Causal Effect Estimation

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Overview

Causal effect estimation asks what would happen to outcomes if people, policies, or systems received different treatments, including average, subgroup-specific, and dose-response effects. Researchers use randomized trials and quasi-experiments alongside observational methods such as matching, propensity weighting, g-computation, instrumental variables, synthetic controls, and doubly robust or debiased machine learning. Current work extends these tools to longitudinal decisions, networks with spillovers, multiple or continuous treatments, and effects on entire outcome distributions, while improving uncertainty estimates and experimental design. A central challenge is that flexible prediction cannot by itself resolve unmeasured confounding, weak overlap, or violated transport assumptions, so credible estimates depend on identification assumptions and careful validation.

Latest papers

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266 papers35 papers in the last four weeks, up 35% on the four weeks before. 0.2% of all new papers.

Apr 13, 2026

Observing the unobserved confounding through its effects: toward randomized trial-like estimates from real-world survival data

Background: Randomized controlled trials (RCTs) are costly, time-consuming, and often infeasible, while treatment-effect estimation from observational data is limited by unobserved confounding. Methods: We developed a three-step framework to address unobserved confounding in observational survival data. First, we infer a latent prognostic factor (U) from restricted mean survival time (RMST) discrepancies between patients with similar observed factors, the same treatment, and divergent outcomes, leveraging the idea that the aggregate effect of unmeasured factors can be inferred even if individual factors cannot. Second, we balance U with observed baseline covariates using prognostic matching, entropy balancing, or inverse probability of treatment weighting. Third, we apply multivariable survival analysis to estimate hazard ratios (HRs). We evaluated the framework in three observational cohorts with RCT benchmarks, two RCT cohorts, and six multicenter observational cohorts. Results: In three observational cohorts (nine comparisons), balancing U improved agreement with trial HRs in all cases; in the strongest settings, it reduced absolute log-HR error by approximately ten-fold versus using observed covariates alone (mean reduction 0.344; p=0.001). In two RCT cohorts, U was balanced across arms (most SMDs <0.1) and adjustment had minimal impact on log-HRs (mean absolute change 0.08). Across six multicenter cohorts, balancing U within centers reduced cross-center dispersion in chemotherapy log-HR estimates (mean reduction 0.147; p=0.016); when populations were directly balanced across centers to account for case-mix differences, cross-center survival differences were narrowed in 75%-100% of comparisons. Conclusions: Inferring and balancing a latent prognostic signal may reduce unobserved confounding and improve treatment-effect estimation from real-world data.

Vasiliki Stoumpou, Dimitris Bertsimas, Samuel Singer +1

Operations Research Center, Massachusetts Institute of Technology, Cambridge, MA, USA · Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA, USA · Department of Surgery, Memorial Sloan Kettering Cancer Center, New York, NY, USA +1

Causal Inference with Unobserved ConfoundingCausal Effect EstimationCausal InferenceSurvival Analysis
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Apr 12, 2026

Orthogonal machine learning for conditional odds and risk ratios

Conditional effects are commonly used measures for understanding how treatment effects vary across different groups, and are often used to target treatments/interventions to groups who benefit most. In this work we review existing methods and propose novel ones, focusing on the odds ratio (OR) and the risk ratio (RR). While estimation of the conditional average treatment effect (ATE) has been widely studied, estimators for the OR and RR lag behind, and cutting edge estimators such as those based on doubly robust transformations or orthogonal risk functions have not been generalized to these parameters. We propose such a generalization here, focusing on the DR-learner and the R-learner. We derive orthogonal risk functions for the OR and RR and show that the associated pseudo-outcomes satisfy second-order conditional-mean remainder properties analogous to the ATE case. We also evaluate estimators for the conditional ATE, OR, and RR in a comprehensive nonparametric Monte Carlo simulation study to compare them with common alternatives under hundreds of different data-generating distributions. Our numerical studies provide empirical guidance for choosing an estimator. For instance, they show that while parametric models are useful in very simple settings, the proposed nonparametric estimators significantly reduce bias and mean squared error in the more complex settings expected in the real world. We illustrate the methods in the analysis of physical activity and sleep trouble in U.S. adults using data from the National Health and Nutrition Examination Survey (NHANES). The results demonstrate that our estimators uncover substantial treatment effect heterogeneity that is obscured by traditional regression approaches and lead to improved treatment decision rules, highlighting the importance of data-adaptive methods for advancing precision health research.

Jiacheng Ge, Iván Díaz

Division of Biostatistics, Department of Population Health, New York University Grossman School of Medicine, New York, NY, USA

Causal Effect EstimationDoubly Robust EstimationConditional Average Treatment Effect Estimation
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Apr 10, 2026

Identifying Causal Effects Using a Single Proxy Variable

Unobserved confounding is a key challenge when estimating causal effects from a treatment on an outcome. In this work, we assume that we observe a single, potentially multi-dimensional proxy variable of the unobserved confounder and that we know the mechanism that generates the proxy from the confounder. Under an assumption called Single Proxy Identifiability of Causal Effects or simply SPICE, we prove that this error mechanism is complete and causal effects are identifiable. We extend the proxy-based causal identifiability results by Kuroki and Pearl (2014); Pearl (2010) to multi-dimensional continuous settings, more flexible functional relationships and a broader class of distributions. Further, we develop a neural network based estimation framework, SPICE-Net, to estimate causal effects, which is applicable to both discrete and continuous treatments.

Silvan Vollmer, Niklas Pfister, Sebastian Weichwald

Department of Mathematical Sciences University of Copenhagen Copenhagen, Denmark · Lakera AI Zurich, Switzerland

Causal Effect EstimationCausal Inference with Unobserved ConfoundingCausal InferenceCausal Identifiability
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Apr 7, 2026

A Large-Scale Empirical Comparison of Meta-Learners and Causal Forests for Heterogeneous Treatment Effect Estimation in Marketing Uplift Modeling

Estimating Conditional Average Treatment Effects (CATE) at the individual level is central to precision marketing, yet systematic benchmarking of uplift modeling methods at industrial scale remains limited. We present UpliftBench, an empirical evaluation of four CATE estimators: S-Learner, T-Learner, X-Learner (all with LightGBM base learners), and Causal Forest (EconML), applied to the Criteo Uplift v2.1 dataset comprising 13.98 million customer records. The near-random treatment assignment (propensity AUC = 0.509) provides strong internal validity for causal estimation. Evaluated via Qini coefficient and cumulative gain curves, the S-Learner achieves the highest Qini score of 0.376, with the top 20% of customers ranked by predicted CATE capturing 77.7% of all incremental conversions, a 3.9x improvement over random targeting. SHAP analysis identifies f8 as the dominant heterogeneous treatment effect (HTE) driver among the 12 anonymized covariates. Causal Forest uncertainty quantification reveals that 1.9% of customers are confident persuadables (lower 95% CI > 0) and 0.1% are confident sleeping dogs (upper 95% CI < 0). Our results provide practitioners with evidence-based guidance on method selection for large-scale uplift modeling pipelines.

Aman Singh

Uplift ModelingConditional Average Treatment Effect EstimationCausal Effect Estimation
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Apr 5, 2026

InferenceEvolve: Towards Automated Causal Effect Estimators through Self-Evolving AI

Causal inference is central to scientific discovery, yet choosing appropriate methods remains challenging because of the complexity of both statistical methodology and real-world data. Inspired by the success of artificial intelligence in accelerating scientific discovery, we introduce InferenceEvolve, an evolutionary framework that uses large language models to discover and iteratively refine causal methods. Across widely used benchmarks, InferenceEvolve yields estimators that consistently outperform established baselines: against 58 human submissions in a recent community competition, our best evolved estimator lay on the Pareto frontier across two evaluation metrics. We also developed robust proxy objectives for settings without semi-synthetic outcomes, with competitive results. Analysis of the evolutionary trajectories shows that agents progressively discover sophisticated strategies tailored to unrevealed data-generating mechanisms. These findings suggest that language-model-guided evolution can optimize structured scientific programs such as causal inference, even when outcomes are only partially observed.

Can Wang, Hongyu Zhao, Yiqun Chen

Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21205, USA · Department of Computer Science, Johns Hopkins University, Baltimore, MD 21218, USA

Causal Effect EstimationAutomated Algorithm DiscoveryLarge Language Model-Guided Scientific DiscoveryEvolutionary Optimization
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Apr 3, 2026

Nonparametric Regression Discontinuity Designs with Survival Outcomes

Quasi-experimental evaluations are central for generating real-world causal evidence and complementing insights from randomized trials. The regression discontinuity design (RDD) is a quasi-experimental design that can be used to estimate the causal effect of treatments that are assigned based on a running variable crossing a threshold. Such threshold-based rules are ubiquitous in healthcare, where predictive and prognostic biomarkers frequently guide treatment decisions. However, standard RD estimators rely on complete outcome data, an assumption often violated in time-to-event analyses where censoring arises from loss to follow-up. To address this issue, we propose a nonparametric approach that leverages doubly robust censoring corrections and can be paired with existing RD estimators. Our approach can handle multiple survival endpoints, long follow-up times, and covariate-dependent variation in survival and censoring. We discuss the relevance of our approach across multiple areas of applications and demonstrate its usefulness through simulations and the prostate component of the Prostate, Lung, Colorectal and Ovarian (PLCO) Cancer Screening Trial where our new approach offers several advantages, including higher efficiency and robustness to misspecification. We have also developed an open-source software package, rdsurvival\texttt{rdsurvival}, for the R\texttt{R} language.

Maximilian Schuessler, Erik Sverdrup, Robert Tibshirani +1

Causal Effect EstimationSurvival AnalysisNonparametric Regression
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Apr 2, 2026

Statistical realism is not evidence that LLMs can estimate treatment effects in social science experiments

Large language models (LLMs) are increasingly used to simulate human responses and estimate treatment effect of interventions when real-world experiments are costly or infeasible. The treatment-effect estimates are often evaluated using statistical realism, the degree to which simulated responses reproduce properties of observed human responses, although whether realism predicts treatment-effect accuracy remains unknown. Here we test this proxy relationship by jointly measuring statistical realism and treatment-effect accuracy on the same simulated responses in a cross-national experiment with 59,508 participants from 62 countries using three LLMs. The correlation between statistical realism and treatment-effect accuracy is weak, and optimizing for statistical realism can even worsen treatment-effect accuracy when selecting models, prompts, and target populations. The pattern replicates in two additional cross-national experiments spanning 12 and 27 countries with 20,785 participants. The divergence between the two reflects distinct error structures and is larger for behavioral outcomes, where models appear to extrapolate behavioral effects from attitudinal patterns. Because this divergence may remain hidden in deployment, errors can propagate into simulation-informed decisions. We introduce a diagnostic framework for LLM-generated synthetic data and discuss how treatment-effect validation should proceed under varying availability of experimental benchmarks. Simulated responses and simulated treatment effects are distinct estimation targets, and evidence for one does not certify the other.

Zonghan Li, Feng Ji

Department of Applied Psychology and Human Development, University of Toronto, ON, Canada

Large Language Model-Based Social SimulationSynthetic Data EvaluationCausal Effect Estimation
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Apr 1, 2026

The Digital Twin Counterfactual Framework: A Validation Architecture for Simulated Potential Outcomes

The fundamental problem of causal inference - that the counterfactual outcome for any individual is never observed - has shaped the entire methodology of the field. Every existing approach substitutes assumptions for missing data: ignorability, parallel trends, exclusion restrictions. None produces the counterfactual itself. This paper proposes the Digital Twin Counterfactual Framework (DTCF): rather than estimating the counterfactual statistically, we simulate it using a digital twin and subject the simulation to a hierarchical validation regime. We formalize the digital twin simulator as a stochastic mapping within the potential outcomes framework and introduce a hierarchy of twin fidelity assumptions - from marginal fidelity through joint fidelity to structural fidelity - each unlocking a progressively richer class of estimands. The central contribution is threefold. First, a five-level validation architecture converts the unfalsifiable claim that the simulator produces correct counterfactuals into falsifiable tests against observable data. Second, a formal decomposition separates causal quantities into those that are marginally validated (ATE, CATE, QTE - testable through observable-arm comparison) and those that are copula-dependent (the ITE distribution, probability of benefit/harm, variance of treatment effects - permanently reliant on the unobservable within-individual dependence structure). Third, bounding, sensitivity, and uncertainty quantification tools make the copula dependence explicit. The DTCF does not resolve the fundamental problem of causal inference. What it provides is a framework in which marginal causal claims become increasingly testable, joint causal claims become explicitly assumption-indexed, and the gap between the two is formally characterized.

Olav Laudy

Counterfactual EvaluationCausal Effect EstimationCausal ReasoningCausal IdentifiabilityDigital Twins
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Apr 1, 2026

Orthogonal Learner for Estimating Heterogeneous Long-Term Treatment Effects

Estimation of heterogeneous long-term treatment effects (HLTEs) is relevant for personalized decision-making in marketing, economics, and medicine, where short-term observational datasets are often combined with long-term observational datasets. However, HLTE estimation is challenging due to limited overlap in treatment assignments or in long-term outcomes for certain subpopulations, which can lead to unstable HLTE estimates with large finite-sample variance. To address this challenge, we introduce the LT-O-learners (Long-Term Orthogonal Learners), a set of novel orthogonal learners for HLTE estimation in the canonical HLTE setting with surrogacy. The key idea of our LT-O-learners is to retarget the loss via custom overlap weights that downweight low-overlap samples. We show that the retargeted loss recovers the true HLTE pointwise and satisfies Neyman-orthogonality. We further prove two key theoretical results: (i) The nuisance error enters the error bound only through higher-order terms, which means our learners are robust to nuisance estimation error. (ii) Under a linear function class, the retargeting effectively controls the asymptotic variance of the HLTE estimator via the overlap weights in low-overlap regimes. We conduct experiments on synthetic and real-world datasets to confirm the theoretical properties of our LT-O-learners, particularly robustness in low-overlap regimes. To our knowledge, ours are the first orthogonal learners for HLTE estimation robust to low overlap in long-term settings.

Haorui Ma, Dennis Frauen, Valentyn Melnychuk +1

AI in Management, LMU Munich; Munich Center for Machine Learning; Munich, Germany

Causal Effect EstimationConditional Average Treatment Effect EstimationRobust Estimation
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Apr 1, 2026

Deconfounding Scores and Representation Learning for Causal Effect Estimation with Weak Overlap

Overlap, also known as positivity, is a key condition for causal treatment effect estimation. Many popular estimators suffer from high variance and become brittle when features differ strongly across treatment groups. This is especially challenging in high dimensions: the curse of dimensionality can make overlap implausible. To address this, we propose a class of feature representations called deconfounding scores, which preserve both identification and the target of estimation; the classical propensity and prognostic scores are two special cases. We characterize the problem of finding a representation with better overlap as minimizing an overlap divergence under a deconfounding score constraint. We then derive closed-form expressions for a class of deconfounding scores under a broad family of generalized linear models with Gaussian features and show that prognostic scores are overlap-optimal within this class. We conduct extensive experiments to assess this behavior empirically.

Oscar Clivio, Alexander D'Amour, Alexander Franks +3

University of California, Berkeley

Causal Effect EstimationCausal Representation LearningCausal Intervention
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Mar 31, 2026

Monodense Deep Neural Model for Determining Item Price Elasticity

Item Price Elasticity is used to quantify the responsiveness of consumer demand to changes in item prices, enabling businesses to create pricing strategies and optimize revenue management. Sectors such as store retail, e-commerce, and consumer goods rely on elasticity information derived from historical sales and pricing data. This elasticity provides an understanding of purchasing behavior across different items, consumer discount sensitivity, and demand elastic departments. This information is particularly valuable for competitive markets and resource-constrained businesses decision making which aims to maximize profitability and market share. Price elasticity also uncovers historical shifts in consumer responsiveness over time. In this paper, we model item-level price elasticity using large-scale transactional datasets, by proposing a novel elasticity estimation framework which has the capability to work in an absence of treatment control setting. We test this framework by using Machine learning based algorithms listed below, including our newly proposed Monodense deep neural network. (1) Monodense-DL network -- Hybrid neural network architecture combining embedding, dense, and Monodense layers (2) DML -- Double machine learning setting using regression models (3) LGBM -- Light Gradient Boosting Model We evaluate our model on multi-category retail data spanning millions of transactions using a back testing framework. Experimental results demonstrate the superiority of our proposed neural network model within the framework compared to other prevalent ML based methods listed above.

Lakshya Garg, Sai Yaswanth, Deep Narayan Mishra +3

Walmart Inc. Hoboken,NJ, USA · Walmart Inc. Seattle,WA, USA · Walmart Inc. Sunnyvale,CA, USA +1

Causal Effect EstimationFeedforward Neural Networks
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Mar 29, 2026

Decomposing Discrimination: Causal Mediation Analysis for AI-Driven Credit Decisions

Statistical fairness metrics in AI-driven credit decisions conflate two causally distinct mechanisms: discrimination operating directly from a protected attribute to a credit outcome, and structural inequality propagating through legitimate financial features. We formalise this distinction using Pearl's framework of natural direct and indirect effects applied to the credit decision setting. Our primary theoretical contribution is an identification strategy for natural direct and indirect effects under treatment-induced confounding -- the prevalent setting in which protected attributes causally affect both financial mediators and the final decision, violating standard sequential ignorability. We show that interventional direct and indirect effects (IDE/IIE) are identified under the weaker Modified Sequential Ignorability assumption, and prove that IDE/IIE provide conservative bounds on the unidentified natural effects under monotone indirect treatment response. We propose a doubly-robust augmented inverse probability weighted (AIPW) estimator for IDE/IIE with semiparametric efficiency properties, implemented via cross-fitting. An E-value sensitivity analysis addresses residual confounding on the direct pathway. Empirical evaluation on 89,465 real HMDA conventional purchase mortgage applications from New York State (2022) demonstrates that approximately 77% of the observed 7.9 percentage-point racial denial disparity operates through financial mediators shaped by structural inequality, while the remaining 23% constitutes a conservative lower bound on direct discrimination. The open-source CausalFair Python package implements the full pipeline for deployment at resource-constrained financial institutions.

Duraimurugan Rajamanickam

VP, Artificial Intelligence, Hudson Valley Credit Union, Poughkeepsie, NY · PhD Candidate, Causal Machine Learning, University of Arkansas at Little Rock

Financial ServicesCausal Effect EstimationCausal Mediation AnalysisAlgorithmic FairnessCausal AttributionCausal Inference+3
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Mar 28, 2026

Maximin Learning of Individualized Treatment Effect on Multi-Domain Outcomes

Precision mental health requires treatment decisions that account for heterogeneous symptoms reflecting multiple clinical domains. However, existing methods for estimating individualized treatment effects (ITE) rely on a single summary outcome or a specific set of observed symptoms or measures, which are sensitive to symptom selection and limit generalizability to unmeasured yet clinically relevant domains. We propose DRIFT, a new maximin framework for estimating robust ITEs from high-dimensional item-level data by leveraging latent factor representations and adversarial learning. DRIFT learns latent constructs via generalized factor analysis, then constructs an anchored on-target uncertainty set that extrapolates beyond the observed measures to approximate the broader hyper-population of potential outcomes. By optimizing worst-case performance over this uncertainty set, DRIFT yields ITEs that are robust to underrepresented or unmeasured domains. We further show that DRIFT is invariant to admissible reparameterizations of the latent factors and admits a closed-form maximin solution, with theoretical guarantees for identification and convergence. In analyses of a randomized controlled trial for major depressive disorder (EMBARC), DRIFT demonstrates superior performance and improved generalizability to external multi-domain outcomes, including side effects and self-reported symptoms not used during training.

Yuying Lu, Wenbo Fei, Yuanjia Wang +1

Department of Biostatistics, Columbia Mailman School of Public Health. · Department of Biostatistics, Peking University Health Science Center. · Beijing International Center for Mathematical Research, Peking University.

Individualized Treatment Effect EstimationCausal Effect EstimationMental HealthDistributionally Robust Optimization
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Mar 24, 2026

Causal AI For AMS Circuit Design: Interpretable Parameter Effects Analysis

Analog-mixed-signal (AMS) circuits are highly non-linear and operate on continuous real-world signals, making them far more difficult to model with data-driven AI than digital blocks. To close the gap between structured design data (device dimensions, bias voltages, etc.) and real-world performance, we propose a causal-inference framework that first discovers a directed-acyclic graph (DAG) from SPICE simulation data and then quantifies parameter impact through Average Treatment Effect (ATE) estimation. The approach yields human-interpretable rankings of design knobs and explicit 'what-if' predictions, enabling designers to understand trade-offs in sizing and topology. We evaluate the pipeline on three operational-amplifier families (OTA, telescopic, and folded-cascode) implemented in TSMC 65nm and benchmark it against a baseline neural-network (NN) regressor. Across all circuits the causal model reproduces simulation-based ATEs with an average absolute error of less than 25%, whereas the neural network deviates by more than 80% and frequently predicts the wrong sign. These results demonstrate that causal AI provides both higher accuracy and explainability, paving the way for more efficient, trustworthy AMS design automation.

Mohyeu Hussain, David Koblah, Reiner Dizon-Paradis +1

University of Florida

Electronic Design AutomationCausal InterpretabilityCausal Effect EstimationCausal Discovery
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Mar 19, 2026

Improving RCT-Based Treatment Effect Estimation Under Covariate Mismatch via Calibrated Alignment

Randomized controlled trials (RCTs) are the gold standard for estimating treatment effects, yet they are often underpowered for detecting effect heterogeneity. Large observational studies (OS) can supplement RCTs for conditional average treatment effect (CATE) estimation, but a key barrier is covariate mismatch: the two sources measure different, only partially overlapping, covariates. We propose CALM (Calibrated ALignment under covariate Mismatch), which learns embeddings that map each source's features into a common representation space. OS outcome models are transferred to the RCT embedding space and calibrated using trial data, preserving causal identification from randomization. Finite-sample risk bounds decompose into alignment error, outcome-model complexity, and calibration complexity terms, making explicit when the learned embedding is accurate enough to reduce variance. We instantiate CALM in two forms: a closed-form linear version, CALM-Lin, and a neural representation-learning version, CALM-NN. Across 51 simulation settings, calibration-based linear methods are effectively tied in linear-CATE regimes, while CALM-NN wins all 22 nonlinear-CATE settings by wide margins. Moreover, on two real-data studies CALM-NN delivers the largest gains over the trial-only baseline.

Amir Asiaee, Samhita Pal

Department of Biostatistics, Vanderbilt University Medical Center, TN 37203, USA

Causal Effect EstimationCausal Representation LearningConditional Average Treatment Effect EstimationCausal InferenceIndividualized Treatment Effect Estimation
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Mar 17, 2026

Conditional Distributional Treatment Effects: Doubly Robust Estimation and Testing

Beyond conditional average treatment effects, treatments may impact the entire outcome distribution in covariate-dependent ways, for example, by altering the variance or tail risks for specific subpopulations. We propose a novel estimand to capture such conditional distributional treatment effects, and develop a doubly robust estimator that is minimax optimal in the local asymptotic sense. Using this, we develop a test for the global homogeneity of conditional potential outcome distributions that accommodates discrepancies beyond the maximum mean discrepancy (MMD), has provably valid type 1 error, and is consistent against fixed alternatives---the first test, to our knowledge, with such guarantees in this setting. We then provide a test that aggregates evidence across a grid of kernel-bandwidth choices. Furthermore, we derive exact closed-form expressions for two natural discrepancies (including the MMD), and provide a computationally efficient, permutation-free algorithm for our test.

Saksham Jain, Alex Luedtke

Department of Statistics, University of Washington, Seattle, USA · Departments of Health Care Policy and Statistics, Harvard University, USA

Causal Effect EstimationCausal InferenceDoubly Robust EstimationStatistical Hypothesis Testing
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Mar 15, 2026

Beyond Means: Topological Causal Effects under Persistent-Homology Ignorability

Average treatment effects (ATE) and conditional average treatment effects (CATE) are foundational causal estimands, but they target changes in expected outcomes and can miss treatment-induced changes in the shape of outcome distributions. A canonical failure mode occurs when control outcomes are unimodal, treated outcomes become bimodal, and both distributions have the same mean. In such cases mean-based causal estimands are zero even though the geometry and topology of the outcome law change substantially. This paper develops a topological causal framework based on persistent homology. We formalize a persistent-homology ignorability condition, define topological analogues of CATE and ATE, and prove that these estimands are identifiable up to an explicit error bound under approximate topological ignorability. We also clarify a subtle but important point: a marginal persistence-diagram effect is not identified from conditional topological ignorability alone because persistent homology does not in general commute with mixtures over covariates. To preserve the original intuition while ensuring scientific correctness, we retain the marginal effect as a motivating quantity, but place the mathematically sound conditional estimands at the center of the theory. A synthetic experiment with mean-preserving topology change shows that mean-based causal estimands remain near zero while the proposed topological effect increases sharply and remains recoverable after adjustment for confounding.

Amir Saki, Usef Faghihi

Université du Québec à Trois-Rivières (UQTR).

Causal Effect EstimationCausal IdentifiabilityConditional Average Treatment Effect EstimationPersistent Homology
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Mar 12, 2026

Frequentist Consistency of Prior-Data Fitted Networks for Causal Inference

Foundation models based on prior-data fitted networks (PFNs) have shown strong empirical performance in causal inference by framing the task as an in-context learning problem. However, it is unclear whether PFN-based causal estimators provide uncertainty quantification that is consistent with classical frequentist estimators. In this work, we address this gap by analyzing the frequentist consistency of PFN-based estimators for the average treatment effect (ATE). (1) We show that existing PFNs, when interpreted as Bayesian ATE estimators, can exhibit prior-induced confounding bias: the prior is not asymptotically overwritten by data, which, in turn, prevents frequentist consistency. (2) As a remedy, we suggest employing a calibration procedure based on a one-step posterior correction (OSPC). We show that the OSPC helps to restore frequentist consistency and can yield a semi-parametric Bernstein-von Mises theorem for calibrated PFNs (i.e., both the calibrated PFN-based estimators and the classical semi-parametric efficient estimators converge in distribution with growing data size). (3) Finally, we implement OSPC through tailoring martingale posteriors on top of the PFNs. In this way, we are able to recover functional nuisance posteriors from PFNs, required by the OSPC. In multiple (semi-)synthetic experiments, PFNs calibrated with our martingale posterior OSPC produce ATE uncertainty that (i) asymptotically matches frequentist uncertainty and (ii) is well calibrated in finite samples in comparison to other Bayesian ATE estimators.

Valentyn Melnychuk, Vahid Balazadeh, Stefan Feuerriegel +1

LMU Munich & Munich Center for Machine Learning (MCML), Munich, Germany · University of Toronto & Vector Institute, Toronto, Canada

Causal Effect EstimationPrior-Data Fitted NetworksBayesian InferenceSemiparametric InferenceProbability Calibration
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Mar 12, 2026

Causal Matrix Completion under Multiple Treatments via Mixed Synthetic Nearest Neighbors

Synthetic Nearest Neighbors (SNN) provides a principled solution to causal matrix completion under missing-not-at-random (MNAR) by exploiting local low-rank structure through fully observed anchor submatrices. However, its effectiveness critically relies on sufficient data availability within each treatment level, a condition that often fails in settings with multiple or complex treatments. In this work, we propose Mixed Synthetic Nearest Neighbors (MSNN), a new entry-wise causal identification estimator that integrates information across treatment levels. We show that MSNN retains the finite-sample error bounds and asymptotic normality guarantees of SNN, while enlarging the effective sample size available for estimation. Empirical results on synthetic and real-world datasets illustrate the efficacy of the proposed approach, especially under data-scarce treatment levels.

Minrui Luo, Zhiheng Zhang

Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China · School of Statistics and Data Science, Shanghai University of Finance and Economics, Shanghai, China

Causal Effect EstimationMatrix Completion
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Mar 12, 2026

Causal Representation Learning with Optimal Compression under Complex Treatments

Estimating Individual Treatment Effects (ITE) in multi-treatment scenarios faces two critical challenges: the Hyperparameter Selection Dilemma for balancing weights and the Curse of Dimensionality in computational scalability. This paper derives a novel multi-treatment generalization bound and proposes a theoretical estimator for the optimal balancing weight αα, eliminating expensive heuristic tuning. We investigate three balancing strategies: Pairwise, One-vs-All (OVA), and Treatment Aggregation. While OVA achieves superior precision in low-dimensional settings, our proposed Treatment Aggregation ensures both accuracy and O(1) scalability as the treatment space expands. Furthermore, we extend our framework to a generative architecture, Multi-Treatment CausalEGM, which preserves the Wasserstein geodesic structure of the treatment manifold. Experiments on semi-synthetic and image datasets demonstrate that our approach significantly outperforms traditional models in estimation accuracy and efficiency, particularly in large-scale intervention scenarios.

Wanting Liang, Haoang Chi, Zhiheng Zhang

Shanghai University of Finance and Economics, Shanghai, China.

Causal Effect EstimationIndividualized Treatment Effect EstimationCausal Representation Learning
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Mar 12, 2026

CAETC: Causal Autoencoding and Treatment Conditioning for Counterfactual Estimation over Time

Counterfactual estimation over time is important in various applications, such as personalized medicine. However, time-dependent confounding bias in observational data still poses a significant challenge in achieving accurate and efficient estimation. We introduce causal autoencoding and treatment conditioning (CAETC), a novel method for this problem. Built on adversarial representation learning, our method leverages an autoencoding architecture to learn a partially invertible and treatment-invariant representation, where the outcome prediction task is cast as applying a treatment-specific conditioning on the representation. Our design is independent of the underlying sequence model and can be applied to existing architectures such as long short-term memories (LSTMs) or temporal convolution networks (TCNs). We conduct extensive experiments on synthetic, semi-synthetic, and real-world data to demonstrate that CAETC yields significant improvement in counterfactual estimation over existing methods.

Nghia D. Nguyen, Pablo Robles-Granda, Lav R. Varshney

Siebel School of Computing and Data Science, University of Illinois Urbana-Champaign · VinUni-Illinois Smart Health Center, VinUniversity · AI Innovation Institute, Stony Brook University +1

Causal Effect EstimationCounterfactual LearningCausal Representation Learning
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Mar 11, 2026

Interventional Time Series Priors for Causal Foundation Models

Prior-data fitted networks (PFNs) have emerged as powerful foundation models for tabular causal inference, yet their extension to time series remains limited by the absence of synthetic data generators that provide interventional targets. Existing time series benchmarks generate observational data with ground-truth causal graphs but lack the interventional data required for training causal foundation models. To address this, we propose CausalTimePrior, a principled framework for generating synthetic temporal structural causal models (TSCMs) with paired observational and interventional time series. Our prior supports configurable causal graph structures, nonlinear autoregressive mechanisms, regime-switching dynamics, and multiple intervention types (hard, soft, time-varying). We demonstrate that PFNs trained on CausalTimePrior can perform in-context causal effect estimation on held-out TSCMs, establishing a pathway toward foundation models for time series causal inference.

Dennis Thumm, Ying Chen

National University of Singapore · Department of Mathematics, Centre for Quantitative Finance, Risk Management Institute, National University of Singapore

Causal Foundation ModelsSynthetic Data GenerationCausal Effect EstimationStructural Causal Models
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Mar 9, 2026

Structural Causal Bottleneck Models

We introduce structural causal bottleneck models (SCBMs), a novel class of structural causal models in which causal effects between high-dimensional variables are mediated by low-dimensional summary statistics, or bottlenecks. SCBMs provide a flexible framework for mechanism-specific, target-dependent dimension reduction while remaining estimable via standard learning algorithms. We prove that bottleneck variables are identifiable up to bijection from observational data, and validate this experimentally. We then study causal effect estimation in linear SCBMs under three standard adjustment strategies. For instrumental variables, we identify a population-level non-identifiability of naïve two-stage least squares when all variables are high-dimensional, and show that bottleneck representations restore identification. For mediation and backdoor adjustment, we prove that conditioning on bottleneck variables yields valid effect estimates with explicit finite-sample efficiency gains over conditioning on full high-dimensional variables. We argue that SCBMs provide a principled alternative to existing causal dimension reduction frameworks such as causal representation learning and causal abstractions.

Simon Bing, Jonas Wahl, Jakob Runge

Equal contribution · Technische Universität Berlin · Department of Computer Science, University of Potsdam +1

Structural Causal ModelsCausal Effect EstimationCausal Identifiability
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Mar 9, 2026

Unifying On- and Off-Policy Variance Reduction Methods

Continuous and efficient experimentation is key to the practical success of user-facing applications on the web, both through online A/B-tests and off-policy evaluation. Despite their shared objective -- estimating the incremental value of a treatment -- these domains often operate in isolation, utilising distinct terminologies and statistical toolkits. This paper bridges that divide by establishing a formal equivalence between their canonical variance reduction methods. We prove that the standard online Difference-in-Means estimator is mathematically identical to an off-policy Inverse Propensity Scoring estimator equipped with an optimal (variance-minimising) additive control variate. Extending this unification, we demonstrate that widespread regression adjustment methods (such as CUPED, CUPAC, and ML-RATE) are structurally equivalent to Doubly Robust estimation. This unified view extends our understanding of commonly used approaches, and can guide practitioners and researchers working on either class of problems.

Olivier Jeunen

aampe Antwerp, Belgium

Causal Effect EstimationA/b TestingVariance ReductionOff-Policy EvaluationDoubly Robust Estimation
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Mar 8, 2026

How Wrong Can Your Counterfactual Be? Quantifying Confounding Bias for Continuous Treatments without a Control Group

Stress testing poses a causal question: how would portfolio credit losses change if the macroeconomy followed an adverse counterfactual path? Yet standard practice remains predictive and might be therefore vulnerable to omitted-variable bias. We propose a partial identification framework for causal stress testing in panel data with a continuous common treatment and no control group. By assuming that the unobserved confounder affects outcome and macro variables additively, we derive a closed-form confounding envelope parameterized by two interpretable sensitivity parameters. We further analyze two practical estimators -- recursive rollout and direct multi-horizon prediction -- derive non-asymptotic error bounds, and characterize when recursive compounding makes direct estimation preferable. For inference, we combine the identification envelope with importance-weighted conformal prediction, yielding finite-sample intervals that separate estimation uncertainty from identification uncertainty under covariate shift. In semi-synthetic experiments built from real U.S. unemployment paths, standard high-accuracy predictive models remain causally biased and substantially under-cover, whereas the proposed framework achieves near-nominal coverage across stress horizons.

Yu Wang, Xiangchen Liu, Siguang Li

Department of Economics, Cornell University. · Department of Family and Consumer Sciences, California State University, Long Beach. · Society Hub, Hong Kong University of Science and Technology (Guangzhou).

Causal Effect EstimationCausal InferencePartial IdentificationSensitivity Analysis
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Mar 7, 2026

TEA-Time: Transporting Effects Across Time

Treatment effects estimated from a randomized controlled trial are local not only to the study population but also to the time at which the trial was conducted. The literature on generalizing experimental findings to new populations is extensive, yet transporting effects across time has received far less attention, and even defining the target estimand is nonobvious. We formalize the transported average treatment effect under a separable temporal effects assumption, derive two identification strategies: replicated trials and common arm, and develop doubly robust, semiparametrically efficient estimators for each. Applied to a large archive of headline A/B tests, the common arm strategy is substantially more precise but exhibits systematic bias when the temporal factor depends on the gap between intervention and measurement rather than on measurement time alone, while the replicated trials strategy, which allows this dependence, tracks the ground truth more faithfully. Simulation studies investigate when each strategy is reliable and when it silently fails.

Harsh Parikh, Gabriel Levin-Konigsberg, Dominique Perrault-Joncas +1

Amazon SCOT, Seattle, USA · Yale University, New Haven, USA · Duke University, Durham, USA

Causal Effect Estimation
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Mar 4, 2026

Observationally Informed Adaptive Causal Experimental Design

Randomized Controlled Trials (RCTs) represent the gold standard for causal inference yet remain a scarce resource. While large-scale observational data is often available, it is utilized only for retrospective fusion, and remains discarded in prospective trial design due to bias concerns. We argue this "tabula rasa" data acquisition strategy is fundamentally inefficient. In this work, we propose Active Residual Learning, a new paradigm that leverages the observational model as a foundational prior. This approach shifts the experimental focus from learning target causal quantities from scratch to efficiently estimating the residuals required to correct observational bias. To operationalize this, we introduce the R-Design framework. Theoretically, we establish two key advantages: (1) a structural efficiency gap, proving that estimating smooth residual contrasts admits strictly faster convergence rates than reconstructing full outcomes; and (2) information efficiency, where we quantify the redundancy in standard parameter-based acquisition (e.g., BALD), demonstrating that such baselines waste budget on task-irrelevant nuisance uncertainty. We propose R-EPIG (Residual Expected Predictive Information Gain), a unified criterion that directly targets the causal estimand, minimizing residual uncertainty for estimation or clarifying decision boundaries for policy. Experiments on synthetic and semi-synthetic benchmarks demonstrate that R-Design significantly outperforms baselines, confirming that repairing a biased model is far more efficient than learning one from scratch.

Erdun Gao, Liang Zhang, Jake Fawkes +5

Australian Institute for Machine Learning, Adelaide University · Hong Kong University of Science and Technology (Guangzhou) · University College London +3

Active Experimental DesignCausal InferenceCausal Effect EstimationAdaptive SamplingBayesian Experimental DesignResidual Learning
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Mar 3, 2026

Generalized Bayes for Causal Inference

Uncertainty quantification is central to many applications of causal machine learning, yet principled Bayesian inference for causal effects remains challenging. Standard Bayesian approaches typically require specifying a probabilistic model for the data-generating process, including high-dimensional nuisance components such as propensity scores and outcome regressions. Standard posteriors are thus vulnerable to strong modeling choices, including complex prior elicitation. In this paper, we propose a generalized Bayesian framework for causal inference. Our framework avoids explicit likelihood modeling; instead, we place priors directly on the causal estimands and update these using an identification-driven loss function, which yields generalized posteriors for causal effects. As a result, our framework turns existing loss-based causal estimators into estimators with full uncertainty quantification. Our framework is flexible and applicable to a broad range of causal estimands (e.g., ATE, CATE). Further, our framework can be applied on top of state-of-the-art causal machine learning pipelines (e.g., Neyman-orthogonal meta-learners). For Neyman-orthogonal losses, we show that the generalized posteriors converge to their oracle counterparts and remain robust to first-stage nuisance estimation error. With calibration, we thus obtain valid frequentist uncertainty even when nuisance estimators converge at slower-than-parametric rates. Empirically, we demonstrate that our proposed framework offers causal effect estimation with calibrated uncertainty across several causal inference settings. To the best of our knowledge, this is the first flexible framework for constructing generalized Bayesian posteriors for causal machine learning.

Emil Javurek, Dennis Frauen, Yuxin Wang +1

LMU Munich · Munich Center for Machine Learning

Generalized Bayesian InferenceCausal InferenceCausal Effect EstimationBayesian Inference
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Mar 2, 2026

Estimating Visual Attribute Effects in Advertising from Observational Data: A Deepfake-Informed Double Machine Learning Approach

Digital advertising increasingly relies on visual content, yet marketers lack rigorous methods for understanding how specific visual attributes causally affect consumer engagement. This paper addresses a fundamental methodological challenge: estimating causal effects when the treatment, such as a model's skin tone, is an attribute embedded within the image itself. Standard approaches like Double Machine Learning (DML) fail in this setting because vision encoders entangle treatment information with confounding variables, producing severely biased estimates. We develop DICE-DML (Deepfake-Informed Control Encoder for Double Machine Learning), a framework that leverages generative AI to disentangle treatment from confounders. The approach combines three mechanisms: (1) deepfake-generated image pairs that isolate treatment variation; (2) DICE-Diff adversarial learning on paired difference vectors, where background signals cancel to reveal pure treatment fingerprints; and (3) orthogonal projection that geometrically removes treatment-axis components. In simulations with known ground truth, DICE-DML reduces root mean squared error by 73-97% compared to standard DML, with the strongest improvement (97.5%) at the null effect point, demonstrating robust Type I error control. Applying DICE-DML to 232,089 Instagram influencer posts, we estimate the causal effect of skin tone on engagement. Standard DML produces diagnostically invalid results (negative outcome R^2), while DICE-DML achieves valid confounding control (R^2 = 0.63) and estimates a marginally significant negative effect of darker skin tone (-522 likes; p = 0.062), substantially smaller than the biased standard estimate. Our framework provides a principled approach for causal inference with visual data when treatments and confounders coexist within images.

Yizhi Liu, Balaji Padmanabhan, Siva Viswanathan

Robert H. Smith School of Business, University of Maryland, College Park, MD, USA

Causal Effect EstimationCausal InferenceDouble MLOnline Advertising
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Mar 2, 2026

De-paradox Tree: Breaking Down Simpson's Paradox via A Kernel-Based Partition Algorithm

Real-world observational datasets and machine learning have revolutionized data-driven decision-making, yet many models rely on empirical associations that may be misleading due to confounding and subgroup heterogeneity. Simpson's paradox exemplifies this challenge, where aggregated and subgroup-level associations contradict each other, leading to misleading conclusions. Existing methods provide limited support for detecting and interpreting such paradoxical associations, especially for practitioners without deep causal expertise. We introduce De-paradox Tree, an interpretable algorithm designed to uncover hidden subgroup patterns behind paradoxical associations under assumed causal structures involving confounders and effect heterogeneity. It employs novel split criteria and balancing-based procedures to adjust for confounders and homogenize heterogeneous effects through recursive partitioning. Compared to state-of-the-art methods, De-paradox Tree builds simpler, more interpretable trees, selects relevant covariates, and identifies nested opposite effects while ensuring robust estimation of causal effects when causally admissible variables are provided. Our approach addresses the limitations of traditional causal inference and machine learning methods by introducing an interpretable framework that supports non-expert practitioners while explicitly acknowledging causal assumptions and scope limitations, enabling more reliable and informed decision-making in complex observational data environments.

Xian Teng, Yu-Ru Lin

University of Pittsburgh, Pittsburgh, Pennsylvania, USA

Causal InferenceCausal ReasoningCausal Effect EstimationDecision Tree LearningConditional Average Treatment Effect Estimation
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