Dennis Frauen

Valentyn Melnychuk, Dennis Frauen, Stefan Feuerriegel

Estimating counterfactual outcomes over time from observational data is relevant for many applications (e.g., personalized medicine). Yet, state-of-the-art methods build upon simple long short-term memory (LSTM) networks, thus rendering inferences for complex, long-range dependencies challenging. In this paper, we develop a novel Causal Transformer for estimating counterfactual outcomes over time. Our model is specifically designed to capture complex, long-range dependencies among time-varying confounders. For this, we combine three transformer subnetworks with separate inputs for time-varying covariates, previous treatments, and previous outcomes into a joint network with in-between cross-attentions. We further develop a custom, end-to-end training procedure for our Causal Transformer. Specifically, we propose a novel counterfactual domain confusion loss to address confounding bias: it aims to learn adversarial balanced representations, so that they are predictive of the next outcome but non-predictive of the current treatment assignment. We evaluate our Causal Transformer based on synthetic and real-world datasets, where it achieves superior performance over current baselines. To the best of our knowledge, this is the first work proposing transformer-based architecture for estimating counterfactual outcomes from longitudinal data.

Dennis Frauen, Fergus Imrie, Alicia Curth et al.

Unobserved confounding is common in many applications, making causal inference from observational data challenging. As a remedy, causal sensitivity analysis is an important tool to draw causal conclusions under unobserved confounding with mathematical guarantees. In this paper, we propose NeuralCSA, a neural framework for generalized causal sensitivity analysis. Unlike previous work, our framework is compatible with (i) a large class of sensitivity models, including the marginal sensitivity model, f-sensitivity models, and Rosenbaum's sensitivity model; (ii) different treatment types (i.e., binary and continuous); and (iii) different causal queries, including (conditional) average treatment effects and simultaneous effects on multiple outcomes. The generality of NeuralCSA is achieved by learning a latent distribution shift that corresponds to a treatment intervention using two conditional normalizing flows. We provide theoretical guarantees that NeuralCSA is able to infer valid bounds on the causal query of interest and also demonstrate this empirically using both simulated and real-world data.

Dennis Frauen, Tobias Hatt, Valentyn Melnychuk et al.

In medical practice, treatments are selected based on the expected causal effects on patient outcomes. Here, the gold standard for estimating causal effects are randomized controlled trials; however, such trials are costly and sometimes even unethical. Instead, medical practice is increasingly interested in estimating causal effects among patient (sub)groups from electronic health records, that is, observational data. In this paper, we aim at estimating the average causal effect (ACE) from observational data (patient trajectories) that are collected over time. For this, we propose DeepACE: an end-to-end deep learning model. DeepACE leverages the iterative G-computation formula to adjust for the bias induced by time-varying confounders. Moreover, we develop a novel sequential targeting procedure which ensures that DeepACE has favorable theoretical properties, i.e., is doubly robust and asymptotically efficient. To the best of our knowledge, this is the first work that proposes an end-to-end deep learning model tailored for estimating time-varying ACEs. We compare DeepACE in an extensive number of experiments, confirming that it achieves state-of-the-art performance. We further provide a case study for patients suffering from low back pain to demonstrate that DeepACE generates important and meaningful findings for clinical practice. Our work enables practitioners to develop effective treatment recommendations based on population effects.

Valentyn Melnychuk, Dennis Frauen, Stefan Feuerriegel

Existing machine learning methods for causal inference usually estimate quantities expressed via the mean of potential outcomes (e.g., average treatment effect). However, such quantities do not capture the full information about the distribution of potential outcomes. In this work, we estimate the density of potential outcomes after interventions from observational data. For this, we propose a novel, fully-parametric deep learning method called Interventional Normalizing Flows. Specifically, we combine two normalizing flows, namely (i) a nuisance flow for estimating nuisance parameters and (ii) a target flow for parametric estimation of the density of potential outcomes. We further develop a tractable optimization objective based on a one-step bias correction for efficient and doubly robust estimation of the target flow parameters. As a result, our Interventional Normalizing Flows offer a properly normalized density estimator. Across various experiments, we demonstrate that our Interventional Normalizing Flows are expressive and highly effective, and scale well with both sample size and high-dimensional confounding. To the best of our knowledge, our Interventional Normalizing Flows are the first proper fully-parametric, deep learning method for density estimation of potential outcomes.

Dennis Frauen, Stefan Feuerriegel

Estimating conditional average treatment effects (CATEs) from observational data is relevant in many fields such as personalized medicine. However, in practice, the treatment assignment is usually confounded by unobserved variables and thus introduces bias. A remedy to remove the bias is the use of instrumental variables (IVs). Such settings are widespread in medicine (e.g., trials where the treatment assignment is used as binary IV). In this paper, we propose a novel, multiply robust machine learning framework, called MRIV, for estimating CATEs using binary IVs and thus yield an unbiased CATE estimator. Different from previous work for binary IVs, our framework estimates the CATE directly via a pseudo outcome regression. (1)~We provide a theoretical analysis where we show that our framework yields multiple robust convergence rates: our CATE estimator achieves fast convergence even if several nuisance estimators converge slowly. (2)~We further show that our framework asymptotically outperforms state-of-the-art plug-in IV methods for CATE estimation, in the sense that it achieves a faster rate of convergence if the CATE is smoother than the individual outcome surfaces. (3)~We build upon our theoretical results and propose a tailored deep neural network architecture called MRIV-Net for CATE estimation using binary IVs. Across various computational experiments, we demonstrate empirically that our MRIV-Net achieves state-of-the-art performance. To the best of our knowledge, our MRIV is the first multiply robust machine learning framework tailored to estimating CATEs in the binary IV setting.

Valentyn Melnychuk, Dennis Frauen, Stefan Feuerriegel

Counterfactual inference aims to answer retrospective "what if" questions and thus belongs to the most fine-grained type of inference in Pearl's causality ladder. Existing methods for counterfactual inference with continuous outcomes aim at point identification and thus make strong and unnatural assumptions about the underlying structural causal model. In this paper, we relax these assumptions and aim at partial counterfactual identification of continuous outcomes, i.e., when the counterfactual query resides in an ignorance interval with informative bounds. We prove that, in general, the ignorance interval of the counterfactual queries has non-informative bounds, already when functions of structural causal models are continuously differentiable. As a remedy, we propose a novel sensitivity model called Curvature Sensitivity Model. This allows us to obtain informative bounds by bounding the curvature of level sets of the functions. We further show that existing point counterfactual identification methods are special cases of our Curvature Sensitivity Model when the bound of the curvature is set to zero. We then propose an implementation of our Curvature Sensitivity Model in the form of a novel deep generative model, which we call Augmented Pseudo-Invertible Decoder. Our implementation employs (i) residual normalizing flows with (ii) variational augmentations. We empirically demonstrate the effectiveness of our Augmented Pseudo-Invertible Decoder. To the best of our knowledge, ours is the first partial identification model for Markovian structural causal models with continuous outcomes.

Dennis Frauen, Valentyn Melnychuk, Stefan Feuerriegel

Algorithmic decision-making in practice must be fair for legal, ethical, and societal reasons. To achieve this, prior research has contributed various approaches that ensure fairness in machine learning predictions, while comparatively little effort has focused on fairness in decision-making, specifically off-policy learning. In this paper, we propose a novel framework for fair off-policy learning: we learn decision rules from observational data under different notions of fairness, where we explicitly assume that observational data were collected under a different potentially discriminatory behavioral policy. For this, we first formalize different fairness notions for off-policy learning. We then propose a neural network-based framework to learn optimal policies under different fairness notions. We further provide theoretical guarantees in the form of generalization bounds for the finite-sample version of our framework. We demonstrate the effectiveness of our framework through extensive numerical experiments using both simulated and real-world data. Altogether, our work enables algorithmic decision-making in a wide array of practical applications where fairness must be ensured.

Dennis Frauen, Athiya Deviyani, Mihaela van der Schaar et al.

Evaluating the performance of large language models (LLMs) from human preference data is crucial for obtaining LLM leaderboards. However, many existing approaches either rely on restrictive parametric assumptions or lack valid uncertainty quantification when flexible machine learning methods are used. In this paper, we propose a nonparametric statistical framework, DMLEval, for comparing and ranking LLMs from preference data using debiased machine learning (DML). For this, we introduce generalized average ranking scores (GARS), which generalize commonly used ranking models, including the Bradley-Terry model or PageRank/ Rank centrality, with complex human responses such as ties. DMLEval comes with the following advantages: (i) It produces statistically efficient estimates of GARS ranking scores. (ii) It naturally allows the incorporation of black-box machine learning methods for estimation. (iii) It can be combined with pre-trained LLM evaluators (e.g., using LLM-as-a-judge). (iv) It suggests optimal policies for collecting preference data under budget constraints. We demonstrate these advantages both theoretically and empirically using both synthetic and real-world preference datasets. In summary, our framework provides practitioners with powerful, state-of-the-art methods for comparing or ranking LLMs.

Dennis Frauen, Marie Brockschmidt, Konstantin Hess et al.

Large language model (LLM) development is currently driven by large-scale empirical iteration over data mixtures, reward models, routing strategies, and evaluation pipelines. Here, we argue that many central questions in LLM development and evaluation are inherently causal: What is the effect of adding a data domain during pretraining? How do annotator preferences change when LLMs generate text in a different style? Should a prompt be routed to a larger or smaller model given inference cost constraints? In general, causal methods are well-suited to such settings where interventions change outcomes but, surprisingly, are underrepresented in LLM development. Our contribution is threefold: (1) We explain how causal methods can help develop modern LLM development and evaluation: LLM development relies heavily on logged data, which are often subject to confounding and distribution shifts; evaluation uses learned but potentially biased judges; and deployment environments are non-stationary. These conditions make purely predictive approaches fragile and create opportunities for principled identification and estimation methods from causal inference. (2) We further map opportunities for causal methods in the entire LLM development pipeline, including pretraining, alignment, routing, agentic workflows, and evaluation. (3) We discuss new research opportunities around leveraging causal methods for LLM development and evaluation. Overall, we argue that causal methods are potentially underutilized for the LLM development and evaluation pipeline, despite the fact that such methods can ensure a reliable and scientifically grounded design.

Konstantin Hess, Valentyn Melnychuk, Dennis Frauen et al.

Treatment effect estimation in continuous time is crucial for personalized medicine. However, existing methods for this task are limited to point estimates of the potential outcomes, whereas uncertainty estimates have been ignored. Needless to say, uncertainty quantification is crucial for reliable decision-making in medical applications. To fill this gap, we propose a novel Bayesian neural controlled differential equation (BNCDE) for treatment effect estimation in continuous time. In our BNCDE, the time dimension is modeled through a coupled system of neural controlled differential equations and neural stochastic differential equations, where the neural stochastic differential equations allow for tractable variational Bayesian inference. Thereby, for an assigned sequence of treatments, our BNCDE provides meaningful posterior predictive distributions of the potential outcomes. To the best of our knowledge, ours is the first tailored neural method to provide uncertainty estimates of treatment effects in continuous time. As such, our method is of direct practical value for promoting reliable decision-making in medicine.

Valentyn Melnychuk, Dennis Frauen, Stefan Feuerriegel

State-of-the-art methods for conditional average treatment effect (CATE) estimation make widespread use of representation learning. Here, the idea is to reduce the variance of the low-sample CATE estimation by a (potentially constrained) low-dimensional representation. However, low-dimensional representations can lose information about the observed confounders and thus lead to bias, because of which the validity of representation learning for CATE estimation is typically violated. In this paper, we propose a new, representation-agnostic refutation framework for estimating bounds on the representation-induced confounding bias that comes from dimensionality reduction (or other constraints on the representations) in CATE estimation. First, we establish theoretically under which conditions CATE is non-identifiable given low-dimensional (constrained) representations. Second, as our remedy, we propose a neural refutation framework which performs partial identification of CATE or, equivalently, aims at estimating lower and upper bounds of the representation-induced confounding bias. We demonstrate the effectiveness of our bounds in a series of experiments. In sum, our refutation framework is of direct relevance in practice where the validity of CATE estimation is of importance.

Dennis Frauen, Konstantin Hess, Stefan Feuerriegel

Estimating heterogeneous treatment effects (HTEs) over time is crucial in many disciplines such as personalized medicine. For example, electronic health records are commonly collected over several time periods and then used to personalize treatment decisions. Existing works for this task have mostly focused on model-based learners (i.e., learners that adapt specific machine-learning models). In contrast, model-agnostic learners -- so-called meta-learners -- are largely unexplored. In our paper, we propose several meta-learners that are model-agnostic and thus can be used in combination with arbitrary machine learning models (e.g., transformers) to estimate HTEs over time. Here, our focus is on learners that can be obtained via weighted pseudo-outcome regressions, which allows for efficient estimation by targeting the treatment effect directly. We then provide a comprehensive theoretical analysis that characterizes the different learners and that allows us to offer insights into when specific learners are preferable. Finally, we confirm our theoretical insights through numerical experiments. In sum, while meta-learners are already state-of-the-art for the static setting, we are the first to propose a comprehensive set of meta-learners for estimating HTEs in the time-varying setting.

Maresa Schröder, Dennis Frauen, Jonas Schweisthal et al.

Uncertainty quantification of causal effects is crucial for safety-critical applications such as personalized medicine. A powerful approach for this is conformal prediction, which has several practical benefits due to model-agnostic finite-sample guarantees. Yet, existing methods for conformal prediction of causal effects are limited to binary/discrete treatments and make highly restrictive assumptions such as known propensity scores. In this work, we provide a novel conformal prediction method for potential outcomes of continuous treatments. We account for the additional uncertainty introduced through propensity estimation so that our conformal prediction intervals are valid even if the propensity score is unknown. Our contributions are three-fold: (1) We derive finite-sample prediction intervals for potential outcomes of continuous treatments. (2) We provide an algorithm for calculating the derived intervals. (3) We demonstrate the effectiveness of the conformal prediction intervals in experiments on synthetic and real-world datasets. To the best of our knowledge, we are the first to propose conformal prediction for continuous treatments when the propensity score is unknown and must be estimated from data.

Maresa Schröder, Dennis Frauen, Stefan Feuerriegel

Fairness for machine learning predictions is widely required in practice for legal, ethical, and societal reasons. Existing work typically focuses on settings without unobserved confounding, even though unobserved confounding can lead to severe violations of causal fairness and, thus, unfair predictions. In this work, we analyze the sensitivity of causal fairness to unobserved confounding. Our contributions are three-fold. First, we derive bounds for causal fairness metrics under different sources of unobserved confounding. This enables practitioners to examine the sensitivity of their machine learning models to unobserved confounding in fairness-critical applications. Second, we propose a novel neural framework for learning fair predictions, which allows us to offer worst-case guarantees of the extent to which causal fairness can be violated due to unobserved confounding. Third, we demonstrate the effectiveness of our framework in a series of experiments, including a real-world case study about predicting prison sentences. To the best of our knowledge, ours is the first work to study causal fairness under unobserved confounding. To this end, our work is of direct practical value as a refutation strategy to ensure the fairness of predictions in high-stakes applications.

Yuchen Ma, Valentyn Melnychuk, Dennis Frauen et al.

Fairness in predictions is of direct importance in practice due to legal, ethical, and societal reasons. This is often accomplished through counterfactual fairness, which ensures that the prediction for an individual is the same as that in a counterfactual world under a different sensitive attribute. However, achieving counterfactual fairness is challenging as counterfactuals are unobservable, and, because of that, existing baselines for counterfactual fairness do not have theoretical guarantees. In this paper, we propose a novel counterfactual fairness predictor for making predictions under counterfactual fairness. Here, we follow the standard counterfactual fairness setting and directly learn the counterfactual distribution of the descendants of the sensitive attribute via tailored neural networks, which we then use to enforce fair predictions through a novel counterfactual mediator regularization. Unique to our work is that we provide theoretical guarantees that our method is effective in ensuring the notion of counterfactual fairness. We further compare the performance across various datasets, where our method achieves state-of-the-art performance.

Emil Javurek, Dennis Frauen, Yuxin Wang et al.

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

Yuxin Wang, Dennis Frauen, Jonas Schweisthal et al.

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

Yuxin Wang, Dennis Frauen, Emil Javurek et al.

The synthetic control method (SCM) estimates causal effects in panel data with a single-treated unit by constructing a counterfactual outcome as a weighted combination of untreated control units that matches the pre-treatment trajectory. In this paper, we introduce the targeted synthetic control (TSC) method, a new two-stage estimator that directly estimates the counterfactual outcome. Specifically, our TSC method (1) yields a targeted debiasing estimator, in the sense that the targeted updating refines the initial weights to produce more stable weights; and (2) ensures that the final counterfactual estimation is a convex combination of observed control outcomes to enable direct interpretation of the synthetic control weights. TSC is flexible and can be instantiated with arbitrary machine learning models. Methodologically, TSC starts from an initial set of synthetic-control weights via a one-dimensional targeted update through the weight-tilting submodel, which calibrates the weights to reduce bias of weights estimation arising from pre-treatment fit. Furthermore, TSC avoids key shortcomings of existing methods (e.g., the augmented SCM), which can produce unbounded counterfactual estimates. Across extensive synthetic and real-world experiments, TSC consistently improves estimation accuracy over state-of-the-art SCM baselines.

Henri Arno, Dennis Frauen, Emil Javurek et al.

Many decision-making problems require ranking individuals by their treatment effects rather than estimating the exact effect magnitudes. Examples include prioritizing patients for preventive care interventions, or ranking customers by the expected incremental impact of an advertisement. Surprisingly, while causal effect estimation has received substantial attention in the literature, the problem of directly learning rankings of treatment effects has largely remained unexplored. In this paper, we introduce Rank-Learner, a novel two-stage learner that directly learns the ranking of treatment effects from observational data. We first show that naive approaches based on precise treatment effect estimation solve a harder problem than necessary for ranking, while our Rank-Learner optimizes a pairwise learning objective that recovers the true treatment effect ordering, without explicit CATE estimation. We further show that our Rank-Learner is Neyman-orthogonal and thus comes with strong theoretical guarantees, including robustness to estimation errors in the nuisance functions. In addition, our Rank-Learner is model-agnostic, and can be instantiated with arbitrary machine learning models (e.g., neural networks). We demonstrate the effectiveness of our method through extensive experiments where Rank-Learner consistently outperforms standard CATE estimators and non-orthogonal ranking methods. Overall, we provide practitioners with a new, orthogonal two-stage learner for ranking individuals by their treatment effects.

Stefan Feuerriegel, Dennis Frauen, Valentyn Melnychuk et al.

Causal machine learning (ML) offers flexible, data-driven methods for predicting treatment outcomes including efficacy and toxicity, thereby supporting the assessment and safety of drugs. A key benefit of causal ML is that it allows for estimating individualized treatment effects, so that clinical decision-making can be personalized to individual patient profiles. Causal ML can be used in combination with both clinical trial data and real-world data, such as clinical registries and electronic health records, but caution is needed to avoid biased or incorrect predictions. In this Perspective, we discuss the benefits of causal ML (relative to traditional statistical or ML approaches) and outline the key components and steps. Finally, we provide recommendations for the reliable use of causal ML and effective translation into the clinic.

Marie Brockschmidt, Santo M. A. R. Thies, Maresa Schröder et al.

In causal inference, confounders are variables that influence both treatment decisions and outcomes. However, unlike as in randomized clinical trials, the treatment assignment mechanism in observational studies is not known, and it is thus unclear which covariates act as confounders. Here, we aim to generate insight for causal inference and answer: which of the observed covariates act as confounders? We introduce ConfoundingSHAP, a Shapley-based method for attributing confounding strength to individual covariates. Our contributions are twofold. First, we propose a Shapley game targeted to infer the confounding strength of the covariates. Our resulting Shapley values differ from the standard applications of SHAP explanations on causal targets, such as understanding treatment effect heterogeneity, which are ill-suited for our task. Second, as our task requires evaluating the value function over many adjustment sets, we provide a scalable TabPFN-based estimation that avoids exhaustive refitting. We demonstrate the practical value across various datasets, where ConfoundingSHAP provides informative explanations of which observed covariates drive confounding and thereby helps to provide more insight for causal inference in practice.

Emil Javurek, Dennis Frauen, Marie Brockschmidt et al.

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

Milan Kuzmanovic, Dennis Frauen, Tobias Hatt et al.

The Sustainable Development Goals (SDGs) of the United Nations provide a blueprint of a better future by 'leaving no one behind', and, to achieve the SDGs by 2030, poor countries require immense volumes of development aid. In this paper, we develop a causal machine learning framework for predicting heterogeneous treatment effects of aid disbursements to inform effective aid allocation. Specifically, our framework comprises three components: (i) a balancing autoencoder that uses representation learning to embed high-dimensional country characteristics while addressing treatment selection bias; (ii) a counterfactual generator to compute counterfactual outcomes for varying aid volumes to address small sample-size settings; and (iii) an inference model that is used to predict heterogeneous treatment-response curves. We demonstrate the effectiveness of our framework using data with official development aid earmarked to end HIV/AIDS in 105 countries, amounting to more than USD 5.2 billion. For this, we first show that our framework successfully computes heterogeneous treatment-response curves using semi-synthetic data. Then, we demonstrate our framework using real-world HIV data. Our framework points to large opportunities for a more effective aid allocation, suggesting that the total number of new HIV infections could be reduced by up to 3.3% (~50,000 cases) compared to the current allocation practice.

Konstantin Hess, Dennis Frauen, Niki Kilbertus et al.

Neural operators are widely used to approximate solution maps of complex physical systems. In many applications, however, the goal is not to recover the full solution trajectory, but to summarize the solution trajectory via a scalar target quantity (e.g., a functional such as time spent in a target range, time above a threshold, accumulated cost, or total energy). In this paper, we introduce DOPE (debiased neural operator): a semiparametric estimator for such target quantities of solution trajectories obtained from neural operators. DOPE is broadly applicable to settings with both partial and irregular observations and can be combined with arbitrary neural operator architectures. We make three main contributions. (1) We show that, in contrast to DOPE, naive plug-in estimation can suffer from first-order bias. (2) To address this, we derive a novel one-step, Neyman-orthogonal estimator that treats the neural operator as a high-dimensional nuisance mapping between function spaces, and removes the leading bias term. For this, DOPE uses a weighting mechanism that simultaneously accounts for irregular observation designs and for how sensitive the target quantity is to perturbations of the underlying trajectory. (3) To learn the weights, we extend automatic debiased machine learning to operator-valued nuisances via Riesz regression. We demonstrate the benefits of DOPE across various numerical experiments.

Yuchen Ma, Dennis Frauen, Emil Javurek et al.

Prior-data fitted networks (PFNs) have recently been proposed as a promising way to train tabular foundation models. PFNs are transformers that are pre-trained on synthetic data generated from a prespecified prior distribution and that enable Bayesian inference through in-context learning. In this paper, we introduce CausalFM, a comprehensive framework for training PFN-based foundation models in various causal inference settings. First, we formalize the construction of Bayesian priors for causal inference based on structural causal models (SCMs) in a principled way and derive necessary criteria for the validity of such priors. Building on this, we propose a novel family of prior distributions using causality-inspired Bayesian neural networks that enable CausalFM to perform Bayesian causal inference in various settings, including for back-door, front-door, and instrumental variable adjustment. Finally, we instantiate CausalFM and explicitly train models to perform in-context learning in these settings. We show that CausalFM achieves competitive in-context learning performance even when compared to baselines that are specifically trained for the task at hand. In sum, our framework can be used as a general recipe to train foundation models for various causal inference settings. In contrast to the current state-of-the-art in causal inference, CausalFM offers a novel paradigm with the potential to fundamentally change how practitioners perform causal inference in medicine, economics, and other disciplines.

Valentyn Melnychuk, Dennis Frauen, Jonas Schweisthal et al.

End-to-end representation learning has become a powerful tool for estimating causal quantities from high-dimensional observational data, but its efficiency remained unclear. Here, we face a central tension: End-to-end representation learning methods often work well in practice but lack asymptotic optimality in the form of the quasi-oracle efficiency. In contrast, two-stage Neyman-orthogonal learners provide such a theoretical optimality property but do not explicitly benefit from the strengths of representation learning. In this work, we step back and ask two research questions: (1) When do representations strengthen existing Neyman-orthogonal learners? and (2) Can a balancing constraint - commonly proposed technique in the representation learning literature - provide improvements to Neyman-orthogonality? We address these two questions through our theoretical and empirical analysis, where we introduce a unifying framework that connects representation learning with Neyman-orthogonal learners (namely, OR-learners). In particular, we show that, under the low-dimensional manifold hypothesis, the OR-learners can strictly improve the estimation error of the standard Neyman-orthogonal learners. At the same time, we find that the balancing constraint requires an additional inductive bias and cannot generally compensate for the lack of Neyman-orthogonality of the end-to-end approaches. Building on these insights, we offer guidelines for how users can effectively combine representation learning with the classical Neyman-orthogonal learners to achieve both practical performance and theoretical guarantees.

Yuxin Wang, Maresa Schröder, Dennis Frauen et al.

Constructing confidence intervals (CIs) for the average treatment effect (ATE) from patient records is crucial to assess the effectiveness and safety of drugs. However, patient records typically come from different hospitals, thus raising the question of how multiple observational datasets can be effectively combined for this purpose. In our paper, we propose a new method that estimates the ATE from multiple observational datasets and provides valid CIs. Our method makes little assumptions about the observational datasets and is thus widely applicable in medical practice. The key idea of our method is that we leverage prediction-powered inferences and thereby essentially `shrink' the CIs so that we offer more precise uncertainty quantification as compared to naïve approaches. We further prove the unbiasedness of our method and the validity of our CIs. We confirm our theoretical results through various numerical experiments. Finally, we provide an extension of our method for constructing CIs from combinations of experimental and observational datasets.

Dennis Frauen, Maresa Schröder, Konstantin Hess et al.

Estimating heterogeneous treatment effects (HTEs) is crucial for personalized decision-making. However, this task is challenging in survival analysis, which includes time-to-event data with censored outcomes (e.g., due to study dropout). In this paper, we propose a toolbox of novel orthogonal survival learners to estimate HTEs from time-to-event data under censoring. Our learners have three main advantages: (i) we show that learners from our toolbox are guaranteed to be orthogonal and thus come with favorable theoretical properties; (ii) our toolbox allows for incorporating a custom weighting function, which can lead to robustness against different types of low overlap, and (iii) our learners are model-agnostic (i.e., they can be combined with arbitrary machine learning models). We instantiate the learners from our toolbox using several weighting functions and, as a result, propose various neural orthogonal survival learners. Some of these coincide with existing survival learners (including survival versions of the DR- and R-learner), while others are novel and further robust w.r.t. low overlap regimes specific to the survival setting (i.e., survival overlap and censoring overlap). We then empirically verify the effectiveness of our learners for HTE estimation in different low-overlap regimes through numerical experiments. In sum, we provide practitioners with a large toolbox of learners that can be used for randomized and observational studies with censored time-to-event data.

Harry Amad, Zhaozhi Qian, Dennis Frauen et al.

Causal inference is essential for developing and evaluating medical interventions, yet real-world medical datasets are often difficult to access due to regulatory barriers. This makes synthetic data a potentially valuable asset that enables these medical analyses, along with the development of new inference methods themselves. Generative models can produce synthetic data that closely approximate real data distributions, yet existing methods do not consider the unique challenges that downstream causal inference tasks, and specifically those focused on treatments, pose. We establish a set of desiderata that synthetic data containing treatments should satisfy to maximise downstream utility: preservation of (i) the covariate distribution, (ii) the treatment assignment mechanism, and (iii) the outcome generation mechanism. Based on these desiderata, we propose a set of evaluation metrics to assess such synthetic data. Finally, we present STEAM: a novel method for generating Synthetic data for Treatment Effect Analysis in Medicine that mimics the data-generating process of data containing treatments and optimises for our desiderata. We empirically demonstrate that STEAM achieves state-of-the-art performance across our metrics as compared to existing generative models, particularly as the complexity of the true data-generating process increases.

Haorui Ma, Dennis Frauen, Valentyn Melnychuk et al.

Estimation of heterogeneous long-term treatment effects (HLTEs) is widely used for personalized decision-making in marketing, economics, and medicine, where short-term randomized experiments are often combined with long-term observational data. However, HLTE estimation is challenging due to limited overlap in treatment or in observing 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. The learners are designed for the canonical HLTE setting that combines a short-term randomized dataset $\mathcal{D}_1$ with a long-term historical dataset $\mathcal{D}_2$. The key idea of our LT-O-Learners is to retarget the learning objective by introducing custom overlap weights that downweight samples with low overlap in treatment or in long-term observation. We show that the retargeted loss is equivalent to the weighted oracle loss and satisfies Neyman-orthogonality, which means our learners are robust to errors in the nuisance estimation. We further provide a general error bound for the LT-O-Learners and give the conditions under which quasi-oracle rate can be achieved. Finally, our LT-O-learners are model-agnostic and can thus be instantiated with arbitrary machine learning models. We conduct empirical evaluations on synthetic and semi-synthetic benchmarks to confirm the theoretical properties of our LT-O-Learners, especially the robustness in low-overlap settings. To the best of our knowledge, ours are the first orthogonal learners for HLTE estimation that are robust to low overlap that is common in long-term outcomes.

Yuchen Ma, Dennis Frauen, Jonas Schweisthal et al.

Estimating treatment effects is crucial for personalized decision-making in medicine, but this task faces unique challenges in clinical practice. At training time, models for estimating treatment effects are typically trained on well-structured medical datasets that contain detailed patient information. However, at inference time, predictions are often made using textual descriptions (e.g., descriptions with self-reported symptoms), which are incomplete representations of the original patient information. In this work, we make three contributions. (1) We show that the discrepancy between the data available during training time and inference time can lead to biased estimates of treatment effects. We formalize this issue as an inference time text confounding problem, where confounders are fully observed during training time but only partially available through text at inference time. (2) To address this problem, we propose a novel framework for estimating treatment effects that explicitly accounts for inference time text confounding. Our framework leverages large language models together with a custom doubly robust learner to mitigate biases caused by the inference time text confounding. (3) Through a series of experiments, we demonstrate the effectiveness of our framework in real-world applications.

Jonas Schweisthal, Dennis Frauen, Maresa Schröder et al.

Reliable estimation of treatment effects from observational data is important in many disciplines such as medicine. However, estimation is challenging when unconfoundedness as a standard assumption in the causal inference literature is violated. In this work, we leverage arbitrary (potentially high-dimensional) instruments to estimate bounds on the conditional average treatment effect (CATE). Our contributions are three-fold: (1) We propose a novel approach for partial identification through a mapping of instruments to a discrete representation space so that we yield valid bounds on the CATE. This is crucial for reliable decision-making in real-world applications. (2) We derive a two-step procedure that learns tight bounds using a tailored neural partitioning of the latent instrument space. As a result, we avoid instability issues due to numerical approximations or adversarial training. Furthermore, our procedure aims to reduce the estimation variance in finite-sample settings to yield more reliable estimates. (3) We show theoretically that our procedure obtains valid bounds while reducing estimation variance. We further perform extensive experiments to demonstrate the effectiveness across various settings. Overall, our procedure offers a novel path for practitioners to make use of potentially high-dimensional instruments (e.g., as in Mendelian randomization).

Haorui Ma, Dennis Frauen, Stefan Feuerriegel

Structural nested mean models (SNMMs) are a principled approach to estimate the treatment effects over time. A particular strength of SNMMs is to break the joint effect of treatment sequences over time into localized, time-specific ``blip effects''. This decomposition promotes interpretability through the incremental effects and enables the efficient offline evaluation of optimal treatment policies without re-computation. However, neural frameworks for SNMMs are lacking, as their inherently sequential g-estimation scheme prevents end-to-end, gradient-based training. Here, we propose DeepBlip, the first neural framework for SNMMs, which overcomes this limitation with a novel double optimization trick to enable simultaneous learning of all blip functions. Our DeepBlip seamlessly integrates sequential neural networks like LSTMs or transformers to capture complex temporal dependencies. By design, our method correctly adjusts for time-varying confounding to produce unbiased estimates, and its Neyman-orthogonal loss function ensures robustness to nuisance model misspecification. Finally, we evaluate our DeepBlip across various clinical datasets, where it achieves state-of-the-art performance.

Konstantin Hess, Dennis Frauen, Mihaela van der Schaar et al.

Estimating heterogeneous treatment effects (HTEs) in time-varying settings is particularly challenging, as the probability of observing certain treatment sequences decreases exponentially with longer prediction horizons. Thus, the observed data contain little support for many plausible treatment sequences, which creates severe overlap problems. Existing meta-learners for the time-varying setting typically assume adequate treatment overlap, and thus suffer from exploding estimation variance when the overlap is low. To address this problem, we introduce a novel overlap-weighted orthogonal (WO) meta-learner for estimating HTEs that targets regions in the observed data with high probability of receiving the interventional treatment sequences. This offers a fully data-driven approach through which our WO-learner can counteract instabilities as in existing meta-learners and thus obtain more reliable HTE estimates. Methodologically, we develop a novel Neyman-orthogonal population risk function that minimizes the overlap-weighted oracle risk. We show that our WO-learner has the favorable property of Neyman-orthogonality, meaning that it is robust against misspecification in the nuisance functions. Further, our WO-learner is fully model-agnostic and can be applied to any machine learning model. Through extensive experiments with both transformer and LSTM backbones, we demonstrate the benefits of our novel WO-learner.

Yuxin Wang, Dennis Frauen, Jonas Schweisthal et al.

Dropout is common in clinical studies, with up to half of patients leaving early due to side effects or other reasons. When dropout is informative (i.e., dependent on survival time), it introduces censoring bias, because of which treatment effect estimates are also biased. In this paper, we propose an assumption-lean framework to assess the robustness of conditional average treatment effect (CATE) estimates in survival analysis when facing censoring bias. Unlike existing works that rely on strong assumptions, such as non-informative censoring, to obtain point estimation, we use partial identification to derive informative bounds on the CATE. Thereby, our framework helps to identify patient subgroups where treatment is effective despite informative censoring. We further develop a novel meta-learner that estimates the bounds using arbitrary machine learning models and with favorable theoretical properties, including double robustness and quasi-oracle efficiency. We demonstrate the practical value of our meta-learner through numerical experiments and in an application to a cancer drug trial. Together, our framework offers a practical tool for assessing the robustness of estimated treatment effects in the presence of censoring and thus promotes the reliable use of survival data for evidence generation in medicine and epidemiology.

Emil Javurek, Valentyn Melnychuk, Jonas Schweisthal et al.

Predicting individualized potential outcomes in sequential decision-making is central for optimizing therapeutic decisions in personalized medicine (e.g., which dosing sequence to give to a cancer patient). However, predicting potential outcomes over long horizons is notoriously difficult. Existing methods that break the curse of the horizon typically lack strong theoretical guarantees such as orthogonality and quasi-oracle efficiency. In this paper, we revisit the problem of predicting individualized potential outcomes in sequential decision-making (i.e., estimating Q-functions in Markov decision processes with observational data) through a causal inference lens. In particular, we develop a comprehensive theoretical foundation for meta-learners in this setting with a focus on beneficial theoretical properties. As a result, we yield a novel meta-learner called DRQ-learner and establish that it is: (1) doubly robust (i.e., valid inference under the misspecification of one of the nuisances), (2) Neyman-orthogonal (i.e., insensitive to first-order estimation errors in the nuisance functions), and (3) achieves quasi-oracle efficiency (i.e., behaves asymptotically as if the ground-truth nuisance functions were known). Our DRQ-learner is applicable to settings with both discrete and continuous state spaces. Further, our DRQ-learner is flexible and can be used together with arbitrary machine learning models (e.g., neural networks). We validate our theoretical results through numerical experiments, thereby showing that our meta-learner outperforms state-of-the-art baselines.

Valentyn Melnychuk, Dennis Frauen, Jonas Schweisthal et al.

The conditional average treatment effect (CATE) is widely used in personalized medicine to inform therapeutic decisions. However, state-of-the-art methods for CATE estimation (so-called meta-learners) often perform poorly in the presence of low overlap. In this work, we introduce a new approach to tackle this issue and improve the performance of existing meta-learners in the low-overlap regions. Specifically, we introduce Overlap-Adaptive Regularization (OAR) that regularizes target models proportionally to overlap weights so that, informally, the regularization is higher in regions with low overlap. To the best of our knowledge, our OAR is the first approach to leverage overlap weights in the regularization terms of the meta-learners. Our OAR approach is flexible and works with any existing CATE meta-learner: we demonstrate how OAR can be applied to both parametric and non-parametric second-stage models. Furthermore, we propose debiased versions of our OAR that preserve the Neyman-orthogonality of existing meta-learners and thus ensure more robust inference. Through a series of (semi-)synthetic experiments, we demonstrate that our OAR significantly improves CATE estimation in low-overlap settings in comparison to constant regularization.

Dennis Frauen, Valentyn Melnychuk, Jonas Schweisthal et al.

Decision-making across various fields, such as medicine, heavily relies on conditional average treatment effects (CATEs). Practitioners commonly make decisions by checking whether the estimated CATE is positive, even though the decision-making performance of modern CATE estimators is poorly understood from a theoretical perspective. In this paper, we study optimal decision-making based on two-stage CATE estimators (e.g., DR-learner), which are considered state-of-the-art and widely used in practice. We prove that, while such estimators may be optimal for estimating CATE, they can be suboptimal when used for decision-making. Intuitively, this occurs because such estimators prioritize CATE accuracy in regions far away from the decision boundary, which is ultimately irrelevant to decision-making. As a remedy, we propose a novel two-stage learning objective that retargets the CATE to balance CATE estimation error and decision performance. We then propose a neural method that optimizes an adaptively-smoothed approximation of our learning objective. Finally, we confirm the effectiveness of our method both empirically and theoretically. In sum, our work is the first to show how two-stage CATE estimators can be adapted for optimal decision-making.

Konstantin Hess, Dennis Frauen, Valentyn Melnychuk et al.

We develop a novel method for personalized off-policy learning in scenarios with unobserved confounding. Thereby, we address a key limitation of standard policy learning: standard policy learning assumes unconfoundedness, meaning that no unobserved factors influence both treatment assignment and outcomes. However, this assumption is often violated, because of which standard policy learning produces biased estimates and thus leads to policies that can be harmful. To address this limitation, we employ causal sensitivity analysis and derive a statistically efficient estimator for a sharp bound on the value function under unobserved confounding. Our estimator has three advantages: (1) Unlike existing works, our estimator avoids unstable minimax optimization based on inverse propensity weighted outcomes. (2) Our estimator is statistically efficient. (3) We prove that our estimator leads to the optimal confounding-robust policy. Finally, we extend our theory to the related task of policy improvement under unobserved confounding, i.e., when a baseline policy such as the standard of care is available. We show in experiments with synthetic and real-world data that our method outperforms simple plug-in approaches and existing baselines. Our method is highly relevant for decision-making where unobserved confounding can be problematic, such as in healthcare and public policy.

Jonas Schweisthal, Dennis Frauen, Mihaela van der Schaar et al.

Estimating the conditional average treatment effect (CATE) from observational data is relevant for many applications such as personalized medicine. Here, we focus on the widespread setting where the observational data come from multiple environments, such as different hospitals, physicians, or countries. Furthermore, we allow for violations of standard causal assumptions, namely, overlap within the environments and unconfoundedness. To this end, we move away from point identification and focus on partial identification. Specifically, we show that current assumptions from the literature on multiple environments allow us to interpret the environment as an instrumental variable (IV). This allows us to adapt bounds from the IV literature for partial identification of CATE by leveraging treatment assignment mechanisms across environments. Then, we propose different model-agnostic learners (so-called meta-learners) to estimate the bounds that can be used in combination with arbitrary machine learning models. We further demonstrate the effectiveness of our meta-learners across various experiments using both simulated and real-world data. Finally, we discuss the applicability of our meta-learners to partial identification in instrumental variable settings, such as randomized controlled trials with non-compliance.

Jonas Schweisthal, Dennis Frauen, Valentyn Melnychuk et al.

Decision-making in personalized medicine such as cancer therapy or critical care must often make choices for dosage combinations, i.e., multiple continuous treatments. Existing work for this task has modeled the effect of multiple treatments independently, while estimating the joint effect has received little attention but comes with non-trivial challenges. In this paper, we propose a novel method for reliable off-policy learning for dosage combinations. Our method proceeds along three steps: (1) We develop a tailored neural network that estimates the individualized dose-response function while accounting for the joint effect of multiple dependent dosages. (2) We estimate the generalized propensity score using conditional normalizing flows in order to detect regions with limited overlap in the shared covariate-treatment space. (3) We present a gradient-based learning algorithm to find the optimal, individualized dosage combinations. Here, we ensure reliable estimation of the policy value by avoiding regions with limited overlap. We finally perform an extensive evaluation of our method to show its effectiveness. To the best of our knowledge, ours is the first work to provide a method for reliable off-policy learning for optimal dosage combinations.

Dennis Frauen, Valentyn Melnychuk, Stefan Feuerriegel

Causal inference from observational data is crucial for many disciplines such as medicine and economics. However, sharp bounds for causal effects under relaxations of the unconfoundedness assumption (causal sensitivity analysis) are subject to ongoing research. So far, works with sharp bounds are restricted to fairly simple settings (e.g., a single binary treatment). In this paper, we propose a unified framework for causal sensitivity analysis under unobserved confounding in various settings. For this, we propose a flexible generalization of the marginal sensitivity model (MSM) and then derive sharp bounds for a large class of causal effects. This includes (conditional) average treatment effects, effects for mediation analysis and path analysis, and distributional effects. Furthermore, our sensitivity model is applicable to discrete, continuous, and time-varying treatments. It allows us to interpret the partial identification problem under unobserved confounding as a distribution shift in the latent confounders while evaluating the causal effect of interest. In the special case of a single binary treatment, our bounds for (conditional) average treatment effects coincide with recent optimality results for causal sensitivity analysis. Finally, we propose a scalable algorithm to estimate our sharp bounds from observational data.