spanning consistency checks with AC, scaling experiments, complex continuous-valued dynamical systems, and a real-world deployed causal machine learning model trained on millions of datapoints.

Foundation Models for Partial Causal Identification

This paper investigates the development of causal foundation models for bounding the effect of interventions and counterfactuals from observational data. We show that a canonical prior can be defined with full support over the space of structural causal models with discrete observables. With this canonical prior, we translate the problem of bounding counterfactuals into that of learning distributions over functions that map data (and possibly structural assumptions) to a causal query of interest. This extends the promising causal foundational modelling paradigm to the estimation of partially-identifiable causal effects, i.e., under unobserved confounding, where multiple values are equally compatible with the observed data and prior structural assumptions.

Orca: Neural Operators for Causal Reasoning in Continuous Time

Structural causal models are the standard language for reasoning about interventions and counterfactuals, but they describe static variables, typically measured once, and usually forbid cyclic dependencies. Many systems we care about, such as patients, climates, and economies, instead evolve continuously in time, are observed at irregular time points, and contain feedback loops. We argue that neural operator learning provides a natural foundation for causal reasoning in this setting, and propose Orca, a framework in which each node of the causal graph is a function of time and each mechanism is a learned map between function spaces. We extend existing neural operator architectures to express causal mechanisms: a mechanism computes the function value of a node from its parent nodes by taking several parent functions as input, respects the arrow of time, and treats latent exogenous noise as a function that can be inferred and reused for counterfactuals. We formalize the model class and demonstrate counterfactual reasoning on synthetic continuous-time examples. Code is available at https://github.com/gerritgr/orca

DoTime: A Synthetic Benchmark Generator for Interventional and Counterfactual Time Series

Most benchmarks for causal inference over time series are observational, small, or domain-specific, leaving interventional and counterfactual estimation under-served exactly where it matters most, such as in healthcare, policy evaluation, and climate science. We introduce \textbf{DoTime}, an open, scalable, and theoretically grounded generator of multivariate temporal structural causal models (TSCMs) with interventions, released as the \code{dotime} PyPI package together with four frozen evaluation suites. Beyond existing work, it adds capabilities absent from prior generators: continuous-time intervention \emph{windows}, counterfactual sampling modes with a positivity guard, regime-switching SCMs as a strict generalization of interrupted time series, non-stationary dynamics by construction with switching SCM parameters, and deterministic ramp and sinusoidal intervention profiles that place trends and structural breaks \emph{inside} the evaluation window. Moreover, it demonstrates the suitability of the generator as a prior for a causal foundation model reference implementation. The released suites span a training-scale snapshot of $100{,}000$ trajectories and eight named identification structures, each with exact ground truth: paired interventional trajectories from the same SCM throughout, and shared-noise counterfactuals in the continuous-time suite. We ship reference baseline implementations with an evaluation harness, and pose a falsifiable claim: interventional training buys a measurable direction-accuracy advantage over an observational model of identical capacity. It is tested across three training seeds per arm. Under structure-matched evaluation on held-out episodes, the interventional prior-fitted network's (PFN) gap is positive in every structure, trajectory length, and seed tested.

WorldKernel: A World Model is the Coupling Kernel of Admissible Possible Worlds

A common assumption holds that enough observational and interventional data, given to a strong enough predictor, suffices. We report a failure mode that contradicts it. Across hundreds of structural causal models, on identified quantities a strong predictor and a Bayesian baseline both succeed, but on unidentified quantities (the couplings between counterfactual worlds) the predictor collapses to a point, on 28% of models to one no valid model can produce, while the truth is an admissible interval more data never narrows. The gap is structural: prediction cannot represent uncertainty over counterfactual couplings. We cast a world model as a single positive semidefinite coupling kernel K(T,T') over admissible worlds, whose diagonal is the ordinary posterior (what a predictor recovers) and whose off-diagonal is the cross-world coupling it cannot, which every counterfactual reads. The paper is the theory of that off-diagonal. It is real: two states with identical posteriors differ on a cross-world query, and the off-diagonal is the coupling that fixes counterfactuals. It can be bounded: positive semidefiniteness is partial-identifying information the marginals lack, and enforcing it bounds counterfactuals in polynomial time where the exact response-type program is intractable. Logical structure sharpens it: ontology axioms tighten the bound by up to a third, propagating to couplings they never touch. It can be acquired: targeted scars, constraints learned from encountered infeasibilities, close the gap several times faster than untargeted ones. Its full reconstruction is approximate counting of the admissible worlds, tractable below the Sly-Sun threshold and inapproximable above; we do not claim to beat the worst case.