Causal effect estimation from observational data is fundamental across various applications. However, selecting an appropriate estimator from dozens of specialized methods demands substantial manual effort and domain expertise. We present CausalPFN, a single transformer that amortizes this workflow: trained once on a large library of simulated data-generating processes that satisfy ignorability, it infers causal effects for new observational datasets out-of-the-box. CausalPFN combines ideas from Bayesian causal inference with the large-scale training protocol of prior-fitted networks (PFNs), learning to map raw observations directly to causal effects without any task-specific adjustment. Our approach achieves superior average performance on heterogeneous and average treatment effect estimation benchmarks (IHDP, Lalonde, ACIC). Moreover, it shows competitive performance for real-world policy making on uplift modeling tasks. CausalPFN provides calibrated uncertainty estimates to support reliable decision-making based on Bayesian principles. This ready-to-use model does not require any further training or tuning and takes a step toward automated causal inference (https://github.com/vdblm/CausalPFN).
Hollmann et al. (Nature 637 (2025) 319-326) recently introduced TabPFN, a transformer-based deep learning model for regression and classification on tabular data, which they claim "outperforms all previous methods on datasets with up to 10,000 samples by a wide margin, using substantially less training time." Furthermore, they have called TabPFN a "foundation model" for tabular data, as it can support "data generation, density estimation, learning reusable embeddings and fine-tuning". If these statements are well-supported, TabPFN may have the potential to supersede existing modeling approaches on a wide range of statistical tasks, mirroring a similar revolution in other areas of artificial intelligence that began with the advent of large language models. In this paper, we provide a tailored explanation of how TabPFN works for a statistics audience, by emphasizing its interpretation as approximate Bayesian inference. We also provide more evidence of TabPFN's "foundation model" capabilities: We show that an out-of-the-box application of TabPFN vastly outperforms specialized state-of-the-art methods for semi-supervised parameter estimation, prediction under covariate shift, and heterogeneous treatment effect estimation. We further show that TabPFN can outperform LASSO at sparse regression and can break a robustness-efficiency trade-off in classification. All experiments can be reproduced using the code provided at https://github.com/qinglong-tian/tabpfn_study (https://github.com/qinglong-tian/tabpfn_study).
In higher education, many institutions use algorithmic alerts to flag at-risk students and deliver advising at scale. While much research has focused on evaluating algorithmic predictions, relatively little is known about how discretionary interventions by human experts shape outcomes in algorithm-assisted settings. We study this question using rich quantitative and qualitative data from a randomized controlled trial of an algorithm-assisted advising program at Georgia State University. Taking a mixed-methods approach, we examine whether and how advisors use context unavailable to an algorithm to guide interventions and influence student success. We develop a causal graphical framework for human expertise in the interventional setting, extending prior work on discretion in purely predictive settings. We then test a necessary condition for discretionary expertise using structured advisor logs and student outcomes data, identifying several interventions that meet the criterion for statistical significance. Accordingly, we estimate that 2 out of 3 interventions taken by advisors in the treatment arm were plausibly "expertly targeted" to students using non-algorithmic context. Systematic qualitative analysis of advisor notes corroborates these findings, showing that advisors incorporate diverse forms of contextual information--such as personal circumstances, financial issues, and student engagement--into their decisions. Finally, we explore the broader implications of human discretion for long-term outcomes and equity, using heterogeneous treatment effect estimation. Our results offer theoretical and practical insight into the real-world effectiveness of algorithm-supported college advising, and underscore the importance of accounting for human expertise in the design, evaluation, and implementation of algorithmic decision systems.
Heterogeneous treatment effect estimation in high-stakes applications demands models that simultaneously optimize precision, interpretability, and calibration. Many existing tree-based causal inference techniques, however, exhibit high estimation errors when applied to observational data because they struggle to capture complex interactions among factors and rely on static regularization schemes. In this work, we propose Dynamic Regularized Causal Boosted Decision Trees (CBDT), a novel framework that integrates variance regularization and average treatment effect calibration into the loss function of gradient boosted decision trees. Our approach dynamically updates the regularization parameters using gradient statistics to better balance the bias-variance tradeoff. Extensive experiments on standard benchmark datasets and real-world clinical data demonstrate that the proposed method significantly improves estimation accuracy while maintaining reliable coverage of true treatment effects. In an intensive care unit patient triage study, the method successfully identified clinically actionable rules and achieved high accuracy in treatment effect estimation. The results validate that dynamic regularization can effectively tighten error bounds and enhance both predictive performance and model interpretability.
Uplift modeling and Heterogeneous Treatment Effect (HTE) estimation aim at predicting the causal effect of an action, such as a medical treatment or a marketing campaign on a specific individual. In this paper, we focus on data from Randomized Controlled Experiments which guarantee causal interpretation of the outcomes. Class and treatment imbalance are important problems in uplift modeling/HTE, but classical undersampling or oversampling based approaches are hard to apply in this case since they distort the predicted effect. Calibration methods have been proposed in the past, however, they do not guarantee correct predictions. In this work, we propose an approach alternative to undersampling, based on flipping the class value of selected records. We show that the proposed approach does not distort the predicted effect and does not require calibration. The method is especially useful for models based on class variable transformation (modified outcome models). We address those models separately, designing a transformation scheme which guarantees correct predictions and addresses also the problem of treatment imbalance which is especially important for those models. Experiments fully confirm our theoretical results. Additionally, we demonstrate that our method is a viable alternative also for standard classification problems.
Merging datasets across institutions is a lengthy and costly procedure, especially when it involves private information. Data hosts may therefore want to prospectively gauge which datasets are most beneficial to merge with, without revealing sensitive information. For causal estimation this is particularly challenging as the value of a merge will depend not only on the reduction in epistemic uncertainty but also the improvement in overlap. To address this challenge, we introduce the first cryptographically secure information-theoretic approach for quantifying the value of a merge in the context of heterogeneous treatment effect estimation. We do this by evaluating the Expected Information Gain (EIG) and utilising multi-party computation to ensure it can be securely computed without revealing any raw data. As we demonstrate, this can be used with differential privacy (DP) to ensure privacy requirements whilst preserving more accurate computation than naive DP alone. To the best of our knowledge, this work presents the first privacy-preserving method for dataset acquisition tailored to causal estimation. We demonstrate the effectiveness and reliability of our method on a range of simulated and realistic benchmarks. The code is available anonymously.
Heterogeneous treatment effect (HTE) estimation is vital for understanding the change of treatment effect across individuals or subgroups. Most existing HTE estimation methods focus on addressing selection bias induced by imbalanced distributions of confounders between treated and control units, but ignore distribution shifts across populations. Thereby, their applicability has been limited to the in-distribution (ID) population, which shares a similar distribution with the training dataset. In real-world applications, where population distributions are subject to continuous changes, there is an urgent need for stable HTE estimation across out-of-distribution (OOD) populations, which, however, remains an open problem. As pioneers in resolving this problem, we propose a novel Stable Balanced Representation Learning with Hierarchical-Attention Paradigm (SBRL-HAP) framework, which consists of 1) Balancing Regularizer for eliminating selection bias, 2) Independence Regularizer for addressing the distribution shift issue, 3) Hierarchical-Attention Paradigm for coordination between balance and independence. In this way, SBRL-HAP regresses counterfactual outcomes using ID data, while ensuring the resulting HTE estimation can be successfully generalized to out-of-distribution scenarios, thereby enhancing the model's applicability in real-world settings. Extensive experiments conducted on synthetic and real-world datasets demonstrate the effectiveness of our SBRL-HAP in achieving stable HTE estimation across OOD populations, with an average 10% reduction in the error metric PEHE and 11% decrease in the ATE bias, compared to the SOTA methods.
Causal inference has gained much popularity in recent years, with interests ranging from academic, to industrial, to educational, and all in between. Concurrently, the study and usage of neural networks has also grown profoundly (albeit at a far faster rate). What we aim to do in this blog write-up is demonstrate a Neural Network causal inference architecture. We develop a fully connected neural network implementation of the popular Bayesian Causal Forest algorithm, a state of the art tree based method for estimating heterogeneous treatment effects. We compare our implementation to existing neural network causal inference methodologies, showing improvements in performance in simulation settings. We apply our method to a dataset examining the effect of stress on sleep.
There is a growing interest in estimating heterogeneous treatment effects across individuals using their high-dimensional feature attributes. Achieving high performance in such high-dimensional heterogeneous treatment effect estimation is challenging because in this setup, it is usual that some features induce sample selection bias while others do not but are predictive of potential outcomes. To avoid losing such predictive feature information, existing methods learn separate feature representations using inverse probability weighting (IPW). However, due to their numerically unstable IPW weights, these methods suffer from estimation bias under a finite sample setup. To develop a numerically robust estimator by weighted representation learning, we propose a differentiable Pareto-smoothed weighting framework that replaces extreme weight values in an end-to-end fashion. Our experimental results show that by effectively correcting the weight values, our proposed method outperforms the existing ones, including traditional weighting schemes. Our code is available at https://github.com/ychika/DPSW.
Heterogeneous treatment effect estimation is an important problem in precision medicine. Specific interests lie in identifying the differential effect of different treatments based on some external covariates. We propose a novel non-parametric treatment effect estimation method in a multi-treatment setting. Our non-parametric modeling of the response curves relies on radial basis function (RBF)-nets with shared hidden neurons. Our model thus facilitates modeling commonality among the treatment outcomes. The estimation and inference schemes are developed under a Bayesian framework using thresholded best linear projections and implemented via an efficient Markov chain Monte Carlo algorithm, appropriately accommodating uncertainty in all aspects of the analysis. The numerical performance of the method is demonstrated through simulation experiments. Applying our proposed method to MIMIC data, we obtain several interesting findings related to the impact of different treatment strategies on the length of ICU stay and 12-hour SOFA score for sepsis patients who are home-discharged.
Deep learning models have demonstrated promising results in estimating treatment effects (TEE). However, most of them overlook the variations in treatment outcomes among subgroups with distinct characteristics. This limitation hinders their ability to provide accurate estimations and treatment recommendations for specific subgroups. In this study, we introduce a novel neural network-based framework, named SubgroupTE, which incorporates subgroup identification and treatment effect estimation. SubgroupTE identifies diverse subgroups and simultaneously estimates treatment effects for each subgroup, improving the treatment effect estimation by considering the heterogeneity of treatment responses. Comparative experiments on synthetic data show that SubgroupTE outperforms existing models in treatment effect estimation. Furthermore, experiments on a real-world dataset related to opioid use disorder (OUD) demonstrate the potential of our approach to enhance personalized treatment recommendations for OUD patients.
Causal machine learning methods can be used to search for treatment effect heterogeneity in high-dimensional datasets even where we lack a strong enough theoretical framework to select variables or make parametric assumptions about data. This paper uses causal machine learning methods to estimate heterogeneous treatment effects in the case of an experimental study carried out in Morocco which evaluated the effect of conditionalizing a cash transfer program on several outcomes including maths test scores which is the focus of this work. We explore treatment effects across a dataset of 1936 pre-treatment variables. For the most part, heterogeneity is modelled by two different factors, participation in education (at the baseline) and more general measures of poverty. Those who are more disadvantaged at the baseline benefit less from any treatment. While conditioning generally has a negative effect this more disadvantaged group is also hurt more by conditioning. The second purpose of this paper is to demonstrate and reflect upon a causal machine learning approach to policy evaluation. We propose a novel causal tree method for interpretable modelling of causal effects and reflect on the difficulty of explaining atheoretical results.
Estimating heterogeneous treatment effects across individuals has attracted growing attention as a statistical tool for performing critical decision-making. We propose a Bayesian inference framework that quantifies the uncertainty in treatment effect estimation to support decision-making in a relatively small sample size setting. Our proposed model places Gaussian process priors on the nonparametric components of a semiparametric model called a partially linear model. This model formulation has three advantages. First, we can analytically compute the posterior distribution of a treatment effect without relying on the computationally demanding posterior approximation. Second, we can guarantee that the posterior distribution concentrates around the true one as the sample size goes to infinity. Third, we can incorporate prior knowledge about a treatment effect into the prior distribution, improving the estimation efficiency. Our experimental results show that even in the small sample size setting, our method can accurately estimate the heterogeneous treatment effects and effectively quantify its estimation uncertainty.
Causal machine learning methods which flexibly generate heterogeneous treatment effect estimates could be very useful tools for governments trying to make and implement policy. However, as the critical artificial intelligence literature has shown, governments must be very careful of unintended consequences when using machine learning models. One way to try and protect against unintended bad outcomes is with AI Fairness methods which seek to create machine learning models where sensitive variables like race or gender do not influence outcomes. In this paper we argue that standard AI Fairness approaches developed for predictive machine learning are not suitable for all causal machine learning applications because causal machine learning generally (at least so far) uses modelling to inform a human who is the ultimate decision-maker while AI Fairness approaches assume a model that is making decisions directly. We define these scenarios as indirect and direct decision-making respectively and suggest that policy-making is best seen as a joint decision where the causal machine learning model usually only has indirect power. We lay out a definition of fairness for this scenario - a model that provides the information a decision-maker needs to accurately make a value judgement about just policy outcomes - and argue that the complexity of causal machine learning models can make this difficult to achieve. The solution here is not traditional AI Fairness adjustments, but careful modelling and awareness of some of the decision-making biases that these methods might encourage which we describe.
This article proposes a meta-learning method for estimating the conditional average treatment effect (CATE) from a few observational data. The proposed method learns how to estimate CATEs from multiple tasks and uses the knowledge for unseen tasks. In the proposed method, based on the meta-learner framework, we decompose the CATE estimation problem into sub-problems. For each sub-problem, we formulate our estimation models using neural networks with task-shared and task-specific parameters. With our formulation, we can obtain optimal task-specific parameters in a closed form that are differentiable with respect to task-shared parameters, making it possible to perform effective meta-learning. The task-shared parameters are trained such that the expected CATE estimation performance in few-shot settings is improved by minimizing the difference between a CATE estimated with a large amount of data and one estimated with just a few data. Our experimental results demonstrate that our method outperforms the existing meta-learning approaches and CATE estimation methods.
We study the problem of inferring heterogeneous treatment effects (HTEs) from time-to-event data in the presence of competing events. Albeit its great practical relevance, this problem has received little attention compared to its counterparts studying HTE estimation without time-to-event data or competing events. We take an outcome modeling approach to estimating HTEs, and consider how and when existing prediction models for time-to-event data can be used as plug-in estimators for potential outcomes. We then investigate whether competing events present new challenges for HTE estimation -- in addition to the standard confounding problem --, and find that, because there are multiple definitions of causal effects in this setting -- namely total, direct and separable effects --, competing events can act as an additional source of covariate shift depending on the desired treatment effect interpretation and associated estimand. We theoretically analyze and empirically illustrate when and how these challenges play a role when using generic machine learning prediction models for the estimation of HTEs.
Personalized treatment effect estimates are often of interest in high-stakes applications -- thus, before deploying a model estimating such effects in practice, one needs to be sure that the best candidate from the ever-growing machine learning toolbox for this task was chosen. Unfortunately, due to the absence of counterfactual information in practice, it is usually not possible to rely on standard validation metrics for doing so, leading to a well-known model selection dilemma in the treatment effect estimation literature. While some solutions have recently been investigated, systematic understanding of the strengths and weaknesses of different model selection criteria is still lacking. In this paper, instead of attempting to declare a global `winner', we therefore empirically investigate success- and failure modes of different selection criteria. We highlight that there is a complex interplay between selection strategies, candidate estimators and the data used for comparing them, and provide interesting insights into the relative (dis)advantages of different criteria alongside desiderata for the design of further illuminating empirical studies in this context.
Estimating how a treatment affects different individuals, known as heterogeneous treatment effect estimation, is an important problem in empirical sciences. In the last few years, there has been a considerable interest in adapting machine learning algorithms to the problem of estimating heterogeneous effects from observational and experimental data. However, these algorithms often make strong assumptions about the observed features in the data and ignore the structure of the underlying causal model, which can lead to biased estimation. At the same time, the underlying causal mechanism is rarely known in real-world datasets, making it hard to take it into consideration. In this work, we provide a survey of state-of-the-art data-driven methods for heterogeneous treatment effect estimation using machine learning, broadly categorizing them as methods that focus on counterfactual prediction and methods that directly estimate the causal effect. We also provide an overview of a third category of methods which rely on structural causal models and learn the model structure from data. Our empirical evaluation under various underlying structural model mechanisms shows the advantages and deficiencies of existing estimators and of the metrics for measuring their performance.
The estimation of heterogeneous treatment effects (HTEs) has attracted considerable interest in many disciplines, most prominently in medicine and economics. Contemporary research has so far primarily focused on continuous and binary responses where HTEs are traditionally estimated by a linear model, which allows the estimation of constant or heterogeneous effects even under certain model misspecifications. More complex models for survival, count, or ordinal outcomes require stricter assumptions to reliably estimate the treatment effect. Most importantly, the noncollapsibility issue necessitates the joint estimation of treatment and prognostic effects. Model-based forests allow simultaneous estimation of covariate-dependent treatment and prognostic effects, but only for randomized trials. In this paper, we propose modifications to model-based forests to address the confounding issue in observational data. In particular, we evaluate an orthogonalization strategy originally proposed by Robinson (1988, Econometrica) in the context of model-based forests targeting HTE estimation in generalized linear models and transformation models. We found that this strategy reduces confounding effects in a simulated study with various outcome distributions. We demonstrate the practical aspects of HTE estimation for survival and ordinal outcomes by an assessment of the potentially heterogeneous effect of Riluzole on the progress of Amyotrophic Lateral Sclerosis.
Estimating how a treatment affects units individually, known as heterogeneous treatment effect (HTE) estimation, is an essential part of decision-making and policy implementation. The accumulation of large amounts of data in many domains, such as healthcare and e-commerce, has led to increased interest in developing data-driven algorithms for estimating heterogeneous effects from observational and experimental data. However, these methods often make strong assumptions about the observed features and ignore the underlying causal model structure, which can lead to biased HTE estimation. At the same time, accounting for the causal structure of real-world data is rarely trivial since the causal mechanisms that gave rise to the data are typically unknown. To address this problem, we develop a feature selection method that considers each feature's value for HTE estimation and learns the relevant parts of the causal structure from data. We provide strong empirical evidence that our method improves existing data-driven HTE estimation methods under arbitrary underlying causal structures. Our results on synthetic, semi-synthetic, and real-world datasets show that our feature selection algorithm leads to lower HTE estimation error.