Causal Effect Estimation

Estimating conditional distributional potential outcomes (CDPOs) over time is important in medicine (e.g., to estimate patient-specific risks under different treatment sequences). However, this task is challenging because of time-varying confounding, yet existing adjustment strategies for this task are limited. In this paper, we aim to learn CDPOs under time-varying treatments using flexible generative models. Our contributions are two-fold. (1) We introduce a tailored adjustment strategy for our setting, namely, generative recursive g-computation. Our adjustment strategy recursively propagates full conditional outcome distributions rather than conditional means, modeling the variables of interest directly rather than full trajectories. Building on our adjustment strategy, we formulate simple generative learners for CDPO estimation. However, these learners can be sensitive to nuisance estimation errors, which motivates an orthogonal learner. (2) We thus introduce OrthoGen, a Neyman-orthogonal and doubly robust generative learner. Importantly, we show that OrthoGen further achieves rate double robustness and quasi-oracle efficiency under suitable conditions. Our learners are flexible and can be instantiated with different generative backbones (e.g., normalizing flows and diffusion models). Across experiments with synthetic, semi-synthetic and real-world datasets, we find that OrthoGen is highly effective. To the best of our knowledge, we are the first to propose a generative orthogonal learner for estimating CDPOs under time-varying treatments.

Policy learning in digital experimentation faces three challenges: weak signal-to-noise ratios, rich covariate spaces, and massive data volumes. We formalize this regime by modeling treatment-effect estimates from increasingly fine covariate partitions as Gaussian observations with bounded signal-to-noise ratios. We establish that, in general, the optimal treatment policy is not learnable in this setting. Even learning the optimal policy value suffers from impractically slow rates. However, when treatment effects vary smoothly, we derive minimax-adaptive policies based on linear smoothers that achieve vanishing welfare regret. We demonstrate the practical value of our framework by applying it to large-scale real-world experiments at Netflix, showing that personalized linear-smoothing policies can dominate unpersonalized policies even in this challenging empirical setting.

Partial identification (PI) entails estimating bounds on causal effects by encoding different assumptions on data generation as a constrained optimization problem. Such bounds can suffice to inform policy decisions even if the causal effect itself is not identifiable. Often vacuous in practice, practitioners seek to exhaustively encode domain knowledge as additional constraints to make the PI bounds more informative. We introduce known data symmetries -- invariance of the causal effect under certain data transformations -- as a new source of constraints to inform PI. We operationalize this as a shape constraint on the causal function, and via a change of measure against which PI is posed using simple data pre-processing. Both approaches are shown to sharpen bounds under two canonical PI models. This is shown both theoretically for the population case, and via experiments in the finite-sample case. More broadly, our framework establishes data symmetries as a natural, underutilized source of background knowledge for robust causal inference.

Off-policy evaluation (OPE) for contextual bandit policies becomes challenging when action-level importance weighting incurs excessive variance. Doubly robust (DR) estimation remains unbiased under common support but retains these high-variance action-level weights. A prior estimator, Off-policy evaluation with Conjunct Effect Model (OffCEM), replaces them with more stable cluster-level weights, at the cost of relying on local correctness of the reward model. In this paper, we show that, under the assumptions required by DR and OffCEM, there exists an unbiased family of estimators that interpolates between OffCEM and DR. Building on this result, we propose the Variance Optimal-CEM (VOCEM) estimator, which selects the interpolation coefficient to minimize variance. We derive the population-optimal coefficient in closed form and show that the resulting estimator has variance no larger than either endpoint, OffCEM or DR. Experiments in controlled synthetic settings and on two large-action benchmarks show that VOCEM improves upon both endpoints in all 23 evaluated conditions, exhibiting greater stability and empirical robustness.

Evaluating the causal effect of new features is a central goal for online platforms. While recent literature addresses limited testing traffic via centralized portfolio optimization, this perspective abstracts away a critical institutional reality: experimentation is operationally decentralized. The experimenters who develop new features also dictate which hypotheses to test, and they are typically rewarded based on empirical average treatment effects that are prone to upward bias. Left unchecked, this principal-agent conflict can severely erode platform value, a structural failure that conventional centralized levers, such as significance thresholds and traffic budgets, cannot resolve. By reframing experimentation as an incentive design problem, we demonstrate that two practical mechanisms, sample splitting and shrinkage, can effectively bridge this gap. Sample splitting aligns incentives perfectly at a bounded traffic cost, while shrinkage consumes no additional traffic and guarantees that interventions with negative expected effects are strictly unprofitable to field.

Estimating causal effects from observational data is central to science and policy, but the effects are not identified when confounders are unmeasured. Proximal causal inference addresses this problem with proxies of the unmeasured confounders. However, existing proxy-based approaches either designate proxy roles and solve an inverse problem, which is ill-posed and hard to estimate with high-dimensional proxies, or use a latent-variable model, which assumes that the learned latent variable matches the hidden confounder and leaves bias when it does not. To address these challenges, we introduce proximal balancing. It carries the classical idea of covariate balancing to confounders that are observed only through proxies: it learns a low-dimensional summary of the covariates and proxies that makes the treatment groups comparable, and then adjusts for this summary. It needs no designated proxy roles, inverse problem, or latent model. We give identification theory, finite-sample guarantees, and a practical algorithm, PROBE. We demonstrate the method on low-dimensional, high-dimensional, and image proxies and on real-world data.

Knowing how much a causal predictor could improve need not reveal the gain of the repair actually learned. We quantify this gap in a scalar Gaussian causal experiment with known intervention geometry: auxiliary data identify effect magnitude up to bounded contamination, while diagnostics identify direction. The target is the squared-loss gain of the realized trained repair relative to a fitted reference. Jointly optimizing the learner and assessor under uniform learning MSE $η$ avoids the trivial solution of making no repair. At the usual $1/k$ learning scale, every feasible learner incurs a $k^{-2}$ assessment floor, even when oracle potential is estimable at a faster rate. In the magnitude-rich regime, we characterize a sharp leading-log frontier: the assessment exponent is $\min{\ell_k,2kη_k/U}$ to first relative order, where $\ell_k=\log(1/(k^2E_k))$ and $E_k$ is auxiliary precision. A diagnostic-abstention rule attains this exponent with unknown nuisance parameters. We also bound the critical allowance window and transfer the frontier to adaptive sampling by exact Gaussian simulation. Finite-grid experiments distinguish sign-tail suppression from total MSE and expose conservative finite-budget behavior. The result isolates how the assessment target changes information requirements in this experiment; it is not a general causal identifiability claim.

Deep Research agents synthesize evidence into cited reports, yet a well-cited report can still reach a misleading conclusion. Citation correctness checks whether cited sources support individual claims. It does not show whether adaptive search exposed a representative view of all documents made available for evaluation, which we call the candidate pool. Early findings redirect later queries, document choices, and stopping, so the documents an agent reads form a selective sample. Existing evaluations rarely account for this selection. We formulate the problem as adaptive evidence sampling and introduce Causal Evidence Selection Correction (CESS). CESS predicts each candidate document's evidence direction and corrects the candidate-pool average using the logged probabilities of selecting each document and reaching each search round. Shrinkage stabilizes short searches, while intervals replace point estimates when some documents cannot be sampled. We also prove that estimating the average evidence direction of a common pool differs from measuring how a change in search policy alters the evidence read. The latter requires intervention. On questions from the MS2 systematic-review benchmark, CESS reduces mean absolute error against the candidate-pool average by $9.2\%$ and reduces the estimate's change under opposing document rankings by $39.4\%$ relative to averaging the evidence scores of documents read. Across trajectories from a public Open Deep Research agent, the corresponding reductions reach $60.1\%$ and $87.2\%$. A further 4,800 trajectories under paired interventions confirm that correcting a pool estimate and measuring a policy effect are different tasks. CESS therefore audits whether the evidence direction underlying a report reflects the documents available for evaluation, while a separate intervention analysis measures the effect of search decisions.

Latent world models are trained to predict what happens next, so nothing in their objective separates what an action caused from what merely co-occurred with it. Object-masking models such as C-JEPA intervene on what the predictor can see; we intervene on what physically happens. From one saved simulator state we run the dynamics under an action $a$ and under a reference action $a_{\varnothing}$, and train the model to predict the difference $Δz=z^{a}-z^{a_{\varnothing}}$ between the two latent futures. The resulting objective, Do-JEPA, has an effect loss, a support loss (where the action enters), a propagation loss (where its effect travels) and invariance losses (what must not change). In a synthetic system with object-aligned variables, support supervision finds the directly intervened object in 99.95% of test cases, where a sparse action mask sends the action to a nuisance slot in every case, and response-onset supervision recovers the ring-shaped propagation graph (edge AUROC 0.975 vs. 0.624). From pixels, the effect loss beats a control trained on exactly the same data: it lowers latent effect error by 28.4% on an end-to-end LeWM model and physical effect error by 13.5% when trained and tested on natural action sequences, and on three independently generated CausalWorld benchmarks it lowers responsive effect error by about 20% under physics shifts and the latent context sensitivity of predicted effects by 66%. Trained from scratch it costs factual accuracy; fine-tuning an existing model with it removes this cost. Together, these results show that intervening on the world, rather than on what the model sees, helps latent world models predict what their actions cause.

Estimating causal effects with continuous treatments in observational studies is challenging due to confounding, model misspecification, and high-dimensional covariates. We propose the Weighted Spline-Expanded Network (WSENet), an end-to-end neural framework that addresses these challenges by combining covariate balancing, structured treatment embedding, and bias-corrected outcome estimation. WSENet first applies Distance Covariate Optimal Weights to induce distributional independence between covariates and treatment without relying on parametric models. It then learns the conditional outcome via a structured network that fuses outcome-relevant representations of covariates with a spline-expanded treatment input, enabling smooth and flexible modeling of the dose-response relationship. To mitigate residual bias, we introduce Weighted Targeted Regularization, a correction technique based on efficient influence functions that yields a doubly robust estimator. Extensive evaluations on semi-synthetic and real-world datasets, including high-dimensional genomic and environmental health data, demonstrate that WSENet consistently outperforms existing baselines in both accuracy and stability.

A central goal when designing treatment policies is often to "do no harm", that is, to avoid interventions that improve average outcomes while worsening outcomes for some individuals. A widely used notion for harm is the fraction of negatively affected (FNA), defined as the probability that an intervention decreases an individual's outcome. However, in many applications, treatments operate through mediators, and a single "total" FNA can obscure whether harm arises primarily through direct pathways or indirect (mediator-induced) pathways. In this work, we introduce a path-specific analogue of the FNA. For this, we disentangle total harm into direct and indirect harm in causal mediation settings. However, these quantities depend on joint distributions of potential outcomes that are not point-identified even in randomised controlled trials. As a remedy, we develop a novel partial identification framework for direct and indirect FNA. In our framework, we (i) derive sharp Makarov bounds for the FNA, and (ii) propose a semiparametrically efficient estimator with valid confidence intervals for these bounds under mild margin conditions. We demonstrate our framework across various numerical experiments. To the best of our knowledge, we are the first to study path-specific decomposition of causal harm and to develop an orthogonal inference framework for its analysis.

On-demand delivery platforms pay riders through incentive activities whose tiers are set from recent completions of riders with a similar history. Operators request such plans for changing periods, rider populations, payment rules and budgets, often for holidays or bad weather, where randomized trials are scarce and take months to collect. We present a request-driven framework that composes four stages (conditional prediction, population reduction, trajectory integration and budget allocation) through seven replaceable modules that exchange conditional trajectory laws, whose award probabilities and award-marked moments give payment and uplift for any activity rule. A response-correction step reweights trajectories from abundant no-offer history to match the moments of a short pilot. We prove that, on a fixed plan menu and given the stage errors, the end-to-end value loss is bounded by the sum of four stage terms, and that for every stage there are instances on which omitting it leaves an error floor the others cannot remove. On 3,000 riders over 45 weekly origins, all 127 windows of a week are answered 11.04x faster with identical scenarios and at most 0.92% value lost by the allocation. On 24 new controlled response laws, the response correction with a one-week pilot lowers regret by 51.2% relative to a trial with the same nominal randomized rider-weeks, and a four-week pilot with exact summation comes within +0.007 of an 18-week trial. In registered studies where windows, populations, rules and binding budgets change from request to request, the framework's regret is below that of a trial with the same nominal rider-weeks and below dose interpolation of the same pilot data, and reusing its one-off preparation answers 60 requests 14.1x and 2.70x faster with identical answers. Against a nine-offer trial fitted with the framework's own dose curve, one-week regret is 0.055 lower.

Reliable intervention-oriented uncertainty quantification from Earth observation (EO) remains challenging when continuous treatment shifts, spatial dependence, limited support, and satellite-outcome uncertainty must be addressed simultaneously. Existing causal, conformal, and spatial approaches address parts of this problem, but their direct combination does not generally recover the appropriate interventional reference law because candidate reassignment jointly alters treatment likelihood, standardized residuals, and graph-dependent residual likelihood. This study presents GeoDose-CP, a support-aware conformal framework for localized stochastic potential outcomes under continuous or mixed continuous-atomic treatment. Its central methodological contribution is a graph-local target-orbit law that jointly represents intervention-induced treatment shift, the inverse outcome-scale Jacobian, and spatial residual dependence. The framework further provides exact weighted candidate inversion, a scalable sparse approximation with explicit discrepancy accounting, and refusal under inadequate support. Evaluation used controlled known-truth experiments, MineDoseBench, treatment-density sensitivity analysis, external conformal comparators, and a multi-mine New South Wales (NSW) study. In MineDoseBench, GeoDose-CP achieved mean selective coverage of 0.9692 across 27 configurations and a minimum local q0.05 of 0.8951; exact-sparse auditing produced nine inclusion disagreements over 2,700 targets. In the NSW study, the absence of an auditable longitudinal rehabilitation treatment rendered treatment-dependent inference nonoperational rather than forcing inference through a proxy exposure.

KITE queries a typed behavioral kernel once per unique state, then executes populations of any size from the table with event-keyed randomness and common random numbers. An expensive flagship model is reserved for sparse paired anchors that estimate intervention effects. Measured human-model discrepancy is propagated as shared error into every conclusion. Population-experiment cost thus scales with unique states and anchors, while uncertainty is governed by evidence about people rather than Monte Carlo noise. On Epstein experiments with 9,070 participants, anchors covering 1.7% of states reduced effect error by 41% (absolute MAE reduction 0.0125). On 37 held-out SocSci210 experiments, 0.5-1.5% anchor coverage raised captured decision gain from 0.27 to 0.39. The kernel passed content-fidelity criteria in all 15 new countries of a 16-country study. Shared discrepancy yielded retrospective coverage of 93% and 96% at nominal 80% and 90%, versus 29% and 36% from human sampling uncertainty alone. A million agents executed 20 tabulated steps in 0.9 seconds on a laptop. This architecture offers a route to screening candidate interventions before human trials, multi-country content audits, and uncertainty-aware policy comparison at the cost of a few thousand kernel calls with sparse flagship anchors. Property-specific evidence records connect each use to its validation scope, correction provenance, and uncertainty, making these applications auditable.

Information systems (IS) researchers increasingly use quasi-experimental methods such as difference-in-differences (DiD) and instrumental variables (IV) to recover causal effects from observational panel data. Power calculations that justify these designs assume i.i.d. errors, but the deeper problem is what even a cluster-robust calculator cannot see. We report a Monte Carlo study over 9837 parameter conditions (approx 9.8 million datasets) and decompose the planned-versus-achieved power gap. The serial-correlation component is recoverable by an AR(1)-aware calculator when rho is known, and partially when rho must be estimated from short pre-periods, but panel attrition, staggered-adoption bias, and parallel-trends pretesting are captured by no closed-form formula; exogenous attrition alone costs approx 8 to 11 percentage points at the few-hundred-to-thousand sample sizes IS studies use. Treatment-correlated, outcome-dependent attrition instead induces bias, not just power loss. For IV, holding first-stage F fixed, larger N neither raises power nor curbs exclusion bias, though with a fixed instrument more data does sharpen the first stage, so identification rests on instrument strength, not sample size.

Estimating the causal effects of medical treatments is difficult when clinically important outcomes are costly to measure or require long follow-up. Short-term or inexpensive surrogate outcomes offer a potential alternative, but surrogate biomarkers may be unavailable or difficult to identify. Advances in artificial intelligence (AI) have enabled increasingly accurate prediction of clinical outcomes from inexpensive, high-dimensional measurements, which creates an opportunity to use AI predictions themselves as surrogates. To this end, we develop a framework for estimating treatment effects from paired measurements obtained before and after treatment for each treated individual. A pretrained AI model is applied to the before and after measurements, and our estimator compares the resulting outcome predictions. We characterize the technical assumptions under which this within-person contrast identifies the average treatment effect on the treated, even when clinical outcomes are never observed for treated individuals. When these assumptions cannot be justified, we use prediction-powered inference to correct bias using a small number of observed clinical outcomes and obtain valid inference. Synthetic and real-world cardio-oncology experiments demonstrate the validity and accuracy of the approach.

Evidence that evaluation material entered training does not reveal how much it affected evaluation. This distinction leaves a contaminated benchmark score difficult to interpret: provenance can establish contact, but only a counterfactual can quantify the performance attributable to that contact. We present LeakScale, an interventional framework for estimating this missing quantity. LeakScale creates fresh executable tasks that require private, family-specific information absent from and non-derivable from the public task, controls access to that information, and estimates the resulting control-adjusted change in executable accuracy. Across 2,048 unique families, two model families, two executable domains, and 262,144 generations, exposure improves accuracy in every model-by-domain combination, with gains ranging from +7.17 to +27.31 percentage points. These findings separate two empirical questions that are often conflated: whether benchmark contact occurred and how strongly a reported score depends on it. LeakScale makes the latter directly measurable.

Causal tabular foundation models amortize effect estimation across synthetic mechanisms, but latent-effect supervision rewards posterior shrinkage rather than encoding the repeated-sample response needed in a fixed deployment population. We introduce fluctuation-supervised pretraining (FSP): each synthetic table is labeled by its average treatment effect plus its efficient influence-function fluctuation; deployment remains a frozen forward pass. Along the path $T_{λ,P}=θ(P)+λP_nψ_P$, we prove an endpoint transition: every fixed $λ<1$ retains label ambiguity of order $(1-λ)^2/n$, whereas full fluctuation makes the Gaussian label observable and reduces optimal finite-stratum causal label-prediction risk to order $n^{-2}$. A finite-pretraining bound combines label, network, episode-sampling, and optimization errors; its sampling defect controls fixed-mechanism bias, mean squared error, variance, Gaussian approximation, and, with variance-head accuracy, studentized coverage. Complementary lower bounds separate local $n^{-1}$ ATE risk from the $\log N/M$ excess risk of generic finite-dictionary episode learning. Experiments trace the learned sampling response. Across 24 nonlinear continuous-covariate cells at trained context lengths, continuous-row FSP lowers checkpoint-mean macro RMSE by 7.0% versus S-learner and wins all 12 weak-overlap cells; validation-selected Summary FSP deploys $11.6\times$ faster per table in our warm one-thread benchmark. Under effect shift, matched Raw FSP lowers mean-checkpoint RMSE by 54.2% and teacher defect by 99.0% versus latent-effect supervision, and RMSE by 10.2% versus the released CausalPFN-S checkpoint. Known-effect semisynthesis tests coverage; two randomized-study evaluations show that lower RMSE can coexist with residual attenuation.

We develop exponential family synthetic controls (EFSC), a distributional version of synthetic controls for a panel of datasets. Each cell of the panel corresponds to a dataset drawn from an exponential family whose natural parameters factorize probabilistically across units and times. We estimate the latent factors using black-box variational inference. This replaces the usual weighted-average view of synthetic controls with a flexible probabilistic model that operates on full distributions. We propose causal estimands based on divergences between pre- and post-intervention distributions induced by the posterior of the natural parameters, together with distributional placebo tests to support causal inference and assess the significance of the estimated effects. We validate the proposed framework on synthetic and real data. Across a variety of exponential-family distributions, EFSC accurately recovers causal effects induced by exponential tilts, together with the corresponding divergences between treated and counterfactual distributions. The framework also captures effects induced by structural perturbations of the latent factors and by heavy-tailed noise contamination. Finally, we apply EFSC to study the expansion of Medicaid under the Affordable Care Act (ACA) and its impact on the distribution of health insurance coverage across U.S. states. Code is available at https://github.com/blei-lab/efsc.

AI and large language models can recover clinically meaningful features from electronic health records (EHRs), but predictive usefulness does not establish admissibility for causal inference. We introduce information set emulation: an AI typed lift attaches source evidence, clinical and recording times, decision-time availability, representation version, proposed causal roles, and unresolved ambiguity to extracted features under a locked target trial. Causal certificates record auditable evidence for those roles. Features with unresolved downstream roles are routed to compatible reporting or separate analyses. Typed evidence defines an observational fiber of causal worlds consistent with the observed law. The locked scalar estimand maps this fiber to a compatible image whose squared Chebyshev radius equals the residual minimax mean squared error when the image is nonempty and compact. This classical identity provides a target-specific measure of information ambiguity. The contribution is its integration with a joint EHR observation map and an auditable certificate architecture. Under explicit exchangeability, positivity, and nuisance-consistency conditions, we give identification and cross-fitted augmented inverse probability weighted estimation, distinguishing empirical and population targets. An EHR compression-drift identity separates the roles of frame presence, treatment assignment, and outcome observation. Artificial simulations and a common-law finite-world example illustrate estimation failures and information-radius reduction. Synthetic Phase 0 notes demonstrate audit diagnostics; a separate role-specific analysis spread illustrates routing and is not an exact fiber radius. All experiments are synthetic. The framework specifies when reconstructed information can support a point claim and when compatible reporting is required.

AI-generated covariates from notes, conversations, images, and wearable streams can change the causal question when their roles are left unspecified. A generated feature may represent a treatment version, pre-action state, history, design variable, mediator, outcome proxy, observation process, or intercurrent event; these roles are not interchangeable. We formulate a causal type discipline for sequential experiments: a versioned representation map, a causal role classifier, a claim-status filter, and an estimand lock. The lock fixes a standardized proximal effect before generated covariates enter the analysis. Under audit correctness and standard identification assumptions, admissible role assignments preserve this estimand. We apply the established conditional-covariance characterization of compression bias to substitution of generated representations for design-relevant states. A standardized decomposition separates compression, conditional-law, and standardization drift. Further results cover mediator adjustment, post-action leakage, marker-intervention conflation, outcome-guided discovery, and state-measurement error. Cluster-level orthogonal estimators distinguish empirical and superpopulation targets under repeated sessions and missing outcomes. Simulations show that refinement helps when it retains design-relevant information, whereas design erasure, leakage, and same-data marker selection can produce bias or undercoverage. The framework places causal semantics and claim status before confirmatory inference with generated representations.

In various fields, such as medicine and marketing, accurately predicting individual treatment effects holds significant promise. However, achieving reliable predictions alone is often insufficient for making informed decisions; it is equally important to understand why the treatment effect is higher for some individuals than for others. To address this two-fold challenge of prediction and interpretation, we introduce an algorithm based on decision trees and random forests for estimating individual treatment effects. Our algorithm is simple: it operates exactly like a standard random forest, but with a different splitting criterion, and requires no additional workarounds such as double machine learning or orthogonalization as used in Generalized random forests. It handles observational studies with varying treatment propensities without requiring separate estimation of the full propensity function. This is achieved by combining two splitting criteria---one targeting heterogeneity in the treatment effect, the other targeting bias correction for the average treatment effect---which together improve split point selection and automatically distinguish confounders from features responsible for heterogeneity. As a result, interpretation follows directly from the fitted tree structure itself, that is, from which features the trees split on and with which split statistics, without requiring separate post-hoc analysis. For the theoretical analysis of this algorithm, we consider a change point model with step functions for potential outcomes and treatment propensity and provide insights into the theoretical underpinnings of our approach. Simulation studies show that our simple algorithm achieves comparable, and often better, prediction accuracy than existing methods, while substantially improving interpretability.

Conformal counterfactual prediction constructs prediction sets with finite-sample coverage guarantees for counterfactual outcomes and individual treatment effects under the no-interference assumption. In this work, we relax this assumption by allowing each unit's potential outcomes to depend on other units' treatments and covariates. In this setting, propensity-score reweighting does not restore weighted exchangeability, and existing methods may fail to achieve valid coverage. To address this issue, we develop interference-adjusted weighted conformal prediction that accounts for interference by constructing an observable upper bound on the ideal and unobserved conformal $p$-value under the target intervention. The resulting prediction sets provide finite-sample marginal coverage guarantees for counterfactual outcomes and individual treatment effects in both transductive and inductive settings. We also derive a sharper construction when intervention-induced changes in nonconformity scores are bounded. Numerical experiments show that our methods preserve nominal coverage, whereas existing methods may not.

Average treatment effect (ATE) estimation in observational studies is a fundamental statistical tool used frequently in social science, medicine, and other fields. These fields often work with sensitive data where privacy protections are important, so a differentially private mechanism for ATE estimation is highly desirable. Here we present two propensity score-based algorithms for ATE estimation on observational data, one improving the inverse probability weighting (IPW) method used in prior work, and the other using blocking on the propensity score (BPS). Both show lower error and less bias than prior work, with the BPS-based algorithm frequently reducing error by 75% or more compared to prior work.

Existing causal-inference benchmarks for LLMs mostly score method descriptions or whether generated code runs, not whether the executed workflow recovers the target causal estimate. CausalVerify studies this verification problem for structured econometric causal-estimation workflows by separating realistic interpretation from verifiable computation. It pairs 259 published economics papers (reconstructed research question, data description, institutional context) with 100 fixed-seed synthetic scenarios that realise CSV datasets for difference-in-differences, event study, instrumental variables, and regression discontinuity designs. Experiment A (real-paper text agreement) scores method-family and direction agreement against four-LLM consensus labels. Experiment B (synthetic execution) runs model-written R code and checks whether the extracted treatment-effect estimate matches a canonical estimator on the same realised dataset; this execution-grounded correctness layer is L2b+, distinct from L2b, which records only whether the code executes. A calibration arm asks whether self-reported confidence separates correct from incorrect workflows. On Experiment B, seven LLMs reach L2b+ pass rates of 10% to 88% at the default 50% tolerance, and 66 of the 426 workflows that execute (15.5%) return a wrong estimate. Execution ranking (L2b) agrees with L2b+ far better than text-direction scoring (L4): Kendall $τ=0.81$ and Spearman $ρ=0.93$, versus Kendall $τ$ between $-0.20$ and $0.10$ for L4. Llama-3.3-70B-Instruct shows the same qualitative gap, and reported confidence does not reliably separate correct from incorrect workflows. The claims are confined to standardized single-shot workflows in these four design families under the evaluated R backend and model panel; the benchmark does not measure general causal-inference ability. Code, data, cached outputs, and a datasheet are released.

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.

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.

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

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.

Short observational pricing panels often contain many data points but very few actual price changes. This paper shows that this sparsity creates a hidden source of error that standard statistical methods miss. When estimating price effects, most of the uncertainty does not come from sample size within a panel, but from the specific history of price movements observed. Standard confidence intervals fail because they only measure variation within the panel, ignoring this broader design-level error. Using simulations, we find that this cross-design variation accounts for most of the estimation error, causing standard methods to significantly understate uncertainty. First, we show that cross-design error decreases predictably as the total volume of price variation increases. Second, adding more data from regions that share the same price trends does not fix the issue; true precision improves only when combining data across units with independent price trajectories. Third, applying a simple variance-component adjustment across independently priced units restores accurate statistical coverage. We confirm these findings in real-world store scanner data, showing that products and pricing zones behave as if they have far fewer independent price movements than their raw counts suggest. Ultimately, reliable inference in passive pricing data requires genuine, independent variation, which can be achieved through controlled regional price testing.