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.

A location-invariant estimator of extremal quantile treatment effects for heavy-tailed distributions

Quantile treatment effects (QTEs) measure the effect of a treatment on the distribution of an outcome, and their estimation at extreme quantile levels is of central interest in applications where the target quantiles lie far beyond the range of the data. For heavy-tailed potential outcomes, existing extremal QTE estimators rely on extrapolation combined with a causal extreme value index (EVI) estimator, but the resulting estimator is not invariant under a common location shift of the potential outcome distributions, even though the population QTE is. We address this issue in two steps. First, we adapt the location-invariant Fraga estimator of the EVI to the causal setting using inverse propensity score weighting. Second, we replace the original extrapolation formula with a difference-based scheme, under which the location parameter cancels when quantile differences are taken. The resulting QTE estimator is therefore location invariant. We establish the consistency and asymptotic normality of the proposed extremal QTE estimators, and provide a consistent variance estimator, leading to asymptotically valid inference. A simulation study confirms the location invariance, the stability with respect to the threshold, and the coverage of the proposed methods.

Symmetries and Causality: Causal Effect Identification Beyond IID Data

In the natural sciences, symmetries and cause-effect relationships are ubiquitous. Yet for complex machine-learning tasks, like world-modeling in reinforcement learning, they appear difficult to harness. We propose a formal description of statistical systems based on symmetries in data leaving causal mechanisms invariant. The result is an abstract, simple and general mathematical language for causal reasoning. This paper provides formal descriptions of models and queries, setting up this language, and the formal infrastructure and strategies for their mathematically rigorous identification from data within this formalism. This approach reproduces and matches standard theoretical results on IID data and transport of experimental and non-experimental data. But its main purpose is to unify and substantially extend the scope of causal reasoning, in going beyond IID data and in approaching complex causal queries not captured by do- or soft-interventions. This new perspective on causally relevant aspects of data-modeling additionally sheds new light on well-known structures like c-components or hedges but also includes aspects of missing data and is inherently well-suited for the description of transfer and robustness properties.

Causal Foundation Models

Causal inference is the practice of estimating the effect of a treatment or intervention from data. It traditionally requires a bespoke pipeline for every new problem: first proposing a causal mechanism, selecting a compatible estimator, and finally training it. Meanwhile, across diverse settings and modalities, much of machine learning has shifted to the paradigm of foundation models: networks pretrained once at scale and applied to new tasks without fine-tuning. Causal foundation models (CFMs) bring this paradigm to causal inference. CFMs are pretrained neural networks that estimate causal quantities, such as the average treatment effect, on entirely new datasets using in-context learning without requiring model updates. This work provides a practical introduction to this emerging area. We summarize the necessary background in causal inference and machine learning before discussing CFMs. Throughout, we include example code and Jupyter notebooks.

Exploring Sparse Autoencoders in Text-Based Causal Confounding Adjustment

In many settings, studying causal questions based on text data requires adjusting for confounding information within texts. Yet there is a tradeoff in constructing text representations for adjustment: they must be sufficiently large and/or dense to preserve the confounding variables necessary for unbiased effect estimation, but sufficiently small and/or sparse to satisfy finite-sample overlap and yield low-variance estimates. To address this tradeoff, we turn to sparse autoencoders (SAEs), and propose a novel causal adjustment pipeline that iteratively selects a minimal set of SAE features via conditional independence tests. We find that SAE representations achieve better adjustments (lower bias and and higher coverage) than alternative representations in standard semi-synthetic evaluations with binary confounders, and their interpretability offers opportunities for falsification. We also introduce a more realistic semi-synthetic evaluation that uses multi-label data as the unobserved confounders and find off-the-shelf adjustment methods require increased investigation for these more complex settings. Code: https://github.com/mianzg/sae-text-confounder

When Can We Work in Embedding Space? What Text Embeddings Preserve

When do text embeddings work as inputs to empirical analysis? Their use rests on an assumption: that we can trade text for its low-dimensional embedding, and lose little in doing so. I make that assumption precise under a generative model in which documents are mixtures of latent topics. I study two uses---clustering units in embedding space and controlling for high-dimensional text. A cluster of embeddings is a set of documents with similar topic mixtures; controlling for the embedding is equivalent to controlling for the topic mixture, so validity reduces to whether that mixture captures the confounding. In an application to 363 U.S. metropolitan areas, embedding-based clusters of LLM-generated economic descriptions recover interpretable economic archetypes and separate local employment dynamics more sharply than clustering on model residuals, or on a curated set of industry and demographic covariates.

When Prediction Error Is Not Enough: Evaluating Nuisance-Function Prediction for Causal Estimation

Prediction error is widely used to evaluate nuisance-function estimators in causal inference, but its relationship with causal estimator performance may differ across performance measures. We studied this question in a partially linear model using Monte Carlo simulations. We compared ordinary least squares (OLS), generalized additive models (GAMs), XGBoost, and Double Machine Learning with XGBoost (DML-XGBoost), evaluating nuisance-function prediction error, bias, RMSE, and 95\% confidence interval coverage. We also examined a simple joint-error measure based on the absolute cross-product of estimation errors from the exposure and outcome nuisance functions. Across the simulated settings, XGBoost had the lowest RMSE among the non-oracle methods, while DML-XGBoost generally provided better confidence interval coverage. Prediction error did not consistently track causal bias across methods and settings, and the method with the best point-estimation performance did not necessarily have the best confidence interval coverage. The joint-error measure was only weakly associated with causal bias and did not provide a useful standalone measure of causal performance. These results suggest that prediction error is useful for assessing nuisance-function estimation, but it should not be treated as a direct measure of the quality of the resulting causal estimator.

When Interference Graphs Evolve: Doubly Robust Estimation of Dynamic Peer Effects

Peer effects are difficult to estimate when interaction graphs evolve because pre-assignment network history, dynamic peer exposure, and post-assignment network change have distinct causal roles. We introduce a controlled contrast framework that indexes potential outcomes by own treatment, temporally aggregated peer exposure, and a post-assignment evolution summary. Differences between the resulting means define own-treatment, peer-exposure, controlled network-evolution, and joint controlled contrasts rather than a mediation decomposition. We develop the Dynamic Network Doubly Robust estimator, DynaNet-DR, which combines a temporally factorized propensity with normalized augmentation. Under consistency, summary sufficiency, sequential exchangeability, positivity, nuisance convergence, and weak dependence, its canonical estimator is consistent when either the outcome regression or the propensity estimator is consistent. The reported implementation adds representative-score prediction, fixed clipping, and finite-sample stabilization. Semi-synthetic benchmarks on fixed real temporal graph sequences show favorable estimation accuracy among methods targeting the full profile. These benchmarks assess summary-indexed contrasts rather than counterfactual edge generation, and the MathOverflow study is an observational illustration under the stated assumptions.

Toward a Semiparametric Efficiency Theory under Equality Constraints in Nested Markov Models

Probabilistic models of Directed Acyclic Graphs (DAGs) with latent variables impose equality constraints on the observed data distribution beyond ordinary conditional independencies. These so-called Verma constraints arise in nested Markov models associated with Acyclic Directed Mixed Graphs, the latent projection of latent-variable DAGs. While nested Markov models have been extensively studied from the perspectives of graphical representation and causal identification, their implications for semiparametric efficiency theory remain less understood. We develop results toward establishing a semiparametric framework for statistical models defined by Verma constraints. Our key observation is that nested Markov constraints admit weighted conditional-moment representations under post-fixing distributions induced by graphical fixing operations. We show that fixing induces weighted orthogonality relations in L2(P), thereby converting Verma constraints into explicit tangent-space restrictions. Building on this representation, we characterize the tangent-space orthocomplement for models defined by a single nested Markov constraint through residualized weighted moment functions. This geometric formulation yields Hilbert-space characterizations of semiparametric efficient influence functions and efficiency bounds via orthogonal projection and equivalent minimum-variance formulations. We further discuss extensions to models involving multiple nested Markov constraints, for which we characterize a subspace of the orthocomplement as sums of the corresponding weighted orthogonality relations, while leaving the complete tangent-space characterization open. More broadly, our results connect nested graphical structure with semiparametric Hilbert-space geometry and provide a foundation for a general efficiency theory for nested Markov models. We illustrate the framework through several latent-variable DAGs.

Scalable and Versatile Identification for Hierarchical Structural Causal Models: A New Look at Project STAR

The STAR (Student-Teacher Achievement Ratio) experiment (1985, Tennessee, USA) is a landmark hierarchical dataset designed to assess the impact of class size on student outcomes, with observations nested within classes. To encode class-level interventions in such hierarchical settings, we develop a complete, scalable, open-source pipeline for Hierarchical Structural Causal Models (HSCM) that bridges symbolic identification and practical estimation. Our approach integrates graph transformations, pyAgrum's do-calculus for automatic identification of causal effects, adaptation of symbolic expression into closed-form HSCM formulas, and numerical estimation from fitted local probability models. A key innovation is our adapted Abstract Syntax Tree (AST), which decomposes pyAgrum's identified formulas into independent density, expectation, and marginalization tasks, enabling parallel and scalable computation. We validate the pipeline on canonical HSCM motifs and benchmark scenarios with known ground truth, then apply it to STAR kindergarten mathematics outcomes. The results show that flat baselines (ignoring hierarchy) recover associations but fail to encode class-level interventions, and that symbolic identification alone is not enough for practical Hierarchical Structural Causal inference; scalable estimation and numerical stability checks are central parts of the scientific object.

Partial Identification under Causal Orders by Linear Programming

Non-parametric (partial) identification of counterfactual queries typically relies on a fully specified causal graph. Motivated by settings with incomplete domain knowledge, we challenge this requirement by leveraging structural assumptions that are inherently implied by the query itself. We show that any counterfactual inquiry induces a, mostly partial, topological ordering over relevant variables, which, in turn, enables an explicit query parametrisation reducing the identification task to a linear program. This allows bounding arbitrary counterfactual and nested counterfactual queries. Our work can be viewed as a generalisation of the classical bounding framework of Tian and Pearl (2000), originally developed for probabilities of causation. We also prove the \emph{tightness} of our bounds by constructing structural causal models that attain the bounds whilst being compatible with both the observed data and the query-implied order. To assess both the generality and practical utility of the proposed bounding procedure, we revisit several case studies from the literature, demonstrating how the derived bounds can be used to yield informative insights even in the absence of an input causal graph.

Counterfactual Evaluation of Temporal Observation Protocols

We study counterfactual protocol evaluation: whether data collected under a realised observation protocol determine the predictive value of alternatives that were never deployed. Protocol value is the population $R^2$ of the Bayes-optimal predictor of a fixed trajectory-level target from the measurements an alternative would collect. We show that even infinite benchmark data need not determine this value: distinct latent covariance structures can induce the same benchmark measurement--target law while assigning different values to the same alternative. We develop a value-specific identification theory in which only latent ambiguity that changes the alternative's value matters. For linear targets, invisible covariance directions certify non-identification, while targeted measurements can restore identification without recovering the full latent covariance; an exact permutation construction extends the result to nonlinear aggregate targets. With finite dense calibration data, uniform error bounds control protocol-selection regret and distinguishable value gaps. Exact marginal gains then support cost-constrained, target-aware observation design. Simulations and retrospective analyses of Sleep-EDF and Long-Term AF show that broad temporal-layout differences can be more reliably distinguished than fine placements selected from finite data. Together, these results connect identification, calibration resolution and observation design for undeployed protocols.

Barycentric Fused Gromov-Wasserstein Balancing for Causal Inference under Multiple Treatments

Estimating heterogeneous single and interaction treatment effects from observational data under multiple simultaneous treatments is crucial for decision-making. To mitigate estimation variance, previous studies balance representation distributions between every pair of treatment patterns. However, such pairwise balancing scales quadratically with the number of treatment patterns and fails to preserve consistent local proximity structures across patterns, which degrades counterfactual estimation. To address these challenges, we propose the Causal Inference for Heterogeneous Single and Interaction Treatment Effects Network (CIHSI-Net), a deep learning framework built on a novel Barycentric Fused Gromov-Wasserstein Balancing (BFG-WB) objective. BFG-WB aligns the representation distribution of each treatment pattern with a shared Wasserstein barycenter, achieving global alignment while reducing the computational complexity from quadratic to linear, and its Fused Gromov-Wasserstein discrepancy preserves the local proximity structures essential for reliable heterogeneous effect estimation. Simulation studies show that CIHSI-Net consistently outperforms state-of-the-art baselines, and an application to real-world marketing data demonstrates its practical utility in complex multi-treatment scenarios.

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.

Let Time Tell: Identification and Gaussian Process Estimation for Interrupted Time Series

We study causal inference in interrupted time series designs where a treatment affects every unit simultaneously, so that the contemporaneous controls used by difference-in-differences and synthetic control are unavailable and the counterfactual must be extrapolated from a unit's own pre-treatment history. We establish identification within the potential outcomes framework and estimate the counterfactual by Gaussian process regression. Rather than committing to a single best-fitting trend, the estimator retains the functions consistent with the pre-treatment series and widens its intervals where extrapolation magnifies their divergence. Connecting it to reproducing kernel Hilbert space theory, we derive a bias decomposition that isolates the component extrapolation inflates and a worst-case bound on that component, justifying the Gaussian process estimator's posterior variance as extrapolation-aware uncertainty quantification. In closed form, the band equals the worst-case divergence the model class permits among functions consistent with the pre-treatment data. The method is illustrated with calibrated simulations and an analysis of handgun purchases after the Supreme Court's Heller decision, a universal treatment whose practical effect concentrates in a single jurisdiction. An R package, gpss, implements the approach.

Causal Generalization of Continuous Treatment Effects under Covariate Shift

Average dose-response functions are widely used to summarize causal effects of continuous treatments, but most existing methods assume that the observed sample represents the target population. We study a covariate-shift setting in which covariates, treatment, and outcome are observed in a labelled source sample, while only covariates are observed in the target sample. We develop a two-sample local polynomial regression framework based on pseudo-outcomes that use source outcomes to address confounding and target covariates to define the population of interest. We further propose a source-to-target extension of distance covariance optimal weighting (DCOW), designed to remove treatment-covariate dependence in the source sample while aligning the weighted source covariate distribution with the target population. A central theoretical contribution is a weight-level analysis of this optimization-based procedure: we show that the population criterion identifies the oracle source-to-target weights and that approximate empirical minimizers, including exact minimizers as a special case, converge uniformly to these weights under regularity conditions. We also establish consistency and asymptotic normality of the resulting estimator. Simulations show that the proposed method improves target dose-response estimation relative to DCOW, generalized-propensity-score weighting, entropy balancing, and unweighted alternatives. We illustrate the method in a county-level analysis of PM2.5 exposure and subsequent heart-disease mortality using a source-target validation design.

Transportable Causal Effect Estimation across Networks under Interference

Estimating causal effects under network interference typically assumes that the network used for training and the network used for deployment coincide. In practice, an intervention is run on one population while the question of interest concerns a different population, and the two generally differ in topology, node-covariate composition, and spillover pathways. Transporting a causal effect across networks is therefore a data-fusion problem that no existing algorithm solves. We employ a selection diagram, extended to the network setting so that covariate shift and structural network shift enter as separate selectors, and derive from it a transport formula for the direct, spillover, and total effects in the deployment population. Each formula makes explicit which interventional mechanism is assumed invariant and which observational distribution must be reweighted. We then turn the formulas into TranCE (Transported Causal Effects), a doubly-robust algorithm combining an interventional outcome model, a domain density-ratio correction, and cross-fitted inference. Extensive experiments on two semi-synthetic benchmarks derived from real-world social networks and on a fully real weather-insurance field experiment, where the transported effects are checked against held-out randomized estimates, confirm the effectiveness of our approach. Our findings have the potential to improve intervention strategies in networked systems, particularly in social networks and public health.

How Many Samples Are Needed to Determine Causal Direction? Sharp Minimax Bounds for Bivariate LiNGAM

We study how many observations are needed to determine the causal direction between two linearly related variables. Classical LiNGAM theory shows that independent non-Gaussian disturbances identify the direction, but does not quantify the difficulty when the causal effect is weak or the disturbances are nearly Gaussian. Let $β$ bound the absolute structural coefficient from below, let $ν$ measure each standardized disturbance's distance from Gaussianity, and let the disturbance scales lie in $[\underlineσ,\overlineσ]$. We prove the sharp local minimax law \[ N_2^\star(β,ν,δ) \asymp \frac{\log(1/δ)} {d_β^2+β^2ν^2}, \qquad d_β= \left[β^2- \left(1-\frac{\underlineσ^2}{\overlineσ^2}\right)\right]_+. \] Previous theory established population identifiability or assumed a fixed separation between the two directions. By contrast, we establish the sharp sample complexity as a joint function of edge strength, distance from Gaussianity, and scale uncertainty, and characterize when identification comes from non-Gaussian dependence or from covariance alone. The proof was independently generated with GPT-5.6 Sol in Codex's Ultra mode during a two-hour session. The human author supplied the prompt and was responsible only forchecking the proof and revising and polishing the manuscript.

Generalised Transportability via Causal Abstractions

Transporting a causal conclusion from a source study population to a target one is a fundamental problem in causal inference. The theory of transportability provides a criterion for when this is possible: given experimental data from the source and observational data from the target, it determines whether a target query is identifiable and does so completely; i.e. if the query can be transported, the criterion finds the exact formula. However, it works one query at a time and returns an expression rather than the value itself. It is also silent in two practically important regimes: when the query is not transportable and when no target data exist at all. To tackle both, we take a model-level perspective grounded in Causal Abstraction theory. Source and target share variables, graph, and interventions, differing only at a known set of mechanisms, which makes transportability a special case of same-level abstraction. Thus, instead of asking whether one query transports, we ask whether a single map aligns the source and target across their interventional behaviour. We characterise when such a map exists in both the Markovian and semi-Markovian settings; when it does, every target query transports at once. Our main contribution lies in the approximate case. When no exact map exists, the best approximate one still yields certified query intervals, recasting abstraction error as a quantitative notion of approximate transportability. We formulate model-level transport as distributionally robust optimisation over mechanism and environment perturbations of the unseen target and derive certificates for both challenging regimes: bounds for non-transportable queries, and guarantees under target-agnostic settings. We evaluate our framework on synthetic Markovian and semi-Markovian benchmarks and a real ecological dataset, and we show that the certified intervals bracket the true interventional query.

Doubly Robust Estimation of Causal Effect on CVR with Targeted Regularization

Post-click conversion rate (CVR) is a key metric in various scenarios including e-commerce and advertising, reflecting the efficiency and user experience in the second stage of the conversion process. Estimating the causal effect on CVR is therefore of great practical importance. However, directly applying existing causal inference methods to clicked samples introduces sample selection bias and increased variance due to the exclusion of non-click data. Recent studies on CVR prediction introduce "ideal loss", which optimizes model parameters using an unbiased estimate of the loss over the full sample. Nevertheless, there is no guarantee that unbiasedness of the loss implies unbiasedness of the final estimator. We revisit this challenge from the perspective of semiparametric theory. Specifically, we develop a new doubly robust causal effect estimator for chain-structured outcomes such as CVR, and derive its theoretical properties in detail. It achieves a faster convergence rate compared to nuisance parameters estimation and is therefore more robust when using flexible nonparametric estimators, including neural networks. Based on these theoretical findings, we further design a framework based on targeted regularization to improve numerical stability and practical applicability. Extensive experiments on synthetic and real-world data demonstrate the effectiveness and robustness of our method. In addition, we find that naively combining loss debiasing with standard causal estimators underperforms our method, highlighting the necessity of developing the new estimator tailored to this CVR-style objective with solid theoretical guarantees.

CAS: A Causal Attribution Score for Local and Global Explainable Artificial Intelligence

Predictive explanation methods attribute a model output; they do not, by themselves, attribute an intervention effect on the real-world outcome. We introduce the Causal Attribution Score (CAS), a compact score architecture for causal explanation. CAS starts from an identified interventional coalition game, allocates the joint intervention contrast with causal Shapley contributions, and converts those raw outcome-scale effects into Local CAS, Signed Local CAS, and two complementary Global CAS summaries. The innovation is not a new Shapley formula, but a local-to-global causal reporting layer with an explicit intervention target. In the known-truth benchmark, eight repeated primary-interaction simulations (n = 2,200 each, three actions) gave mean Local CAS MAE of 0.107 for coalition-aware CAS, compared with 0.173 for one-at-a-time normalisation and 0.213 for a global normalised absolute ATE vector. The paired advantage over one-at-a-time normalisation increased from -0.003 under additivity to 0.091 under strong interactions. On both empirical DoubleML datasets, 401(k) eligibility/net financial assets (n = 9,915) and Pennsylvania reemployment bonus/unemployment duration (n = 5,099), predictive SHAP/TreeSHAP rankings differed materially from Feature-CAS rankings of treatment-effect modifiers. In Pennsylvania, dep1 (exactly one dependent) moved from predictive global rank 13 to Feature-CAS rank 2 and was the leading local Feature-CAS modifier. These results isolate the added value of separating what predicts the outcome from what explains heterogeneity in an estimated causal effect.

COMPACT: Spectral Adjustment Scores from a Complete and Irreducible Causal Criterion

Observational datasets frequently contain many baseline variables, yet investigators estimating causal effects may not know which variables to include in the adjustment set. Confounding information may also be distributed weakly across many variables. Propensity scores can simplify adjustment by reducing high-dimensional covariates to a scalar with binary treatment. Although the propensity score is the coarsest balancing score, this distributional optimality does not imply maximal specificity over causal graphs. We instead examine all causal graphs among a candidate score, treatment, and outcome while allowing latent variables. Under faithfulness, we identify the largest set of unconditional and conditional dependence relations whose truth is invariant to whether treatment causes the outcome, leaving treatment-effect estimation to the downstream analysis. This criterion defines the maximally specific graph class expressible through these relations. We then develop the proposed algorithm, which operationalizes the criterion through a generalized eigenvalue problem whose score space targets the span of a balancing coordinate and an outcome-guided coordinate. We show that sufficiently informative proxies can recover this span without direct observation of the adjustment variables, characterize the resulting estimation and causal errors, and establish bootstrap validity for the complete procedure. Simulations and a real-data application demonstrate superior performance over several alternatives.

CLAM: Causal Spatial Disaggregation to Infer Local Effects From Coarse Data

Learning fine-grained spatial patterns from coarse-resolution data is challenging, especially in causal settings where high-resolution effects must be inferred from aggregated interventions and outcomes. We introduce CLAM, a method for estimating localized causal effects from coarse observations by exploiting high-resolution contextual covariates that modulate these effects. By jointly learning the causal mechanism and a disaggregation mapping, CLAM captures interactions that are missed when addressing these problems independently. The method supports localized effect estimation, counterfactual reasoning, and principled outcome disaggregation, and reliably captures spatially varying causal effects across diverse settings. This is particularly relevant for applications such as public health and environmental policy, where decisions are made at broad scales despite substantial local heterogeneity. Code is available at https://github.com/gerritgr/clam

Adversarial Causal Intervention Falsification

Generative models can reproduce an observational distribution while encoding an incorrect causal structure. We study a sequential game in which a structural causal generator proposes observational and interventional distributions, while an adversarial experimentalist selects interventions intended to maximally falsify the generator. The discriminator is therefore not merely a real-versus-synthetic classifier: it is indexed by an intervention and tests whether the generator reproduces the corresponding post-intervention law. We introduce Adversarial Causal Intervention Falsification (ACIF), formulate oracle and implementable versions of the game, and distinguish three objects that are often conflated: observational fit, interventional equivalence over an admissible query class, and point identification of a structural causal model. For finite model and intervention classes, we prove: (i) an exact reduction of the adversarial objective to a worst-intervention integral probability metric; (ii) identification up to interventional equivalence, with point identification under a separating intervention family; (iii) existence of mixed-strategy equilibria; (iv) finite-sample uniform convergence and margin-based model-selection guarantees; and (v) a logarithmic elimination guarantee for a disagreement-driven sequential design under a balanced-separation condition. We also give a complete linear-Gaussian example in which two observationally indistinguishable causal directions are separated by a single well-chosen intervention. The framework clarifies what an adversarial causal discriminator can and cannot certify, and provides a principled bridge between causal generative modeling, active causal discovery, and experimental design.

A Unified Causal Inference Framework for the Desirability of Outcome Ranking Paradigm in Benefit-Risk Evaluation

We developed a unified covariate-adjusted causal inference framework for estimating the desirability of outcome ranking (DOOR) probability for benefit-risk evaluation in randomized trials and observational studies. The framework expresses the DOOR probability as a bilinear functional of the marginal ordinal outcome distributions under the two treatment strategies, estimates conditional ordinal distributions through sequential risk-set hazards, and derives the efficient influence function (EIF) of the DOOR probability. The point-estimation simulations compared G-computation, normalized inverse probability weighting (IPW), augmented IPW (AIPW), and targeted maximum likelihood estimation (TMLE), with nuisance functions estimated using generalized linear models or Super Learner (SL). TMLE-SL showed the strongest and most consistent point-estimation performance, with AIPW-SL ranking second. EIF-based inference was then evaluated for AIPW-SL and TMLE-SL, with and without cross-fitting, across settings varying in overlap, treatment-effect heterogeneity, and treatment allocation. CVTMLE-SL showed the strongest overall performance across DOOR-scale bias, recovery of the underlying ordinal distributions, standard-error accuracy, and confidence-interval coverage. We illustrate the methodology using data from the multidrug-resistant organism network of the Antibacterial Resistance Leadership Group.

Causal Inference with Unstructured Outcomes

Causal inference has traditionally centered on scalar outcomes: whether a patient recovers, how much a worker earns, or how many visits a website receives. Modern studies increasingly ask causal questions about outcomes with richer form, such as clinical notes, open-ended survey responses, and images. A hospital may want to know how an AI documentation tool changes the notes physicians write, or how a nurse training program alters what patients say in survey responses. For such outcomes, the usual average treatment effect is ill-defined: one cannot meaningfully subtract one text or image from another. To this end, we propose a causal query for unstructured outcomes. The key idea is to learn what features of the outcome are most causally affected by the treatment, which we call the maximally contrasting feature (MCF). To estimate the MCF, we learn a feature-scoring function that maps each outcome to a scalar and exposes the sharpest contrast between treated and control potential outcomes. We develop identification conditions and estimation algorithms for this query, and extend it to heterogeneous effects by allowing the feature-scoring function to depend on observed covariates. We also handle settings where both the treatment and the outcome are unstructured. Empirical studies on text and images show that the algorithm recovers salient aspects of an outcome changed by a treatment.

Calibrated Bayesian Inference for Stochastic Intervention Effects

Causal inference increasingly extends beyond classical causal effects defined by deterministic treatment assignments, such as the average treatment effect, to stochastic intervention effects that can weaken positivity requirements and offer greater policy relevance. Nonparametric Bayesian models are attractive for estimating these effects due to their flexibility and inherent uncertainty propagation, but this posterior uncertainty need not be well calibrated for the causal effect of interest. We develop a simple post-processing correction that can be applied to posterior samples without changing the prior or fitting algorithm. We prove that, for a broad class of stochastic interventions, the corrected posterior yields asymptotically efficient inference and credible intervals with asymptotically valid frequentist coverage; formally, it satisfies a semiparametric Bernstein-von Mises theorem. The theory covers interventions specified independently of the observed treatment process, as well as interventions that modify it, including incremental propensity score interventions and a new power-tilt intervention. A central contribution is new theory for SoftBART, including conditions under which this flexible tree-based Bayesian model supports calibrated Bayesian inference for stochastic intervention effects. In simulations, the correction reduces bias and improves coverage relative to the uncorrected Bayesian analysis while remaining competitive with frequentist alternatives. We illustrate the method by estimating how expected LDL cholesterol would change under hypothetical increases or decreases in the odds of receiving statin therapy.

Spatiotemporal Proximal Causal Inference under Hidden Confounding and Interference

Estimating causal effects from real-world spatiotemporal data is challenging due to hidden confounders and interference. Standard causal identification methods assume conditional exchangeability given observed covariates, which fails whenever hidden confounders affect both treatment and outcomes - a common setting in domains such as climate, environmental policy, epidemiology, and regional economics. In this paper, we propose a novel spatiotemporal proximal causal inference framework that extends proximal identification theory to spatiotemporal settings. The proposed method jointly captures local and neighborhood-level confounding information by introducing treatment- and outcome-inducing proxies, and we derive a spatiotemporal outcome confounding bridge function that identifies the potential outcome without requiring direct recovery of the hidden confounder. We establish the identifiability of this bridge function under proxy exclusion restrictions and a spatiotemporal completeness condition, and show that the resulting estimator recovers the outcome through a proximal generalization of the g-computation formula. To operationalize this identification result, we propose a neural architecture that learns proxies via transformer-based spatiotemporal encoders - coupled with a conditional mutual information critic to enforce exclusion restrictions and a moment-matching network to guarantee that the learned bridge function satisfies the underlying identifying equation. We further introduce a stabilized weighting scheme to address treatment support imbalance. Experiments on synthetic datasets demonstrate that our approach achieves comparable performance to baseline causal inference methods, while providing, to our knowledge, the first theoretically grounded outcomes for the hidden confounding in the presence of spatiotemporal interference through a proximal causal inference framework.

UpliftBench: Revealing Outcome-Regime and Objective Mismatch in Uplift Evaluation

Uplift modeling (conditional-average-treatment-effect estimation) drives personalized targeting, yet published uplift benchmarks frequently disagree on which estimator performs best; we show the disagreement is substantially about metrics, not models. UpliftBench evaluates 12 uplift estimators under an outer-test-isolated, multi-objective protocol across seven dataset families; its two findings are identified where a reference objective exists -- F1 on the standard continuous benchmark (IHDP), F2 in a within-sample case study on Jobs. On that benchmark, Qini shows no detectable alignment with effect accuracy -- across all 100 IHDP realizations its mean rank correlation with effect accuracy is +0.07, 95% CI [-0.03, +0.16] -- while AUUC is consistently more aligned (paired prefix-mean-AUUC-over-Qini gap +0.49 [+0.40, +0.59]; the shipped cumulative-gain AUUC aligns better still, +0.73). On Jobs, ranking metrics are structurally insufficient for a sign-threshold policy because they discard the score level; empirically, within the released split-rotation analysis direct policy-risk selection yields lower benchmark regret than random model selection while Qini, AUUC, and uplift-at-$k$ do not (14-15% regret). Calibrating the decision threshold removes 81% of the Qini-selection regret. Both findings are bounded, not universal: F1 is not detected on either validation family (the ACIC and Revenue-Synthetic gaps are both indistinguishable from zero), and F2 vanishes under a budgeted-value objective where rank suffices. UpliftBench releases versioned loaders, fixed protocols, result artifacts, and a reproducible living leaderboard; the public repository accompanies the paper.

Augmented Inverse Hybrid Weighting: Robust Inference under Deterministic and Random Distribution Shifts

Reweighting source samples to match a target covariate distribution is a standard response to distribution shift when generalizing evidence from one population to another. This strategy is well suited to deterministic, learnable covariate discrepancies, but can be insufficient when source--target population differences also contain changes beyond covariate shift or when estimation of the density-ratio weights is unstable. To address this challenge, we introduce a new model that allows non-systematic changes between two population laws after systematic shifts are accounted for. Such residual shift is modeled as random perturbations to the probability space that cannot be represented in a learnable way. In this way, we separate systematic shifts, treated as bias and corrected by reweighting, from residual random perturbations, treated as distributional uncertainty and handled through dataset pooling. Under pure random perturbations, this principle yields Augmented Inverse Distance Weighting (AIDW), which uses regression augmentation and variance-optimal dataset-level pooling. For mixed shifts, we develop Augmented Inverse Hybrid Weighting (AIHW), which interpolates between AIDW and standard augmented importance weighting. Both methods trade off sampling uncertainty and distributional uncertainty via a \emph{distributional distance} that describes the strength of random perturbations. We establish asymptotic properties of the methods, together with plug-in guidance for choosing tuning parameters and model diagnostic tools. Experiments on three real-world multi-site datasets demonstrate consistent reductions in mean-squared error compared with standard weighting baselines, along with substantially improved empirical coverage in settings where covariate-shift adjustment alone undercovers, showing the robustness of the proposed methods across diverse distribution shift scenarios.