Causal Effect Estimation

Estimating causal effects is particularly challenging when outcomes arise in complex, non-Euclidean spaces, where conventional methods often fail to capture meaningful structural variation. We develop a framework for topological causal inference that defines treatment effects through differences in the topological structure of potential outcomes, summarized by power-weighted silhouette functions of persistence diagrams. We develop an efficient, doubly robust estimator in a fully nonparametric model, establish functional weak convergence, and construct a formal test of the null hypothesis of no topological effect. Empirical studies illustrate that the proposed method reliably quantifies topological treatment effects across diverse complex outcome types.

We study experiments on interacting populations of humans and AI agents, where both unit types and the interaction network remain unobserved. Although causal effects propagate throughout the system, the goal is to estimate effects on humans. Examples include online platforms where human users interact alongside AI-driven accounts. We assume a human-AI prior that gives each unit a probability of being human. While humans cannot be distinguished at the unit level, the prior allows us to compute the average human composition within large subpopulations. We then model outcome dynamics through a causal message passing (CMP) framework and analyze sample-mean outcomes across subpopulations. We show that by constructing subpopulations that vary in expected human composition and treatment exposure, one can consistently recover human-specific causal effects. Our results characterize when distributional knowledge of population composition (without observing unit types or the interaction network) is sufficient for identification. We validate the approach on a simulated human-AI platform driven by behaviorally differentiated LLM agents. Together, these results provide a theoretical and practical framework for experimentation in emerging human-AI systems.

A fundamental challenge in causal inference with observational data is correct specification of a causal model. When there is model uncertainty, analysts may seek to use estimates from multiple candidate models that rely on distinct, and possibly partially overlapping, sets of identifying assumptions to infer the causal effect, a process known as triangulation. Principled methods for triangulation, however, remain underdeveloped. Here, we develop a framework for causal effect triangulation that combines model testability methods from causal discovery with statistical inference methods from semiparametric theory, while avoiding explicit model selection and post-selection inference problems. We propose a triangulation functional that combines identified functionals from each model with data-driven measures of model validity. We provide a bound on the distance of the functional from the true causal effect along with conditions under which this distance can be taken to zero. Finally, we derive valid statistical inference for this functional. Our framework formalizes robustness under causal pluralism without requiring agreement across models or commitment to a single specification. We demonstrate its performance through simulations and an empirical application.

Precision medicine promises to transform health care by offering individualised treatments that dramatically improve clinical outcomes. A necessary prerequisite is to identify subgroups of patients who respond differently to different therapies. Current approaches are limited to static measures of treatment success, neglecting the repeated measures found in most clinical trials. Our approach combines the concept of partly conditional modelling with treatment effect estimation based on the Virtual Twins method. The resulting time-specific responses to treatment are characterised using survLIME, an extension of Local Interpretable Model-agnostic Explanations (LIME) to survival data. Performance was evaluated using synthetic data and applied to clinical trials examining the effectiveness of panitumumab to treat metastatic colorectal cancer. An area under the receiver operating characteristic curve (AUC) of 0.77 for identifying fixed responders was achieved in a 1000 patient simulation. When considering dynamic responders, partly conditional modelling increased the AUC from 0.597 to 0.685. Applying the approach to colorectal cancer trials found genetic mutations, sites of metastasis, and ethnicity as important factors for response to treatment. Our approach can accommodate a dynamic response to treatment while potentially providing better performance than existing methods in instances of a fixed response to treatment. When applied to clinical data we attain results consistent with the literature.

Causal identification functionals often require integration over conditional densities of continuous variables, such as those arising in nonparametric identification theory of total and mediated causal effects in DAGs with hidden variables. Estimating these densities and evaluating the resulting integrals can be statistically and computationally demanding. A common workaround is to discretize the continuous variable and replace integrals with finite sums. Although convenient, discretization alters the population-level functional and can induce non-negligible approximation bias, even when identification is correct. Under smoothness conditions, we show that the resulting coarsening error is first order in the bin width and arises at the level of the target functional, distinct from statistical estimation error. We propose a simple debiased coarsened functional that evaluates the outcome regression at within-bin conditional means, eliminating the leading coarsening error term and yielding a second-order approximation error. We derive plug-in and one-step estimators for this debiased coarsened functional. Simulations demonstrate substantial bias reduction and near-nominal confidence interval coverage, even under coarse binning. Our results provide a simple framework for controlling the impact of variable discretization on both parameter approximation and statistical estimation.

Many benchmarks for automated causal inference evaluate a system's performance based on a single numerical output, such as an Average Treatment Effect (ATE). This approach conflates two distinct steps in causal analysis: identification, formulating a valid research design under stated assumptions, and estimation, implementing that design numerically on finite data. We introduce CausalReasoningBenchmark, a benchmark of 174 queries across 139 real-world datasets, curated from 73 peer-reviewed research papers and three widely used causal-inference textbooks. For each query, a system must produce (i) a structured identification specification that names the strategy, the treatment, outcome, and control variables, and all design-specific elements, and (ii) a point estimate with a standard error. By scoring these two components separately, our benchmark enables granular diagnosis: it distinguishes failures in causal reasoning from errors in numerical execution. Baseline results with a state-of-the-art LLM show that, while the model correctly identifies the high-level strategy in 81% of cases, full identification-specification correctness drops to only 38%, revealing that the bottleneck lies in the nuanced details of research design rather than in computation. CausalReasoningBenchmark is publicly available on Hugging Face and is designed to foster the development of more robust automated causal-inference systems.

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.

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

Efficient estimation of causal and structural parameters can be automated using the Riesz representation theorem and debiased machine learning (DML). We present genriesz, an open-source Python package that implements automatic DML and generalized Riesz regression, a unified framework for estimating Riesz representers by minimizing empirical Bregman divergences. This framework includes covariate balancing, nearest-neighbor matching, calibrated estimation, and density ratio estimation as special cases. A key design principle of the package is automatic regressor balancing (ARB): given a Bregman generator $g$ and a representer model class, genriesz} automatically constructs a compatible link function so that the generalized Riesz regression estimator satisfies balancing (moment-matching) optimality conditions in a user-chosen basis. The package provides a modulr interface for specifying (i) the target linear functional via a black-box evaluation oracle, (ii) the representer model via basis functions (polynomial, RKHS approximations, random forest leaf encodings, neural embeddings, and a nearest-neighbor catchment basis), and (iii) the Bregman generator, with optional user-supplied derivatives. It returns regression adjustment (RA), Riesz weighting (RW), augmented Riesz weighting (ARW), and TMLE-style estimators with cross-fitting, confidence intervals, and $p$-values. We highlight representative workflows for estimation problems such as the average treatment effect (ATE), ATE on treated (ATT), and average marginal effect estimation. The Python package is available at https://github.com/MasaKat0/genriesz and on PyPI.

This study addresses a central tactical dilemma for football coaches: whether to employ a defensive strategy, colloquially known as "parking the bus", or a more offensive one. Using an advanced Double Machine Learning (DML) framework, this project provides a robust and interpretable tool to estimate the causal impact of different formations on key match outcomes such as goal difference, possession, corners, and disciplinary actions. Leveraging a dataset of over 22,000 matches from top European leagues, formations were categorized into six representative types based on tactical structure and expert consultation. A major methodological contribution lies in the adaptation of DML to handle categorical treatments, specifically formation combinations, through a novel matrix-based residualization process, allowing for a detailed estimation of formation-versus-formation effects that can inform a coach's tactical decision-making. Results show that while offensive formations like 4-3-3 and 4-2-3-1 offer modest statistical advantages in possession and corners, their impact on goals is limited. Furthermore, no evidence supports the idea that defensive formations, commonly associated with parking the bus, increase a team's winning potential. Additionally, red cards appear unaffected by formation choice, suggesting other behavioral factors dominate. Although this approach does not fully capture all aspects of playing style or team strength, it provides a valuable framework for coaches to analyze tactical efficiency and sets a precedent for future research in sports analytics.

Understanding the causal effects of text on downstream outcomes is a central task in many applications. Estimating such effects requires researchers to run controlled experiments that systematically vary textual features. While large language models (LLMs) hold promise for generating text, producing and evaluating controlled variation requires more careful attention. In this paper, we present an end-to-end pipeline for the generation and causal estimation of latent textual interventions. Our work first performs hypothesis generation and steering via sparse autoencoders (SAEs), followed by robust causal estimation. Our pipeline addresses both computational and statistical challenges in text-as-treatment experiments. We demonstrate that naive estimation of causal effects suffers from significant bias as text inherently conflates treatment and covariate information. We describe the estimation bias induced in this setting and propose a solution based on covariate residualization. Our empirical results show that our pipeline effectively induces variation in target features and mitigates estimation error, providing a robust foundation for causal effect estimation in text-as-treatment settings.

In online advertising, marketing interventions such as coupons introduce significant confounding bias into Click-Through Rate (CTR) prediction. Observed clicks reflect a mixture of users' intrinsic preferences and the uplift induced by these interventions. This causes conventional models to miscalibrate base CTRs, which distorts downstream ranking and billing decisions. Furthermore, marketing interventions often operate as multi-valued treatments with varying magnitudes, introducing additional complexity to CTR prediction. To address these issues, we propose the Unified Multi-Valued Treatment Network (UniMVT). Specifically, UniMVT disentangles confounding factors from treatment-sensitive representations, enabling a full-space counterfactual inference module to jointly reconstruct the debiased base CTR and intensity-response curves. To handle the complexity of multi-valued treatments, UniMVT employs an auxiliary intensity estimation task to capture treatment propensities and devise a unit uplift objective that normalizes the intervention effect. This ensures comparable estimation across the continuous coupon-value spectrum. UniMVT simultaneously achieves debiased CTR prediction for accurate system calibration and precise uplift estimation for incentive allocation. Extensive experiments on synthetic and industrial datasets demonstrate UniMVT's superiority in both predictive accuracy and calibration. Furthermore, real-world A/B tests confirm that UniMVT significantly improves business metrics through more effective coupon distribution.

Causal inference from observational data can provide strong evidence for finding the best action in a decision-making scenario without having to perform expensive randomized trials. The causal effect of an action is often not pointwise identifiable even with infinite data due to unobserved confounding factors. Furthermore, having only finitely many samples adds another layer of uncertainty to causal effect estimation. Several existing methods can be used to obtain upper and lower bounds to the causal effect, ranging from symbolic methods to the more recent neural network-based approaches, which implicitly incorporate both sources of uncertainty. However, these methods do not inform whether collecting more samples may or may not help identify the best action from observational data, leaving experts in the dark about their data collection strategies. We address this problem with a novel framework that can distinguish the range of causal effect values that might be eliminated by collecting more samples from the range of values that, with high probability, cannot be eliminated with more observational samples. We show that this partitioning can be obtained by solving max-min and min-max optimization problems. We leverage neural causal models to approximately recover this decomposition in practice. We demonstrate via experiments on synthetic and real-world datasets that our algorithm can determine when collecting more samples will not help determine the best action. Our framework can help practitioners decide when to resort to non-observational studies or seek to measure some of the unmeasured confounders for optimal decision-making.

We study the pricing behavior of third-party platforms facing strategic agents. Assuming the platform is a revenue maximizer, it observes market features that generally affect demand. Since only transacted quantities and prices can be observed, this presents a general demand learning problem under confounding. Mathematically, we develop an algorithm with optimal regret of $\Tilde{\mathcal{O}}(\sqrt{T}\wedgeσ_S^{-2})$. Our results reveal that supply-side noise fundamentally affects the learnability of demand, leading to a phase transition in regret. Technically, we show that non-i.i.d. actions can serve as instrumental variables for learning demand. We also propose a novel homeomorphic construction that allows us to establish estimation bounds without assuming star-shapedness, providing the first efficiency guarantee for learning demand with deep neural networks. Finally, we use simulations and offline counterfactuals from Talabat and Lyft data to illustrate the potential revenue implications of our approach.

Most major retailers today have multiple divisions focused on various aspects, such as marketing, supply chain, online customer experience, store customer experience, employee productivity, and vendor fulfillment. They also regularly collect data corresponding to all these aspects as dashboards and weekly/monthly/quarterly reports. Although several machine learning and statistical techniques have been in place to analyze and predict key metrics, such models typically lack interpretability. Moreover, such techniques also do not allow the validation or discovery of causal links. In this paper, we aim to provide a recipe for applying model interpretability and causal inference for deriving sales insights. In this paper, we review the existing literature on causal inference and interpretability in the context of problems in e-commerce and retail, and apply them to a real-world dataset. We find that an inherently explainable model has a lower variance of SHAP values, and show that including multiple confounders through a double machine learning approach allows us to get the correct sign of causal effect.

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.

Causal inference in spatial domains faces two intertwined challenges: (1) unmeasured spatial factors, such as weather, air pollution, or mobility, that confound treatment and outcome, and (2) interference from nearby treatments that violate standard no-interference assumptions. While existing methods typically address one by assuming away the other, we show they are deeply connected: interference reveals structure in the latent confounder. Leveraging this insight, we propose the Spatial Deconfounder, a two-stage method that reconstructs a substitute confounder from local treatment vectors using a conditional variational autoencoder (C-VAE) with a spatial prior, then estimates causal effects with a flexible outcome model. We show that this enables nonparametric identification of direct and spillover effects under weak assumptions--without multiple treatment types or a known latent-field model. Empirically, we extend SpaCE, a benchmark suite for spatial confounding, to include treatment interference, and show that the Spatial Deconfounder consistently improves effect estimation across real-world environmental health and social science datasets. By turning local interference into a multi-cause proxy for latent spatial confounding, our framework advances robust causal inference for spatial data.

Socio-economic causal effects depend heavily on their institutional and environmental contexts. The same intervention can produce different, even opposite, effects across regulatory regimes, market conditions, time periods, or populations. This poses a challenge for large language models (LLMs) in decision-support roles: can they infer the direction of a causal effect under a specified context, and revise that judgment when the context changes? To address this, we introduce EconCausal, a large-scale benchmark of 10,490 context-annotated causal triplets extracted from 2,595 high-quality empirical studies in top-tier economics and finance journals, constructed through a rigorous four-stage pipeline with multi-run consensus, context refinement, and multi-critic filtering. Across 19 models, we observe source-sign over-transfer in cross-context prediction. While top models reach ~84% accuracy in single-context prediction, mean accuracy is 74.75% overall but drops to 44.27% when source and target signs disagree. On these cases, accuracy is 11.54 percentage points (pp) lower with the signed source example than with the target input alone. Mean accuracy is below 60% under corrupted source signs. Models also struggle to predict study-reported nonsignificant effects (19.16% accuracy). The dataset and benchmark are publicly available at https://anonymous.4open.science/r/econcausal-benchmark-6F12.

Causal identification asks whether a causal target can be recovered from the observational distribution in an idealized infinite-data setting. In practice, only finite samples are available, and identifiability alone does not determine how much data are needed for reliable estimation. We introduce Probably Approximately Correct Causal (PACC) learnability, which formalizes uniform accuracy-confidence guarantees over a causal model class. From a PAC-learning perspective, we ask how many samples are sufficient to estimate a causal target to accuracy $ε$ with probability at least $1-δ$. We show that PACC sample complexity is shaped by three recurring factors: causal identification strength, target complexity, and nuisance complexity, and derive a general sufficient bound linking them to finite-sample causal learning. We illustrate the framework through self-controlled case series, instrumental variables, and propensity-score-based estimation, showing how distinct causal methods can be analyzed within a common framework.

Predicting post-intervention distributions from observational data is central to many scientific and decision-making problems, but remains challenging due to causal ambiguity, restrictive modeling assumptions, and the lack of amortization across tasks. We introduce ACTIVA, a transformer-based conditional variational autoencoder for amortized estimation of full interventional distributions from observational data and intervention queries. ACTIVA learns a conditional latent prior that amortizes causal knowledge across diverse training tasks, so that a new causal model drawn from the training distribution is handled in a single forward pass, without interventional data, a causal graph, or per-task fitting. Beyond the training distribution, only a parametric shift of the simulator is tested. We provide a population-level characterization of ACTIVA's estimand, showing that, under idealized expressivity and infinite samples assumptions, ACTIVA's learning objective targets a simulator-weighted mixture over the interventional distributions of causal models that are observationally compatible with the input. Empirically, on synthetic datasets and biologically realistic gene-expression simulations, ACTIVA substantially outperforms a correlational baseline, reduces spurious non-descendant effects, and achieves competitive performance relative to strong amortized baselines. On a pair of observationally equivalent models sharing a single observational dataset, ACTIVA recovers the predicted mixture, validating the theory in a finite-capacity model. Our results show that ACTIVA is a promising approach for estimating interventional distributions from observational data.

Estimating causal effects under networked interference from observational data is a crucial yet challenging problem. Most existing methods mainly rely on the networked unconfoundedness assumption, which guarantees the identification of networked effects. However, this assumption is often violated due to the latent confounders inherent in observational data, thereby hindering the identification of networked effects. To address this issue, we leverage the rich interaction patterns between units in networks, which provide valuable information for recovering these latent confounders. Building on this insight, we develop a confounder recovery framework that explicitly characterizes three categories of latent confounders in networked settings: those affecting only the unit, those affecting only the unit's neighbors, and those influencing both. Based on this framework, we design a networked effect estimator using identifiable representation learning techniques. From a theoretical standpoint, we prove the identifiability of all three types of latent confounders and, by leveraging the recovered confounders, establish a formal identification result for networked effects. Extensive experiments validate our theoretical findings and demonstrate the effectiveness of the proposed method.

We consider experimentation in the presence of non-stationarity, inter-unit (spatial) interference, and carry-over effects (temporal interference), where we wish to estimate the global average treatment effect (GATE), the difference between average outcomes having exposed all units at all times to treatment or to control. We suppose spatial interference is described by a graph, where a unit's outcome depends on its neighborhood's treatments, and that temporal interference is described by an MDP, where the transition kernel under either treatment (action) satisfies a rapid mixing condition. We propose a clustered switchback design, where units are grouped into clusters and time steps are grouped into blocks, and each whole cluster-block combination is assigned a single random treatment. Under this design, we show that for graphs that admit good clustering, a truncated Horvitz-Thompson estimator achieves a $\tilde O(1/NT)$ mean squared error (MSE), matching the lower bound up to logarithmic terms for sparse graphs. Our results simultaneously generalize the results from \citet{hu2022switchback,ugander2013graph} and \citet{leung2022rate}. Simulation studies validate the favorable performance of our approach.

Identifying the effects of causes and causes of effects is vital in virtually every scientific field. Often, however, the needed probabilities may not be fully identifiable from the available data sources. This paper shows how approximate identifiability is still possible for several probabilities of causation. We term this epsilon-identifiability and demonstrate its usefulness in cases where the behavior of certain subpopulations can be restricted within sufficiently narrow bounds. In particular, we show how unidentifiable causal effects and counterfactual probabilities can be epsilon-identified when such allowances are made. Often, these allowances are easily measured and reasonably assumed. Finally, epsilon-identifiability is applied to the unit selection problem.

We propose a generalization of the synthetic control methods to the setting with dynamic treatment effects, in which each unit receives multiple treatments sequentially, according to an adaptive policy that depends on a latent, endogenously time-varying confounding state. Under a low-rank latent factor model assumption, which admits linear time-varying and time-invariant dynamic triangular systems as special cases, we develop an identification strategy for any unit-specific mean outcome under any sequence of interventions. Our method, which we term synthetic blips, is a backward induction process in which the blip effect of a treatment at each period for a target unit is recursively expressed as a linear combination of the blip effects of other units that received the designated treatment, avoiding the combinatorial donor requirements of naive synthetic control extensions. We provide easy-to-implement estimation algorithms that yield consistent estimators. Using unique Korean firm-level panel data, we estimate individualized dynamic treatment effects and optimal allocation rules in the context of financial support for exporting firms.

In many applications, researchers are interested in the direct and indirect causal effects of a treatment or exposure on an outcome of interest. Mediation analysis offers a rigorous framework for identifying and estimating these causal effects. For binary treatments, efficient estimators for the direct and indirect effects are presented by Tchetgen Tchetgen and Shpitser (2012) based on the influence function of the parameter of interest. These estimators possess desirable properties such as multiple-robustness and asymptotic normality while allowing for slower than root-n rates of convergence for the nuisance parameters. However, in settings involving continuous treatments, these influence function-based estimators are not readily applicable without making strong parametric assumptions. In this work, utilizing a kernel smoothing approach, we propose an estimator suitable for settings with continuous treatments inspired by the influence function-based estimation strategy. Our proposed approach employs cross-fitting, relaxing the smoothness requirements on the nuisance functions and allowing them to be estimated at slower rates than the target parameter. Additionally, similar to influence function-based estimators, our proposed estimator is multiply robust and asymptotically normal, allowing for inference in settings where parametric assumptions may not be justified.

This paper studies experimental designs for estimation and inference on policies with spillover effects. Units are organized into a finite number of large clusters and interact in unknown ways within each cluster. First, we introduce a single-wave experiment that estimates the marginal effect of a change in treatment probabilities, taking spillover effects into account. Using the marginal effect, we propose a policy optimality test and improve the population's average outcome through marginal changes. Second, we design a multi-wave experiment to estimate optimal treatment rules, with strong regret guarantees. We provide an implementation in a large-scale field experiment studying climate adaptation.