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

Previous work has focused primarily on developing ML-based "meta-learners" that can provide point estimates of the conditional

Estimating Heterogeneous Treatment Effects (HTE) in industrial applications such as AdTech and healthcare presents a dual challenge: extreme class imbalance and heavy-tailed outcome distributions. While the X-Learner framework effectively addresses imbalance through cross-imputation, we demonstrate that it is fundamentally vulnerable to "Outlier Smearing" when reliant on Mean Squared Error (MSE) minimization. In this failure mode, the bias from a few extreme observations ("whales") in the minority group is propagated to the entire majority group during the imputation step, corrupting the estimated treatment effect structure. To resolve this, we propose the Robust X-Learner (RX-Learner). This framework integrates a redescending γ-divergence objective -- structurally equivalent to the Welsch loss under Gaussian assumptions -- into the gradient boosting machinery. We further stabilize the non-convex optimization using a Proxy Hessian strategy grounded in Majorization-Minimization (MM) principles. Empirical evaluation on a semi-synthetic Criteo Uplift dataset demonstrates that the RX-Learner reduces the Precision in Estimation of Heterogeneous Effect (PEHE) metric by 98.6% compared to the standard X-Learner, effectively decoupling the stable "Core" population from the volatile "Periphery".

Previous work has focused primarily on developing ML-based "meta-learners" that can provide point estimates of the conditional

The estimation of Conditional Average Treatment Effects (CATE) is crucial for understanding the heterogeneity of treatment effects in clinical trials. We evaluate the performance of common methods, including causal forests and various meta-learners, across a diverse set of scenarios, revealing that each of the methods struggles in one or more of the tested scenarios. Given the inherent uncertainty of the data-generating process in real-life scenarios, the robustness of a CATE estimator to various scenarios is critical for its reliability. To address this limitation of existing methods, we propose two new ensemble methods that integrate multiple estimators to enhance prediction stability and performance - Stacked X-Learner which uses the X-Learner with model stacking for estimating the nuisance functions, and Consensus Based Averaging (CBA), which averages only the models with highest internal agreement. We show that these models achieve good performance across a wide range of scenarios varying in complexity, sample size and structure of the underlying-mechanism, including a biologically driven model for PD-L1 inhibition pathway for cancer treatment. Furthermore, we demonstrate improved performance by the Stacked X-Learner also when comparing to other ensemble methods, including R-Stacking, Causal-Stacking and others.

Individualized treatment decisions can improve health outcomes, but using data to make these decisions in a reliable, precise, and generalizable way is challenging with a single dataset. Leveraging multiple randomized controlled trials allows for the combination of datasets with unconfounded treatment assignment to better estimate heterogeneous treatment effects. This paper discusses several non-parametric approaches for estimating heterogeneous treatment effects using data from multiple trials. We extend single-study methods to a scenario with multiple trials and explore their performance through a simulation study, with data generation scenarios that have differing levels of cross-trial heterogeneity. The simulations demonstrate that methods that directly allow for heterogeneity of the treatment effect across trials perform better than methods that do not, and that the choice of single-study method matters based on the functional form of the treatment effect. Finally, we discuss which methods perform well in each setting and then apply them to four randomized controlled trials to examine effect heterogeneity of treatments for major depressive disorder.

Conditional Average Treatment Effects (CATE) estimation is one of the main challenges in causal inference with observational data. In addition to Machine Learning based-models, nonparametric estimators called meta-learners have been developed to estimate the CATE with the main advantage of not restraining the estimation to a specific supervised learning method. This task becomes, however, more complicated when the treatment is not binary as some limitations of the naive extensions emerge. This paper looks into meta-learners for estimating the heterogeneous effects of multi-valued treatments. We consider different meta-learners, and we carry out a theoretical analysis of their error upper bounds as functions of important parameters such as the number of treatment levels, showing that the naive extensions do not always provide satisfactory results. We introduce and discuss meta-learners that perform well as the number of treatments increases. We empirically confirm the strengths and weaknesses of those methods with synthetic and semi-synthetic datasets.

In recent years there has been a growing interest in the estimation of causal effects using machine learning algorithms, particularly in the field of economics (Athey, 2018). The newly emerging synthesis of machine learning methods with causal inference has a large potential for a more comprehensive estimation of causal effects (Lechner, 2018). On the one hand, it enables a more flexible estimation of average effects which are of main interest in microeconometrics (Imbens & Wooldridge, 2009). On the other hand, it advances the estimation beyond the average effects and allows for a systematic analysis of effect heterogeneity (Athey & Imbens, 2017). Both of these aspects contribute to a better description of the causal mechanisms and thus to a possibly more efficient treatment allocation (Zhao, Zeng, Rush, & Kosorok, 2012; Kitagawa & Tetenov, 2018; Athey & Wager, 2021; Nie, Brunskill, & Wager, 2021). Hence, applied empirical researchers can greatly benefit from the usage of machine learning methods ranging from evaluation of public policies and business decisions to designing personalized interventions (Andini, Ciani, de Blasio, D'Ignazio, & Salvestrini, 2018; Bansak et al., 2018). Machine learning estimators as such are, however, primarily designed for prediction problems and thus cannot be used directly for causal inference. Therefore, new approaches for the estimation of causal parameters using machine learning emerged (see Athey & Imbens, 2019, for an overview). In particular, the development of the so-called meta-learners have received considerable attention (see e.g.

A new meta-algorithm for estimating the conditional average treatment effects is proposed in the paper. The main idea underlying the algorithm is to consider a new dataset consisting of feature vectors produced by means of concatenation of examples from control and treatment groups, which are close to each other. Outcomes of new data are defined as the difference between outcomes of the corresponding examples comprising new feature vectors. The second idea is based on the assumption that the number of controls is rather large and the control outcome function is precisely determined. This assumption allows us to augment treatments by generating feature vectors which are closed to available treatments. The outcome regression function constructed on the augmented set of concatenated feature vectors can be viewed as an estimator of the conditional average treatment effects. A simple modification of the Co-learner based on the random subspace method or the feature bagging is also proposed. Various numerical simulation experiments illustrate the proposed algorithm and show its outperformance in comparison with the well-known T-learner and X-learner for several types of the control and treatment outcome functions. Keywords: treatment effect, meta-learner, regression, treatment, control, simulation 1 Introduction One the most important problems in medicine is to choose the most appropriate treatment for a certain patient which may differ from other patients in her/his clinical or other characteristics [25]. With the increase of the amount of data and with the developing the electronic health record concept in medicine, there is a growing interest to apply machine learning methods to solve the problem of the most appropriate treatment by estimating treatment effects directly from observational data. The main peculiarity of observational data is that it contains past actions, their outcomes, but without direct access to the mechanism which gave rise to the action. Shalit at al. [34] give a clear example of observational data, when we have patient characteristics, medications (action), and outcomes, 1 arXiv:1909.03894v1

--Uplift modeling is an emerging machine learning approach for estimating the treatment effect at an individual or subgroup level. It can be used for optimizing the performance of interventions such as marketing campaigns and product designs. Uplift modeling can be used to estimate which users are likely to benefit from a treatment and then prioritize delivering or promoting the preferred experience to those users. An important but so far neglected use case for uplift modeling is an experiment with multiple treatment groups that have different costs, such as for example when different communication channels and promotion types are tested simultaneously. In this paper, we extend standard uplift models to support multiple treatment groups with different costs. We evaluate the performance of the proposed models using both synthetic and real data. We also describe a production implementation of the approach. Uplift modeling [1]-[8] is a technique to estimate and predict the individual-level or subgroup-level causal effects of different treatments in an experiment. This type of information is useful for designing and offering a personalized experience to improve user experience, satisfaction, and engagement. Uplift modeling is therefore commonly used in areas such as marketing, customer service, and product offering. It is helpful to think about uplift modeling in the context of randomized experiments (also known as A/B testing [9]-[11]). In a typical experiment, users are randomly assigned to each treatment group and causal effects are then estimated for the population.