Causal Effect Estimation

Adaptive experimentation enables efficient estimation of causal effects, but existing methods are not designed for survival data with censoring, where event times are only partially observed (e.g., overall survival in cancer trials but with dropout). In this paper, we develop a novel framework for adaptive experimentation to estimate causal effects under right censoring. For this, we derive the semiparametric efficiency bound for the average survival effect curve as a function of the treatment allocation policy and thereby obtain a closed-form efficiency-optimal allocation policy. The policy generalizes classical Neyman allocation to survival settings by prioritizing patient strata where both event and censoring dynamics induce high uncertainty. Building on this, we propose the Adaptive Survival Estimator (ASE), an adaptive framework that learns the allocation policy and estimates the average survival effect curve sequentially. Our framework has three main benefits: (i) it accommodates arbitrary machine learning models for nuisance estimation; (ii) it is guided by a closed-form efficiency-optimal allocation policy; and (iii) it admits strong theoretical guarantees, including asymptotic normality via a martingale central limit theorem. We demonstrate our framework across various numerical experiments to show consistent efficiency gains over uniform randomization and censoring-agnostic baselines.

Individualized treatment selection with continuous actions requires accurate causal response estimation in decision-relevant regions, rather than uniformly over the entire action space. Estimating a global causal response surface and then choosing the treatment that maximizes it can therefore be suboptimal, since standard estimation objectives allocate modeling effort according to the observed treatment distribution rather than the regions that determine the optimal decision. While decision-aware approaches have been studied in unconfounded settings, this problem remains underexplored in proximal causal inference, where proxy variables and bridge functions enable identification under suitable assumptions even in the presence of hidden confounding. Despite recent progress, proximal methods have primarily focused on treatment-effect and potential-outcome estimation rather than treatment selection and optimal decision-making. To bridge this gap, we introduce a policy-targeted weighted bridge loss that emphasizes decision-relevant treatment regions while retaining global stabilization. We prove a regret bound showing that the proposed weighted bridge loss controls treatment-selection regret through a weighted ill-posedness constant. We instantiate the framework in decision-aware variants of several proximal bridge solvers, yielding practical algorithms that alternate between weighted bridge estimation, response-surface projection, policy update, and weight refinement. Empirically, we find that decision-aware weighting reduces regret across several bridge solvers, suggesting improved treatment selection in proximal settings.

Clinical decision-making is a feedback system where risk estimates influence treatment, which in turn changes disease trajectories, and both shape clinicians' measurement practices. Static prediction often fails clinically: models trained on observational care logs conflate disease biology with clinician behavior, particularly under treatment confounder feedback and irregular or informative observation. This Review focuses on intervention-aware disease trajectory modeling in clinical AI--methods estimating patient-specific longitudinal disease evolution and assessing trajectory changes under alternative treatments. We organize the field around six linked components: three decision tasks (factual forecasting, counterfactual estimation, policy evaluation) and three data-generating mechanisms (disease evolution, treatment assignment, observation process) that determine identifiability. We present the first unified framework bridging forecasting, counterfactual trajectories, and policy evaluation across discrete/continuous time, explicitly addressing treatment assignment, time-varying confounding, and observation bias. We synthesize key method families (multistate/joint models, temporal point-process, deep sequence architectures, longitudinal causal inference), map them to relevant components, and align evaluation with claim strength via overlap diagnostics, uncertainty quantification, off-policy robustness, and target-trial validation. This synthesis advances benchmark prediction to decision-grade clinical evidence, enabling treatment-sensitive individualized futures, pre-deployment policy stress-testing, and safer closed-loop learning health systems that adapt/abstain when evidence is insufficient.

Causal inference, estimating causal effects from observational data, is a fundamental tool in many disciplines. Of particular importance across a variety of domains is the continuous treatment setting, where the variable of intervention has a continuous range. This setting is far less explored and represents a substantial shift from the binary treatment setting, with models needing to represent effects across a continuum of treatment values. In this paper, we present the first causal foundation model for the continuous treatment setting. Our model meta-learns the ability to predict causal effects across a wide variety of unseen tasks without additional training or fine-tuning. First, we design a novel prior over data-generating processes with continuous treatment variables in order to generate a rich causal training corpus. We then train a transformer to reconstruct individual treatment-response curves given only observational data, leveraging in-context learning to amortize expensive Bayesian posterior inference. Our model achieves state-of-the-art performance on individual treatment-response curve reconstruction tasks compared to causal models which are trained specifically for those tasks. Inference code (including trained model weights) can be found at https://github.com/layer6ai-labs/CCPFN-inference .

Comparative evaluation of multiple dynamic treatment policies is essential for healthcare and policy decisions, yet conventional longitudinal causal inference methods estimate each in isolation, preventing information sharing across counterfactuals. We demonstrate that this separate estimation paradigm induces a structurally uncontrolled second-order bias, inflating finite-sample variance even after standard debiasing with longitudinal targeted maximum likelihood estimation(LTMLE). To address this, we propose a policy-aware reparameterization of Iterative Conditional Expectation (ICE) Q-functions that enables joint estimation through shared representations. We implement this approach in the Policy-Encoded Q Network (PEQ-Net), an architecture centered on a shared policy encoder. The encoder is trained using kernel mean embeddings, ensuring that the learned representation space reflects population-level policy dissimilarities. After applying an LTMLE correction step, we prove this design imposes a structural constraint on the second-order remainder, thereby stabilizing finite-sample variance. Experiments on semi-synthetic datasets demonstrate that PEQ-Net consistently outperforms existing ICE-based methods, achieving substantial reductions in root-mean-square error, particularly when evaluating closely related policies.

Selection bias is pervasive in observational studies. For example, large scale biobanks data can exhibit ``healthy volunteer bias'' when respondents are healthier and of higher socio-economic status than the population they are meant to represent. Recovering causal effects from such sub-population is an important problem in causal inference, as estimating average treatment effects (ATE) from selected populations can result in a severely biased estimate of the ATE from the whole population. In this paper, we investigate the identifiability of the ATE under selection bias. We provide necessary and sufficient conditions for ATE identifiability, leveraging weak assumptions on probability classes to characterize propensity score and selection probability. Compared to previous works, our results extend existing graphical identifiability criteria and offer a more comprehensive understanding of causal effect identification with strictly weaker conditions in the presence of selection bias.

The instrumental-variables (IV) setting is standard for partial identification of causal effects when unobserved confounding makes point identification impossible. Existing approaches face methodological bottlenecks: closed-form bound estimands are required -- e.g., Balke-Pearl equations in binary IV -- and even when available, designing accurate estimators requires manual effort tailored to each estimand. While direct Bayesian inference of the causal effects, instead of the bounds, circumvents these challenges, it is often computationally intensive and suffers from high prior sensitivity or under-dispersed posteriors. As a remedy, we introduce IV-ICL, an amortized Bayesian in-context learning method that learns the marginal posterior distribution of the causal effects directly and derives bounds as its quantiles. Unlike standard variational inference that optimizes exclusive KL divergence, amortized Bayesian inference minimizes the expected inclusive KL, a mass-covering objective. We empirically observe that optimizing inclusive KL can recover the entire identified set across diverse data-generating processes, while exclusive-KL (e.g. with variational inference) of the same Bayesian formulation collapses onto a single mode and fails to cover the identified set. We evaluate IV-ICL on synthetic and semi-synthetic IV benchmarks and show it produces intervals that are more reliably valid and more informative compared to efficient semi-parametric, Bayesian, and plug-in baselines, at 20-500x lower inference time. Beyond methodology, we propose a procedure to convert randomized controlled trials into IV benchmarks with provably preserved ground-truth causal effects that enables a more realistic evaluation of partial-identification methods.

Experimental design has emerged as a powerful approach for improving the sample efficiency of A/B testing, yet existing designs rely critically on correctly specified models. We study robust sequential experimental design under model misspecification and develop a unified framework that covers both contextual bandit and dynamic settings. Theoretically, we prove that our design bounds the worst-case mean squared error of the estimated treatment effect. Empirically, we demonstrate the effectiveness of the proposed approach using synthetic and real-world datasets from a leading technology company.

Single-arm trials are an important study design for evaluating drug efficacy and safety without enrolling patients into a control arm. Although they do not provide the gold-standard evidence of randomized controlled trials, they are increasingly used in clinical development as they offer an efficient, ethical, and practical alternative. A wide variety of approaches can be used to construct control comparators and estimate treatment effects, from fixed comparators informed by clinical knowledge to data-based and model-based patient-level comparators, also known as synthetic controls. Powerful and flexible machine learning models can allow outcome-model-based synthetic controls to overcome key limitations of direct data-based approaches, yield more robust estimates of treatment effects, and provide a principled way to incorporate corrections or encode additional assumptions when external data are not directly comparable. In this work, we argue that outcome-model-based synthetic control arms are an important tool for single-arm trials. We focus on digital twins, personalized predictions of disease progression generated from machine learning models trained on historical datasets, which naturally leverage these flexible approaches. We review doubly robust estimators, present power and sample size formulas, and discuss trade-offs in selecting historical data for training and analysis. We also outline practical considerations for deploying digital twins within the framework of recent FDA draft guidance on the use of artificial intelligence in drug development. Finally, we reanalyze data from trials in amyotrophic lateral sclerosis and Huntington's disease to demonstrate the proposed methods.

Surrogate endpoints are used in place of long-term outcomes in randomized experiments when observing the real outcome for a large enough cohort is prohibitively expensive or impractical. A short-term surrogate is good if the result of an experiment using the surrogate is predictive of the result of a hypothetical study using the real outcome. Much attention has been paid to formalizing this property in causal terms, but most criteria are unidentifiable and cannot be turned into practical algorithms for learning surrogate endpoints from data. To address this, we study plug-in composite surrogates, functions of post-treatment variables that may be substituted directly for the primary outcome in a randomized experiment. We propose two methods for learning plug-in surrogates that maximize effect predictiveness, and characterize the possibility of finding endpoints that yield unbiased effect estimates in representative scenarios. Finally, in both synthetic experiments with known effects and in data from a real-world experiment, we find that our method, based on directly modeling the surrogate effect, returns plug-in endpoints more predictive of the primary effect than established methods.

The trustworthiness of AI decision-making systems is increasingly important. A key feature of such systems is the ability to provide recommendations for how an individual may reverse a negative decision, a problem known as algorithmic recourse. Existing approaches treat recourse outcomes as counterfactuals of a fixed unit, ignoring that real-world recourse involves repeated decisions on the same individual under possibly different latent conditions. We develop a causal framework that models recourse as a process over pre- and post-intervention outcomes, allowing for partial stability and resampling of latent variables. We introduce post-recourse stability conditions that enable reasoning about recourse from observational data alone, and develop a copula-based algorithm for inferring the effects of recourse under these conditions. For settings where paired observations of the same individual before and after intervention are available (called recourse data), we develop methods for inferring copula parameters and performing goodness-of-fit testing. When the copula model is rejected, we provide a distribution-free algorithm for learning recourse effects directly from recourse data. We demonstrate the value of the proposed methods on real and semi-synthetic datasets.

Causal sensitivity analysis aims to provide bounds for causal effect estimates in the presence of unobserved confounding. However, existing methods for causal sensitivity analysis are per-instance procedures, meaning that changes to the dataset, causal query, sensitivity level, or treatment require new computation. Here, we instead present an in-context learning approach. Specifically, we propose an amortized approach to causal sensitivity analysis based on prior-data fitted networks. A key challenge is that the sensitivity bounds are not directly available when sampling training data. To address this, we develop a general prior-data construction that is applicable across the class of generalized treatment sensitivity models. Our construction involves a Lagrangian scalarization of the objective to generate training labels for the bounds through a tradeoff between causal effect min/max-imization and sensitivity model violation, which avoids model-specific analytical derivations. We further show that, under standard convexity and linearity conditions, our objective recovers the full Pareto frontier of solutions. Empirically, we demonstrate our amortized approach across various datasets, causal queries, and sensitivity levels, where our approach achieves a test-time computation that is orders of magnitude faster than per-instance methods. To the best of our knowledge, ours is the first foundation model for in-context learning for causal sensitivity analysis.

Estimating heterogeneous treatment effects with machine learning has attracted substantial attention in both academic research and industrial practice. However, the two communities often evaluate models under markedly different conditions. Methodological work typically relies on semi-simulated benchmarks and metrics that require counterfactual outcomes, whereas real-world applications rely on observable metrics based on ranking or test outcomes. Despite the well-known gap between methodological progress and practical deployment, the relationship between these evaluation regimes has not been examined systematically. We conduct a large-scale empirical study of treatment effect evaluation across standard semi-simulated benchmark families and real-world datasets. Our benchmark covers meta-learners paired with multiple base learners, as well as specialized causal machine learning models. We evaluate these methods using observable metrics common in application-oriented literature, alongside counterfactual metrics commonly used in methods papers. Our results reveal two complementary gaps. First, counterfactual metrics do not reliably recover the estimators preferred by observable metrics, even on the same semi-simulated benchmarks. Second, rankings obtained on semi-simulated benchmarks do not transfer to real datasets. We further find that simple meta-learners with strong base models are consistently competitive, in contrast to specialized causal models. Overall, our findings suggest that progress in treatment effect estimation research should not be assessed solely through counterfactual metrics and semi-simulated benchmarks, but it would benefit from incorporating observable metrics and real-data validation.

Distributional causal inference requires estimating not only average treatment effects but also interventional outcome distributions, including quantiles, tail risks, and policy-dependent uncertainty. As a method for distributional causal inference, generative adversarial network (GAN)-based counterfactual methods are flexible tools for this task. However, these methods have several limitations. First, the objectives of certain techniques do not coincide with the statistical risk of the identifiable causal target, and therefore provide limited theoretical guarantees regarding estimable counterfactual distributions or optimality. Second, they tend to rely on unstable density-based methods, such as density ratio estimation. In this paper, we propose GANICE (GAN for Interventional Conditional Estimation) with several advantages: it (i) clarifies the conditional interventional distribution for each treatment--covariate state as the causal estimation target; (ii) estimates the conditional distribution such that its averaged Wasserstein risk is minimized; (iii) establishes minimax optimality. GANICE achieves these advantages through the introduction of the extended Wasserstein distance, the incorporation of a cellwise critic in its dual, and an optimality proof based on Besov space theory. Our experiments demonstrate that GANICE consistently outperforms existing methods.

Unobserved confounding prevents standard covariate adjustment from identifying causal response functions in observational studies. Proxy causal learning addresses this problem through bridge equations involving treatment- and outcome-inducing proxies, avoiding direct recovery of the latent confounder. Existing doubly robust proxy estimators combine outcome and treatment bridges, but typically rely on fixed kernels, sieves, or low-dimensional semiparametric models; existing neural proxy methods are more flexible, but are largely single-bridge estimators. We develop a neural doubly robust framework for proxy causal learning with continuous and structured treatments. Our method introduces a neural mean-embedding estimator for the treatment bridge, combines it with a neural outcome bridge, and estimates the doubly robust correction through a final regression stage. The framework covers population, heterogeneous, and conditional dose-response functions, yielding full response-curve estimators rather than binary-treatment effects. The algorithms use two stages for each bridge and history-aware updates of the final linear layers to stabilize stochastic multi-stage training. We prove consistency of the algorithms showing that the doubly robust error is controlled by the final averaging and regression errors together with the smaller of the outcome- and treatment-side weak-norm bridge errors. Across synthetic and image-valued benchmarks, the proposed estimators outperform existing baselines and single-bridge neural estimators, showing the benefit of combining learned outcome and treatment bridges in a doubly robust construction. Our implementation is available at https://github.com/BariscanBozkurt/DRPCL-Neural-Mean-Embedding.

We introduce the Sinkhorn treatment effect, an entropic optimal transport measure of divergence between counterfactual distributions. Unlike classical quantities such as the average treatment effect, this measure captures differences across entire distributions. We analyze this divergence as a statistical functional and show it can be written as a smooth transformation of counterfactual mean embeddings with an appropriate kernel. This characterization allows us to establish first-order pathwise differentiability in general, and second-order pathwise differentiability under the null hypothesis of equal counterfactual distributions. Leveraging this smoothness, we construct debiased estimators and use them to obtain asymptotically valid tests for distributional treatment effects with a fixed entropic regularization parameter. Because the power of the test depends on this unknown parameter, we further propose an aggregated test that combines evidence across a grid of regularization choices. Experiments on simulated and image data demonstrate the practical advantages of our estimator and testing procedure.

Distributional treatment effects can be invisible to means: a treatment may preserve average outcomes while changing tails, modes, dispersion, or rare-event probabilities. Kernel tests can detect discrepancies between interventional outcome laws, but global tests do not reveal where the laws differ. We propose DR-ME, to our knowledge the first semiparametrically efficient finite-location test for interpretable distributional treatment effects. DR-ME evaluates an interventional kernel witness at learned outcome locations, returning causal-discrepancy coordinates rather than only a global rejection. From observational data, we derive orthogonal doubly robust kernel features whose centered oracle form is the canonical gradient of this finite witness. For fixed locations, we characterize the local testing limit: DR-ME is chi-square calibrated under the null, has noncentral chi-square local power, and uses the covariance whitening that optimizes local signal-to-noise for discrepancies visible through the selected coordinates. This efficient local-power geometry yields a principled location-learning criterion, with sample splitting preserving post-selection validity. Experiments show near-nominal type-I error, competitive power against global doubly robust kernel tests, and interpretable learned locations that localize distributional effects in a semi-synthetic medical-imaging study.

Causal inference, especially in observational studies, relies on untestable assumptions about the true data-generating process. Sensitivity analysis helps us determine how robust our conclusions are when we alter these underlying assumptions. Existing frameworks for sensitivity analysis are concerned with worst-case changes in assumptions. In this work, we argue that using such pessimistic criteria can often become uninformative or lead to conclusions contradicting our prior knowledge about the world. To demonstrate this claim, we generalize the recent s-value framework (Gupta & Rothenhäusler, 2023) to estimate the sensitivity of three different common assumptions in causal inference. Empirically, we find that, indeed, worst-case conclusions about sensitivity can rely on unrealistic changes in the data-generating process. To overcome this, we extend the s-value framework with a new sensitivity analysis criterion: Bayesian Sensitivity Value (BSV), which computes the expected sensitivity of an estimate to assumption violations under priors constructed from real-world evidence. We use Monte Carlo approximations to estimate this quantity and illustrate its applicability in an observational study on the effect of diabetes treatments on weight loss.

Marketing decisions reflect the interaction of latent consumer heterogeneity, time-varying internal states, and explicit interventions, a structure that current prediction- and language-oriented models do not capture in a unified manner. We propose a Three-in-One world-model architecture in which a Deep Boltzmann Machine (DBM) learns a frozen belief representation from demographics, time, and lagged actions and outcomes, with lightweight task-specific adapters attached on top. The same belief supports three tasks within a single framework: (i) energy-based consistency evaluation through the DBM's free energy, (ii) outcome prediction through adapters, and (iii) counterfactual inference by holding the belief fixed and varying only the action input given to the adapter. Using a controlled simulation in which the latent price sensitivity, promotion responsiveness, and base preference of each consumer are known, we show that the adapters match a strong MLP baseline on visit- and purchase-AUC while recovering heterogeneous treatment effects substantially better than S-, T-, X-, and DR-learner meta-learners and a Causal Forest baseline built on the same raw features, with the largest gap on a confounded price-promotion intervention. Complementing this, free-energy clamps systematically penalize counterfactual purchase trajectories that lack prior promotional exposure, and the penalty itself depends on the latent base preference in the expected direction. These results indicate that DBM beliefs disentangle latent traits in a form that survives counterfactual queries, providing an integrated world-model substrate for marketing intervention.

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

Instrumental-variable (IV) regression enables causal estimation under endogeneity, but modern IV problems often involve nonlinear structural effects and high-dimensional covariates. Existing methods typically operate in observed or generic learned feature spaces, and they often yield point estimates without uncertainty quantification. We introduce BGM-IV, a Bayesian generative modeling approach that performs nonlinear IV regression through posterior inference in a causally structured latent space. BGM-IV separates covariate variation by the role in the treatment and outcome mechanism, and accounts for endogeneity through an IV-integrated pseudo-likelihood that averages over instrument-induced treatment variation. The resulting model provides both structural-function estimates and predictive intervals for outcomes under intervention. Across various benchmark datasets, BGM-IV outperforms existing nonlinear IV methods overall, with significant gains in high-dimensional settings, while achieving near-nominal predictive coverage. These results highlight structured latent generative modeling as a flexible approach to uncertainty-aware IV inference with rich covariates. The code of BGM-IV is available at https://github.com/liuq-lab/BGM-IV.

Causal queries are often only partially identifiable from observational data, and experiments that could tighten the resulting bounds are typically costly. We study the problem of selecting, prior to observing experimental outcomes, a cost-constrained subset of experiments that maximally tightens bounds on a target query. We formalize this as the max-potency problem, where epistemic potency measures the worst-case reduction in bound width guaranteed by an experiment, and show that this problem is NP-hard via a reduction from 0-1 knapsack. Building on the polynomial-programming framework of Duarte et al. (2023), we give a general procedure for evaluating epistemic potency in discrete settings. To control the super-exponential search space, we introduce two graphical pruning criteria that depend only on the causal graph and the query: a novel path-interception rule that exploits district structure to certify zero potency in linear time, and an identifiability check based on the ID algorithm. On Erdos-Renyi random graphs and 11 bnlearn benchmark networks, the two criteria together prune 50-88% of candidate experiments on average without solving a single polynomial program. For the general subset search, we show that ID-pruned experiments are combinatorially inert, yielding a super-exponential reduction in the number of subsets evaluated. We close with an end-to-end demonstration on observational NHANES data, selecting optimal experiments for estimating the effect of physical activity on diabetes.

Randomized controlled trials typically assume that prognostic covariates are known and available at no cost. In practice, obtaining high-dimensional pretreatment data is costly, forcing a trade-off between covariate-adaptive precision and a measurement budget. We introduce Dynamic Adaptive Rerandomization via Thompson Sampling (DARTS), which treats covariate acquisition as a sequential optimization problem embedded within a design-based causal inference task. A budgeted combinatorial Thompson sampler learns which covariates are most prognostic across successive batches; selected covariates then drive rerandomization and regression adjustment to reduce batch-level average treatment effect variance. Our primary theoretical contribution is a decoupling result: adaptive covariate selection based on past batches preserves batch-level randomization validity, and the cumulative inverse-variance weighted estimator achieves at least nominal asymptotic coverage. We further derive a Bayes risk bound for the acquisition layer that matches the minimax lower bound up to logarithmic factors. Empirically, DARTS systematically concentrates the budget on informative features, significantly closing the efficiency gap to oracle designs while maintaining strict inferential validity.

This position paper argues that, in debiased machine learning, balancing functions should be derived from the Neyman orthogonal score, not chosen only as functions of covariates. Covariate balancing is effective when the regression error entering the score can be represented by functions of covariates alone, and it is the natural finite-dimensional approximation for targets such as ATT counterfactual means. For ATE estimation under treatment effect heterogeneity, however, the score error generally contains treatment-specific components because the outcome regression is a function of the full regressor $X=(D,Z)$. In that case, balancing common functions of $Z$ can leave the treatment-specific component unbalanced. We therefore advocate regressor balancing, implemented by Riesz regression with basis functions of $X$, as the general balancing principle for DML. The position is not that covariate balancing is invalid, but that covariate balancing should be understood as the special case that is appropriate when the score-relevant regression error is a function of covariates alone.

Estimating causal effects from observational data requires identifying valid adjustment sets. This task is especially challenging in realistic settings where latent confounding and feedback loops are present. Existing approaches typically assume acyclicity or rely on global causal structure learning, limiting applicability and computational efficiency. In this work, we study a local, data-driven method for covariate selection based on conditional independence information. While this method is known to be sound and complete in acyclic causal models, its validity in the presence of cycles has remained unclear. Our main contribution is to show that these guarantees extend to cyclic causal models. In particular, our result relies on the invariance of conditional independence assertions under $σ$-acyclification. These findings establish a unified, cycle-agnostic perspective on covariate selection and causal effect estimation, showing that the method applies across cyclic and acyclic settings without modification. Empirically, we validate this on extensive synthetic data, showing reliable performance in cyclic causal models.

Instrumental variable (IV) and control function (CF) methods are powerful tools for causal effect estimation in the presence of unmeasured confounding, yet most existing approaches target only mean effects and/or demand substantial fitting and tuning effort. In this paper, we introduce a simple method, TabCF, for control function regression using tabular foundation models, which enables accurate, fast, identification-transparent, and tuning-light causal estimation of distributional quantities, such as interventional means and quantiles; we also propose a copula-based approximation for multivariate outcomes. TabCF performs favorably against representative methods across a broad range of small- to medium-sized synthetic and real data scenarios. The central message is two-fold: for practitioners, it highlights that TabCF is an effective tool for distributional causal inference; for researchers, it suggests that the proposed approach could be considered a strong baseline for future method development. Code is available at https://github.com/GepingChen/TabCF.

Estimating causal effects from observational data has become increasingly critical in diverse fields including healthcare, economics, and social policy. The fundamental challenge in causal inference arises from the missing counterfactuals and the selection bias. Existing methods are largely limited to point estimates and lack the capacity for distribution modeling. In this work, we propose RepFlow, a novel framework that formulates causal effect estimation as a joint optimization problem integrating representation learning with Conditional Flow Matching (CFM). RepFlow mitigates selection bias by minimizing the entropically regularized Wasserstein distance between treated and control representations. To enhance numerical stability, we further introduce an $L_2$ normalization constraint on latent representations. This balanced representation enables the flow model to accurately capture the distribution of potential outcomes. Extensive experiments across a wide range of benchmarks demonstrate that RepFlow consistently outperforms existing methods in both point and distributional causal effect estimation.

Estimating individualized treatment effects from longitudinal observational data is central to data-driven medicine, yet existing methods face a fundamental limitation: reducing confounding bias often suppresses clinically informative heterogeneity, degrading patient-specific predictions. Here, we identify this tension as a bias-precision paradox in causal representation learning and introduce sampling-based maximum mean discrepancy (sMMD), a stochastic alignment strategy that replaces global adversarial balancing with subset-level matching. We instantiate this approach in a framework for counterfactual outcome prediction with attribution-grounded interpretability. Across two large-scale ICU cohorts (n = 27,783), our framework improves accuracy under distribution shift, reducing error by up to 11.5% and substantially increasing recall in high-risk tasks. Mechanistic analyses show that sMMD selectively preserves clinically decisive variables. In human-AI evaluation, our method outperforms clinicians-in-training and large language models, and improves clinician accuracy by 14.7% while reducing decision time, enabling interpretable, real-time clinical decision support.

Target trial emulation (TTE) enables causal questions to be studied with observational data when randomized controlled trials (RCTs) are infeasible. Yet treatment-effect methods often address causal estimation, missingness, and temporal structure separately, limiting their robustness in electronic health records (EHRs), where time-varying confounding and missing-not-at-random (MNAR) biomarkers can reach 50%--80%. We propose a two-stage pipeline for treatment effect estimation from incomplete longitudinal EHRs. First, CausalFlow-T, a directed acyclic graph (DAG)-constrained normalizing flow with long short-term memory (LSTM)-encoded patient history, performs exact invertible counterfactual inference, avoiding approximation errors from variational inference and separating confounding through explicit causal structure. Ablations on four synthetic and one semi-synthetic benchmark with known counterfactuals show that DAG constraints and exact inference address distinct failure modes: neither compensates for the other. Second, because CausalFlow-T requires completed inputs, we introduce an LLM-driven evolutionary imputer that proposes executable imputation operators rather than individual entries, and evaluate it with three large language model (LLM) backends, including two open-source models. Across 30%--80% MNAR missingness, this imputer achieves the best pooled rank over biomarker and causal metrics, leading in point-wise accuracy and temporal extrapolation while preserving average treatment effect (ATE) recovery as statistical baselines degrade. On Swiss primary-care EHRs from adults with type 2 diabetes initiating a GLP-1 receptor agonist or SGLT-2 inhibitor, the pipeline estimates a per-protocol weight-loss difference of -0.98 kg [95% CI -1.01, -0.96] favoring GLP-1 receptor agonists, consistent with randomized evidence and obtained from realistically incomplete real-world EHRs.

Published transfer-BO comparisons often estimate an average treatment effect of acquisition choice over hidden regime variables, while practitioners need the conditional effect for their specific prior quality, budget ratio, and metric. An audit of 40 transfer-BO papers from NeurIPS, ICML, ICLR, AISTATS, UAI, TMLR, JMLR, and AutoML-Conf (2022-2025) finds that 98% never vary B/|A| as a controlled axis. On the same GDSC2 benchmark, changing only the budget reverses the ranking: at B=50, Greedy outperforms UCB by 0.050 Hit@1, while at B=100, UCB outperforms Greedy by 0.035. We capture this transition with the Portable Regime Score PRS=(B/|A|)(1-rho), where rho is the prior rank correlation and can be estimated from pilot contexts before the main comparison. Across 79 conditions spanning chemistry, drug-response biology, and HPO, a hierarchical model gives beta=0.50 (p=1.1e-9), and 19% of conditions fall in an equivalence zone where |advantage|<0.01 Hit@1. In five published reversal cases, PRS predicts the winner from pre-comparison observables. A No-Free-Leaderboard proposition explains why unconditional rankings are unstable: when CATE changes sign across regimes, the reported ATE becomes a function of benchmark mixture. RegimePlanner, which estimates rho online and switches acquisition accordingly, wins all 16 HPO-B search spaces at B=100 and exceeds the matched {Greedy,UCB} per-context oracle on GDSC2 by 18%. Pre-registered predictions achieve 27/40=67.5% overall accuracy and above 90% within EMA prior families. The practical protocol is simple: report B/|A|, rho, K, and metric alongside any claimed acquisition advantage.