Conditional Average Treatment Effect Estimation

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Overview

Conditional average treatment effect (CATE) estimation asks how a treatment changes outcomes for people or groups with different observed characteristics, supporting decisions about whom to treat and where resources are most effective. Common approaches include S-, T-, X- and R-learners, causal forests and trees, and doubly robust or orthogonal methods that combine outcome and treatment-assignment models; Bayesian and neural methods extend these tools to uncertainty estimation and complex representations. Researchers apply them to randomized trials and observational data, including marketing, health, policy, and survival settings, and evaluate both effect accuracy and the value of resulting treatment policies. A central challenge is making estimates and uncertainty reliable under confounding, weak treatment overlap, distribution shift, and noisy outcomes, while choosing benchmarks and ranking metrics that match the decision being made.

Latest papers

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51 papers8 papers in the last four weeks, up 33% on the four weeks before. 0.0% of all new papers.

Jun 5, 2026

Heterogeneous Effects of Green Finance on Urban Decarbonization: Evidence from 285 Cities in China

While green finance has become a key instrument for low-carbon city transitions, its actual decarbonization effects and transmission mechanisms remain unclear. This study employs econometric models and machine learning-based analysis to examine whether and how green finance reduces city-level carbon intensity. Results show that green finance significantly lowers carbon intensity, with green bonds and green investment having the strongest impacts and evident spatial spillovers. The effects vary by development level, being most pronounced in Fourth- and Fifth-tier cities. Mediation analysis reveals that green finance operates mainly through energy structure optimization, followed by industrial upgrading, foreign direct investment, and technological innovation. SHAP analysis confirms substantial differences across financial instruments, with green bonds, funds, and credit contributing most to decarbonization. Moreover, the marginal impact is stronger in cities with low technological capacity, high industrial dependency, and coal-based energy mixes. These findings provide theoretical support and policy guidance for building a multi-level, regionally differentiated green finance system to promote inclusive low-carbon transitions. Keywords: Green Finance; Carbon Intensity; Decarbonization Effect; Machine Learning; City

Xueyang Li, Jinlei Ma

1and2School of Business, Anhui University of Technology, Anhui 243002, China

Conditional Average Treatment Effect Estimation
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Jun 5, 2026

Transfer learning for causal forest

Transfer learning addresses the challenge of transfering knowledge from one domain to another. Traditional transfer learning focuses on adapting models trained on a source domain (with a lot of observations) to improve performance on a target domain (with few observations). In this work we consider the case of a model shift and we focus on the transfer learning applied to a causal forest namely HTERF. This causal forest aims to estimate the Conditional Average Treatment Effect (CATE). The approach considered is the offset method presented by Wang (2016) adapted to a causal context. This method relies on the use of intermediate models in order to estimate the offset between source and target distributions. Our main result is a bound on the CATE error of HTERF on target depending on the error of the intermediate models. Simulation studies show the good performances of this approach in different settings on simulations and on a real-world dataset.

Bérénice-Alexia Jocteur, Véronique Maume-Deschamps, Pierre Ribereau

ICJ, PSPM · Universit´e Lyon 1, Centrale Lyon, INSA Lyon · Universit´e Jean Monnet, CNRS, ICJ UMR5208, 69622 Villeurbanne, France. +1

Causal Effect EstimationConditional Average Treatment Effect EstimationCross-Domain Transfer LearningTransfer LearningIndividualized Treatment Effect Estimation
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May 28, 2026

Improved Guarantees for Heterogeneous Treatment-Effect Estimation via Matrix Completion

A central goal of modern causal inference is estimating heterogeneous treatment effects to answer questions like "how does an intervention affect each unit," rather than only on average. We study this problem with panel-data where we observe nn units across mm times under unknown, non-uniform treatment assignments. The data in this setting is naturally represented as a matrix of all unit--time treatment effects. Estimating heterogeneous treatment effects can then be expressed as obtaining a good estimation of each row's average in this matrix. This allows us to formulate the problem as matrix completion, which can be solved under natural low-rankness assumptions. However, existing matrix-completion guarantees are not powerful enough to get meaningful bounds for the per-row guarantee required for estimating the heterogeneous treatment effect; roughly speaking, they are only useful for estimating average treatment effect bounds, as also illustrated in a recent line of work. We give a simple, computationally efficient estimator that, without knowledge of the propensities and under standard low-rankness and regularity assumptions, achieves a row-wise ℓ2\ell_2 error of O~(1n+nm2)\tilde{O}(\sqrt{\frac{1}{n} + \frac{n}{m^2}}). Technically, our analysis establishes the first sharp row-wise ℓ2\ell_2-perturbation bound for low-rank approximation, complementing existing spectral-, Frobenius-, and entrywise perturbation theory.

Anay Mehrotra, Phuc Tran, Van H. Vu +1

Vin University · The University of Hong Kong · Yale University

Causal Effect EstimationConditional Average Treatment Effect EstimationLow-Rank ApproximationIndividualized Treatment Effect EstimationMatrix Completion
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May 26, 2026

Calibrated Inference for the Conditional Average Treatment Effect in the Few-Placebo Regime via Gaussian Processes

Estimating how much an intervention helps a given individual the conditional average treatment effect (CATE) is increasingly central to decision-making in medicine, economics, and policy, where an estimate is most useful when accompanied by a calibrated uncertainty interval. We study the few-placebo regime, in which one treatment arm is much smaller than the other, as arises in unequal-allocation trials and small-holdout A/BA/B tests. The standard estimator in this setting is the X-Learner, and a natural way to obtain credible intervals is to make its second stage Bayesian. We show that these intervals under-cover: they contain the true effect less often than their nominal level. We trace this to a structural cause the X-Learner's regression target inherits the bias of a nuisance model fitted to the small arm, so the posterior is centered away from the true effect and we find that the standard remedy, regressing an orthogonal doubly-robust score, is also unreliable here, since the regime's limited overlap leaves the estimator either highly variable or, once stabilized, biased once more. Both consequences reflect a pattern that extends beyond causal inference: a separately estimated variance is attached to a point estimate of a hard-to-learn quantity, and the point estimate's bias is not captured by that variance. We propose GP-CATE, which models each arm's outcome surface with a Gaussian process, so the scarce arm's uncertainty enters the posterior directly rather than as an unmodelled bias. Across synthetic and semi-synthetic benchmarks, GP-CATE attains calibrated coverage where the estimators we compare against including Causal Forest and BART do not, at the cost of intervals that are appropriately wide when the data are uninformative.

Eichi Uehara

AFLO

Causal Effect EstimationConditional Average Treatment Effect EstimationCausal InferenceIndividualized Treatment Effect EstimationUncertainty Calibration
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May 25, 2026

Beyond Differences: Doubly Robust Meta-Learners for Ratio-Based Treatment Effects

When treatment effects are naturally expressed as ratios -- as in medicine, pricing, and marketing -- the ratio-based CATE τ(x)=E[Y∣W=1,X=x]/E[Y∣W=0,X=x]τ(x) = E[Y|W=1,X=x] / E[Y|W=0,X=x] is the appropriate estimand. Yet existing estimators either impose a log-linear parametric structure or apply generic regression without robustness guarantees for this functional. We introduce the Q-Learner, which decomposes τ(x)τ(x) into a product of two odds ratios, reducing ratio-CATE estimation for binary outcomes to two propensity classification tasks. We further derive doubly robust augmentations for both S/T- and Q-style ratio learners and characterize their distinct robustness properties. In benchmarks on seven RCT datasets, the Q-Learner is the most consistently competitive method in low-conversion regimes, where its propensity-only construction sidesteps the imbalanced regression that hurts outcome-based estimators. On four observational datasets, where propensity must be estimated and confounding cannot be ruled out, the DR learners introduced here decisively come out on top, making them practitioners' natural default for confounded observational data.

Michael Fuchs, Dominik Kreiss

Actuarial Department Allianz Versicherungs-AG Munich, Germany

Causal Effect EstimationConditional Average Treatment Effect EstimationCausal InferenceIndividualized Treatment Effect EstimationDoubly Robust EstimationRobust Estimation
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May 21, 2026

CausalGuard: Conformal Inference under Graph Uncertainty

Estimating treatment effects from observational data requires choosing an adjustment set, but valid adjustment depends on an unknown causal graph. Graph misspecification can cause under-coverage, while graph-agnostic conformal wrappers may regain nominal coverage only through large padding. We introduce CausalGuard, a structure-weighted conformal framework that calibrates after aggregating graph-conditional doubly robust pseudo-outcomes. Candidate DAGs are proposed from an LLM-derived edge prior, pruned by conditional-independence tests, and reweighted by Bayesian Information Criterion. A composite nonconformity score then calibrates the posterior-weighted pseudo-outcome. CausalGuard provides distribution-free finite-sample marginal coverage for this aggregated pseudo-outcome; under causal identification, overlap, conditional-mean nuisance stability, and concentration on target-aligned valid adjustment strategies, its conditional mean converges to the true Conditional Average Treatment Effect. Across five benchmarks, CausalGuard attains mean coverage above the nominal 90% level for the directly evaluable target and reduces width when graph-agnostic conformal baselines require large padding. Stress tests show that CausalGuard suppresses invalid collider adjustment and remains stable under misspecified priors when the retained candidate set is data-supported.

Vikash Singh, Weicong Chen, Debargha Ganguly +12

1Case Western Reserve University

Causal Effect EstimationConditional Average Treatment Effect EstimationConformal PredictionConformal Risk Control
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May 8, 2026

Three-in-One World Model: Energy-Based Consistency, Prediction, and Counterfactual Inference for Marketing Intervention

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.

Junichiro Niimi

1Meijo University

Causal Effect EstimationWorld Model LearningConditional Average Treatment Effect EstimationEnergy-Based ModelsCounterfactual ReasoningRestricted Boltzmann Machines+2
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May 6, 2026

Regime-Conditioned Evaluation in Multi-Context Bayesian Optimization

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.

Noel Thomas

Mohamed bin Zayed University of Artificial Intelligence Abu Dhabi, UAE

Causal Effect EstimationConditional Average Treatment Effect EstimationBayesian OptimizationBenchmark DesignSafe Bayesian OptimizationHyperparameter Optimization
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Apr 30, 2026

Bayesian X-Learner: Calibrated Posterior Inference for Heterogeneous Treatment Effects under Heavy-Tailed Outcomes

Conditional Average Treatment Effect (CATE) estimation in practice demands three properties simultaneously: heterogeneous effects τ(x)τ(x), calibrated uncertainty over them, and robustness to the heavy tails that contaminate real outcome data. Meta-learners (Künzel et al., 2019) give (i); causal forests and BART give (i)-(ii) with Gaussian-tail assumptions; no widely used tool gives all three. We present Bayesian X-Learner, an X-Learner built on cross-fitted doubly robust pseudo-outcomes (Kennedy, 2020) with a full MCMC posterior over τ(x)τ(x) via a Welsch redescending pseudo-likelihood. On Hill's IHDP benchmark the default configuration attains mean εPEHE=0.56\sqrt{\varepsilon_{\mathrm{PEHE}}} = 0.56 on 5 replications (lowest mean; differences from S-/T-/X-learners, full-config Causal BART, and a causal forest baseline are not significant at α=0.05α=0.05, and rank ordering is unstable at 10 replications -- IHDP comparisons are competitive rather than dominant). On contaminated "whale" DGPs with up to 20-25% tail density, a one-flag extension (contamination_severity) that selects a Huber-δδ nuisance loss per Huber's minimax-δδ relation recovers RMSE ≈0.13\approx 0.13 with tight credible intervals (single-cross-fit 30-seed coverage 83% [Wilson 66%, 93%] at 20% density; modular-Bayes pooling with Bayesian-bootstrap nuisance draws restores nominal 95% coverage).

Eichi Uehara

Independent researcher

Robust RegressionCausal Effect EstimationConditional Average Treatment Effect EstimationBayesian InferenceHeavy-Tailed DistributionsIndividualized Treatment Effect Estimation+1
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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 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 3, 2026

Transfer Learning for Meta-analysis Under Covariate Shift

Randomized controlled trials often do not represent the populations where decisions are made, and covariate shift across studies can invalidate standard IPD meta-analysis and transport estimators. We propose a placebo-anchored transport framework that treats source-trial outcomes as abundant proxy signals and target-trial placebo outcomes as scarce, high-fidelity gold labels to calibrate baseline risk. A low-complexity (sparse) correction anchors proxy outcome models to the target population, and the anchored models are embedded in a cross-fitted doubly robust learner, yielding a Neyman-orthogonal, target-site doubly robust estimator for patient-level heterogeneous treatment effects when target treated outcomes are available. We distinguish two regimes: in connected targets (with a treated arm), the method yields target-identified effect estimates; in disconnected targets (placebo-only), it reduces to a principled screen--then--transport procedure under explicit working-model transport assumptions. Experiments on synthetic data and a semi-synthetic IHDP benchmark evaluate pointwise CATE accuracy, ATE error, ranking quality for targeting, decision-theoretic policy regret, and calibration. Across connected settings, the proposed method is best or near-best and improves substantially over proxy-only, target-only, and transport baselines at small target sample sizes; in disconnected settings, it retains strong ranking performance for targeting while pointwise accuracy depends on the strength of the working transport condition.

Zilong Wang, Ali Abdeen, Turgay Ayer

Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA

Causal InferenceIndividualized Treatment Effect EstimationConditional Average Treatment Effect EstimationCovariate ShiftDoubly Robust Estimation
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Apr 2, 2026

VALOR: Value-Aware Revenue Uplift Modeling with Treatment-Gated Representation for B2B Sales

B2B sales organizations must identify "persuadable" accounts within zero-inflated revenue distributions to optimize expensive human resource allocation. Standard uplift frameworks struggle with treatment signal collapse in high-dimensional spaces and a misalignment between regression calibration and the ranking of high-value "whales." We introduce VALOR (Value Aware Learning of Optimized (B2B) Revenue), a unified framework featuring a Treatment-Gated Sparse-Revenue Network that uses bilinear interaction to prevent causal signal collapse. The framework is optimized via a novel Cost-Sensitive Focal-ZILN objective that combines a focal mechanism for distributional robustness with a value-weighted ranking loss that scales penalties based on financial magnitude. To provide interpretability for high-touch sales programs, we further derive Robust ZILN-GBDT, a tree based variant utilizing a custom splitting criterion for uplift heterogeneity. Extensive evaluations confirm VALOR's dominance, achieving a 20% improvement in rankability over state-of-the-art methods on public benchmarks and delivering a validated 2.7x increase in incremental revenue per account in a rigorous 4-month production A/B test.

Vamshi Guduguntla, Kavin Soni, Debanshu Das

Google, California, USA

Uplift ModelingConditional Average Treatment Effect EstimationLearning to RankGradient-Boosted Decision Trees
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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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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 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 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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Feb 23, 2026

Detecting and Mitigating Group Bias in Heterogeneous Treatment Effects

Heterogeneous treatment effects (HTEs) are increasingly estimated using machine learning models that produce highly personalized predictions of treatment effects. In practice, however, predicted treatment effects are rarely interpreted, reported, or audited at the individual level but, instead, are often aggregated to broader subgroups, such as demographic segments, risk strata, or markets. We show that such aggregation can induce systematic bias of the group-level causal effect: even when models for predicting the individual-level conditional average treatment effect (CATE) are correctly specified and trained on data from randomized experiments, aggregating the predicted CATEs up to the group level does not, in general, recover the corresponding group average treatment effect (GATE). We develop a unified statistical framework to detect and mitigate this form of group bias in randomized experiments. We first define group bias as the discrepancy between the model-implied and experimentally identified GATEs, derive an asymptotically normal estimator, and then provide a simple-to-implement statistical test. For mitigation, we propose a shrinkage-based bias-correction, and show that the theoretically optimal and empirically feasible solutions have closed-form expressions. The framework is fully general, imposes minimal assumptions, and only requires computing sample moments. We analyze the economic implications of mitigating detected group bias for profit-maximizing personalized targeting, thereby characterizing when bias correction alters targeting decisions and profits, and the trade-offs involved. Applications to large-scale experimental data at major digital platforms validate our theoretical results and demonstrate empirical performance.

Joel Persson, Jurriën Bakker, Dennis Bohle +2

Spotify · Munich Center for Machine Learning & LMU Munich · ETH Zurich

Shrinkage EstimationCausal Effect EstimationIndividualized Treatment Effect EstimationConditional Average Treatment Effect Estimation
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Feb 23, 2026

Orthogonal Uplift Learning with Permutation-Invariant Representations for Combinatorial Treatments

We study uplift estimation for combinatorial treatments. Uplift measures the pure incremental causal effect of an intervention (e.g., sending a coupon or a marketing message) on user behavior, modeled as a conditional individual treatment effect. Many real-world interventions are combinatorial: a treatment is a policy that specifies context-dependent action distributions rather than a single atomic label. Although recent work considers structured treatments, most methods rely on categorical or opaque encodings, limiting robustness and generalization to rare or newly deployed policies. We propose an uplift estimation framework that aligns treatment representation with causal semantics. Each policy is represented by the mixture it induces over contextaction components and embedded via a permutation-invariant aggregation. This representation is integrated into an orthogonalized low-rank uplift model, extending Robinson-style decompositions to learned, vector-valued treatments. We show that the resulting estimator is expressive for policy-induced causal effects, orthogonally robust to nuisance estimation errors, and stable under small policy perturbations. Experiments on large-scale randomized platform data demonstrate improved uplift accuracy and stability in long-tailed policy regimes

Xinyan Su, Jiacan Gao, Mingyuan Ma +6

Didi Chuxing, Beijing, China · School of Statistics, East China Normal University, Shanghai, China · School of Mathematics and Statistics, Beijing Jiaotong University, Beijing, China +2

Uplift ModelingCausal Effect EstimationConditional Average Treatment Effect EstimationOrthogonal Representation Learning
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Nov 23, 2025

Reliable Selection of Heterogeneous Treatment Effect Estimators

We study the problem of selecting the best heterogeneous treatment effect (HTE) estimator from a collection of candidates in settings where the treatment effect is fundamentally unobserved. We cast estimator selection as a multiple testing problem and introduce a ground-truth-free procedure based on a cross-fitted, exponentially weighted test statistic. A key component of our method is a two-way sample splitting scheme that decouples nuisance estimation from weight learning and ensures the stability required for valid inference. Leveraging a stability-based central limit theorem, we establish asymptotic familywise error rate control under mild regularity conditions. Empirically, our procedure provides reliable error control while substantially reducing false selections compared with commonly used methods across ACIC 2016, IHDP, and Twins benchmarks, demonstrating that our method is feasible and powerful even without ground-truth treatment effects.

Jiayi Guo, Zijun Gao

Peking University · Marshall School of Business, University of Southern California

Causal Effect EstimationConditional Average Treatment Effect EstimationIndividualized Treatment Effect EstimationMultiple Hypothesis TestingStatistical Hypothesis Testing
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May 21, 2025

Generative Flows for Potential Outcomes and Counterfactuals

Average treatment effects summarize how interventions change outcomes, but individualized decisions require predictions and outcome distributions of what would have happened to the same individual under an alternative treatment. We develop PO-Flow, a continuous normalizing flow framework that represents treatment-specific outcome distributions through invertible transport maps. It supports potential-outcome generation, conditional average treatment-effect estimation, factual-conditioned counterfactual prediction, and density evaluation. To address treatment imbalance in observational data, we incorporate cross-fitted inverse-probability weighting into the flow-matching loss. We establish sufficient conditions under which encoding a factual outcome and decoding under an alternative treatment recovers the individual counterfactual. Under shared exogenous noise and a common encoded reference distribution, scalar recovery follows from increasing noise-to-latent maps. For multivariate outcomes, we assume triangularity or a convex-gradient structure. These conditions distinguish fitting outcome distributions from recovering their causal correspondence. Experiments on four scalar benchmarks and seven multivariate or image settings, with dimensions up to 784, compare against ten scalar and five multivariate baselines. Controlled ablations show IPW improves all reported scalar counterfactual RMSE, PEHE, and potential-outcome RMSE. PO-Flow achieves the lowest PEHE and potential-outcome RMSE on all four scalar benchmarks and attains or ties the lowest mean in 26 of 35 multivariate dataset--metric comparisons.

Dongze Wu, David I. Inouye, Yao Xie

School of Industrial and Systems Engineering Georgia Institute of Technology Atlanta, GA · Elmore Family School of Electrical and Computer Engineering Purdue University West Lafayette, IN

Counterfactual PredictionConditional Average Treatment Effect EstimationContinuous Normalizing Flows
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