This paper studies the problem of Continuous-Time Counterfactual Quantile Learning (CT-CQL) for risk-sensitive policy optimization. In many real-world applications such as patient blood pressure monitoring, financial market analysis, and autonomous driving, data is high-frequency and continuously evolving. However, most existing causal inference methods focus on expectation-based or discrete-time counterfactual reasoning, which fail to capture fine-grained temporal dynamics. As a result, policies optimized under these frameworks may overlook critical risks—e.g., a treatment policy with good average outcomes may still expose patients to life-threatening episodes. To overcome these limitations, we propose CT-CQL, a framework built upon a novel identification theory and featuring three key components: (1) modeling full counterfactual outcome distributions via Stochastic Differential Equations (SDEs) governed by the Fokker–Planck Equation (FPE); (2) enhancing robustness through a minimax objective that minimizes FPE residuals under adversarial perturbations; and (3) mitigating confounding bias using a double-robust AIPW loss. CT-CQL enables robust policy optimization by identifying optimal intervention strategies that maximize expected utility while adhering to real-world budget and safety constraints. Experiments on widely-used benchmarks and the real-world MIMIC-III dataset demonstrate the validation and superiority of the proposed method. The project is available at: https://github.com/Eliza-YiHe/CT-CQL/

Clinical notes contain rich patient information, such as diagnoses or medications, making them valuable for patient representation learning.Recent advances in large language models have further improved the ability to extract meaningful representations from clinical texts.However, clinical notes are often missing.For example, in our analysis of the MIMIC-IV dataset, 24.5% of patients have no available discharge summaries.In such cases, representations can be learned from other modalities such as structured data, chest X-rays, or radiology reports.Yet the availability of these modalities is influenced by clinical decision-making and varies across patients, resulting in modality missingnot-at-random (MMNAR) patterns.We propose a causal representation learning framework that leverages observed data and informative missingness in multimodal clinical records.It consists of: (1) an MMNAR-aware modality fusion component that integrates structured data, imaging, and text while conditioning on missingness patterns to capture patient health and clinician-driven assignment; (2) a modality reconstruction component with contrastive learning to ensure semantic sufficiency in representation learning; and (3) a multitask outcome prediction model with a rectifier that corrects for residual bias from specific modality observation patterns.Comprehensive evaluations across MIMIC-IV and eICU show consistent gains over the strongest baselines, achieving up to 13 .8% improvement for hospital readmission and 13 .1 % for ICU admission (AUC, relative to best baseline).

Networked interference, also known as the peer effect in social science and spillover effect in economics, has drawn increasing interest across various domains. This phenomenon arises when a unit’s treatment and outcome are influenced by the actions of its peers, posing significant challenges to causal inference, particularly in treatment assignment and effect estimation in real applications, due to the violation of the SUTVA assumption. While extensive graph models have been developed to identify treatment effects, these models often rely on structural assumptions about networked interference, assuming it to be identical to the social network, which can lead to misspecification issues in real applications. To address these challenges, we propose an Interference-Agnostic Causal Graph Transformer (CauGramer), which aggregates peers information via $L$-order Graph Transformer and employs cross-attention to infer aggregation function for learning interference representations. By integrating confounder balancing and minimax moment constraints, CauGramer fully incorporates peer information, enabling robust treatment effect estimation. Extensive experiments on two widely-used benchmarks demonstrate the effectiveness and superiority of CauGramer. The code is available at https://github.com/anpwu/CauGramer.

Generalizing causal effects from Randomized Controlled Trials (RCTs) to target populations across diverse environments is of significant practical importance, as RCTs are often costly and logistically complex to conduct. A key challenge is environmental shift, defined as changes in the distribution and availability of covariates between source and target environments. A common approach addressing this challenge is to identify a separating set–covariates that govern both treatment effect heterogeneity and environmental differences–and combine RCT samples with target populations matched on this set. However, this approach assumes that the separating set is fully observed and shared across datasets, an assumption often violated in practice. We propose a novel Two-Stage Doubly Robust (2SDR) method that relaxes this assumption by allowing the separating set to be observed in only one of the two datasets. 2SDR leverages shadow variables to impute missing components of the separating set and generalize treatment effects across environments in a two-stage procedure. We show the identification of causal effects in target environments under 2SDR and demonstrate its effectiveness through extensive experiments on both synthetic and real-world datasets.

Uplift modeling is crucial for identifying individuals likely to respond to a treatment in applications like marketing and customer retention, but evaluating these models is challenging due to the inaccessibility of counterfactual outcomes in real-world settings. In this paper, we identify a fundamental limitation in existing evaluation metrics, such as the uplift and Qini curves, which fail to rank individuals with binary negative outcomes accurately. This can lead to biased evaluations, where biased models receive higher curve values than unbiased ones, resulting in suboptimal model selection. To address this, we propose the Principled Uplift Curve (PUC), a novel evaluation metric that assigns equal curve values of individuals with both positive and negative binary outcomes, offering a more balanced and unbiased assessment. We then derive the Principled Uplift Loss (PUL) function from the PUC and integrate it into a new uplift model, the Principled Treatment and Outcome Network (PTONet), to reduce bias during uplift model training. Experiments on both simulated and real-world datasets demonstrate that the PUC provides less biased evaluations, while PTONet outperforms existing methods. The source code is available at: https://github.com/euzmin/PUC.

Treatment effect estimation from observational data is a fundamental problem in causal inference, and its critical challenge is to address the confounding bias arising from the confounders. The effectiveness of the conventional methods proposed to solve this problem depends on the unconfoundedness assumption. In practice, however, the unconfoundedness assumption is frequently violated since we cannot guarantee that all the confounders are measured. To this end, recent studies suggest using auxiliary network architectures to mine information about unmeasured confounders in the data to relax this assumption. However, these methods cannot address the confounding bias from unmeasured confounders unrelated to the network information. Inspired by the insight that some neighboring features that influence one's treatment choice (e.g., which movie to watch) but do not affect the outcome (e.g., assessment of the movie) can be treated as instrumental variables (IVs), we propose a novel Network Instrumental Variable Regression (NetIV) framework exploits IV information from neighborhoods to perform a two-stage regression for treatment effect estimation. Extensive experiments demonstrate that our NetIV method outperforms the state-of-the-art methods for treatment effect estimation in the presence of unmeasured confounders.

Estimating the individuals' potential response to varying treatment doses is crucial for decision-making in areas such as precision medicine and management science. Most recent studies predict counterfactual outcomes by learning a covariate representation that is independent of the treatment variable. However, such independence constraints neglect much of the covariate information that is useful for counterfactual prediction, especially when the treatment variables are continuous. To tackle the above issue, in this paper, we first theoretically demonstrate the importance of the balancing and prognostic representations for unbiased estimation of the heterogeneous dose-response curves, that is, the learned representations are constrained to satisfy the conditional independence between the covariates and both of the treatment variables and the potential responses. Based on this, we propose a novel Contrastive balancing Representation learning Network using a partial distance measure, called CRNet, for estimating the heterogeneous dose-response curves without losing the continuity of treatments. Extensive experiments are conducted on synthetic and real-world datasets demonstrating that our proposal significantly outperforms previous methods.

One of the significant challenges in treatment effect estimation is collider bias, a specific form of sample selection bias induced by the common causes of both the treatment and outcome. Identifying treatment effects under collider bias requires well-defined shadow variables in observational data, which are assumed to be related to the outcome and independent of the sample selection mechanism, conditional on the other observed variables. However, finding a valid shadow variable is not an easy task in real-world scenarios and requires domain-specific knowledge from experts. Therefore, in this paper, we propose a novel method that can automatically learn shadow-variable representations from observational data without prior knowledge. To ensure the learned representations satisfy the assumptions of the shadow variable, we introduce a tester to perform hypothesis testing in the representation learning process. We iteratively generate representations and test whether they satisfy the shadow-variable assumptions until they pass the test. With the help of the learned shadow-variable representations, we propose a novel treatment effect estimator to address collider bias. Experiments show that the proposed methods outperform existing treatment effect estimation methods under collider bias and prove their potential application value.

Latent confounding bias and collider bias are two key challenges of causal inference in observational studies. Latent confounding bias occurs when failing to control the unmeasured covariates that are common causes of treatments and outcomes, which can be addressed by using the Instrumental Variable (IV) approach. Collider bias comes from non-random sample selection caused by both treatments and outcomes, which can be addressed by using a different type of instruments, i.e., shadow variables. However, in most scenarios, these two biases simultaneously exist in observational data, and the previous methods focusing on either one are inadequate. To the best of our knowledge, no approach has been developed for causal inference when both biases exist. In this paper, we propose a novel IV approach, Two-Stage Shadow Inclusion (2SSI), which can simultaneously address latent confounding bias and collider bias by utilizing the residual of the treatment as a shadow variable. Extensive experimental results on benchmark synthetic datasets and a real-world dataset show that 2SSI achieves noticeable performance improvement when both biases exist compared to existing methods.

Accurate estimation of treatment effects is essential for decision-making across various scientific fields. This task, however, becomes challenging in areas like social sciences and online marketplaces, where treating one experimental unit can influence outcomes for others through direct or indirect interactions. Such interference can lead to biased treatment effect estimates, particularly when the structure of these interactions is unknown. We address this challenge by introducing a new class of estimators based on causal message-passing, specifically designed for settings with pervasive, unknown interference. Our estimator draws on information from the sample mean and variance of unit outcomes and treatments over time, enabling efficient use of observed data to estimate the evolution of the system state. Concretely, we construct non-linear features from the moments of unit outcomes and treatments and then learn a function that maps these features to future mean and variance of unit outcomes. This allows for the estimation of the treatment effect over time. Extensive simulations across multiple domains, using synthetic and real network data, demonstrate the efficacy of our approach in estimating total treatment effect dynamics, even in cases where interference exhibits non-monotonic behavior in the probability of treatment.

Estimating individual treatment effects in networked observational data is a crucial and increasingly recognized problem. One major challenge of this problem is violating the stable unit treatment value assumption (SUTVA), which posits that a unit’s outcome is independent of others’ treatment assignments. However, in network data, a unit’s outcome is influenced not only by its treatment (i.e., direct effect) but also by the treatments of others (i.e., spillover effect) since the presence of interference. Moreover, the interference from other units is always heterogeneous (e.g., friends with similar interests have a different influence than those with different interests). In this article, we focus on the problem of estimating individual treatment effects (including direct effect and spillover effect) under heterogeneous interference in networks. To address this problem, we propose a novel dual weighting regression (DWR) algorithm by simultaneously learning attention weights to capture the heterogeneous interference from neighbors and sample weights to eliminate the complex confounding bias in networks. We formulate the learning process as a bi-level optimization problem. Theoretically, we give a generalization error bound for the expected estimation error of the individual treatment effects. Extensive experiments on four benchmark datasets demonstrate that the proposed DWR algorithm outperforms the state-of-the-art methods in estimating individual treatment effects under heterogeneous network interference.

The advent of the big data era brought new opportunities and challenges to draw treatment effect in data fusion, that is, a mixed dataset collected from multiple sources (each source with an independent treatment assignment mechanism). Due to possibly omitted source labels and unmeasured confounders, traditional methods cannot estimate individual treatment assignment probability and infer treatment effect effectively. Therefore, we propose to reconstruct the source label and model it as a Group Instrumental Variable (GIV) to implement IV-based Regression for treatment effect estimation. In this paper, we conceptualize this line of thought and develop a unified framework (Meta-EM) to (1) map the raw data into a representation space to construct Linear Mixed Models for the assigned treatment variable; (2) estimate the distribution differences and model the GIV for the different treatment assignment mechanisms; and (3) adopt an alternating training strategy to iteratively optimize the representations and the joint distribution to model GIV for IV regression. Empirical results demonstrate the advantages of our Meta-EM compared with state-of-the-art methods. The project page with the code and the Supplementary materials is available at https://github.com/causal-machine-learning-lab/meta-em.

Estimating heterogeneous treatment effects (HTE) is crucial for identifying the variation of treatment effects across individuals or subgroups. Most existing methods estimate HTE by removing the confounding bias from imbalanced treatment assignments. However, these methods may produce unreliable estimates of treatment effects and potentially allocate suboptimal treatment arms for underrepresented populations. To improve the estimation accuracy of HTE for underrepresented populations, we propose a novel Stable CounterFactual Regression (StableCFR) to smooth the population distribution and upsample the underrepresented subpopulations, while balancing confounders between treatment and control groups. Specifically, StableCFR upsamples the underrepresented data using uniform sampling, where each disjoint subpopulation is weighted proportional to the Lebesgue measure of its support. Moreover, StableCFR balances covariates by using an epsilon-greedy matching approach. Empirical results on both synthetic and real-world datasets demonstrate the superior performance of our StableCFR on estimating HTE for underrepresented populations.

Domain generalization (DG) aims to learn from multiple source domains a model that can generalize well on unseen target domains. Existing DG methods mainly learn the representations with invariant marginal distribution of the input features, however, the invariance of the conditional distribution of the labels given the input features is more essential for unknown domain prediction. Meanwhile, the existing of unobserved confounders which affect the input features and labels simultaneously cause spurious correlation and hinder the learning of the invariant relationship contained in the conditional distribution. Interestingly, with a causal view on the data generating process, we find that the input features of one domain are valid instrumental variables for other domains. Inspired by this finding, we propose an instrumental variable-driven DG method (IV-DG) by removing the bias of the unobserved confounders with two-stage learning. In the first stage, it learns the conditional distribution of the input features of one domain given input features of another domain. In the second stage, it estimates the relationship by predicting labels with the learned conditional distribution. Theoretical analyses and simulation experiments show that it accurately captures the invariant relationship. Extensive experiments on real-world datasets demonstrate that IV-DG method yields state-of-the-art results.

In this paper, we focus on the problem of stable prediction across unknown test data, where the test distribution might be different from the training one and is always agnostic when model training. In such a case, previous machine learning methods might exploit subtly spurious correlations induced by non-causal variables in training data for prediction. Those spurious correlations are changeable across data, leading to instability of prediction across unknown test data. To address this problem, we propose a conditional independence test based algorithm to screen out part of non-causal features and reduce those spurious correlations for a more stable prediction by leveraging a seed variable. We show, both theoretically and with empirical experiments, that our algorithm can precisely screen out the isolated non-causal variables, which have no causal relationship with other variables, and remove the spurious correlations induced by them, increasing the stability of prediction across unknown test data. Extensive experiments on both synthetic and real-world datasets demonstrate that our algorithm outperforms state-of-the-art methods for stable prediction across unknown test data.

For many machine learning algorithms, two main assumptions are required to guarantee performance. One is that the test data are drawn from the same distribution as the training data, and the other is that the model is correctly specified. In real applications, however, we often have little prior knowledge on the test data and on the underlying true model. Under model misspecification, agnostic distribution shift between training and test data leads to inaccuracy of parameter estimation and instability of prediction across unknown test data. To address these problems, we propose a novel Decorrelated Weighting Regression (DWR) algorithm which jointly optimizes a variable decorrelation regularizer and a weighted regression model. The variable decorrelation regularizer estimates a weight for each sample such that variables are decorrelated on the weighted training data. Then, these weights are used in the weighted regression to improve the accuracy of estimation on the effect of each variable, thus help to improve the stability of prediction across unknown test data. Extensive experiments clearly demonstrate that our DWR algorithm can significantly improve the accuracy of parameter estimation and stability of prediction with model misspecification and agnostic distribution shift.

In many important machine learning applications, the training distribution used to learn a probabilistic classifier differs from the distribution on which the classifier will be used to make predictions. Traditional methods correct the distribution shift by reweighting training data with the ratio of the density between test and training data. However, in many applications training takes place without prior knowledge of the testing distribution. Recently, methods have been proposed to address the shift by learning the underlying causal structure, but those methods rely on diversity arising from multiple training data sets, and they further have complexity limitations in high dimensions. In this paper, we propose a novel Deep Global Balancing Regression (DGBR) algorithm to jointly optimize a deep auto-encoder model for feature selection and a global balancing model for stable prediction across unknown environments. The global balancing model constructs balancing weights that facilitate estimation of partial effects of features (holding fixed all other features), a problem that is challenging in high dimensions, and thus helps to identify stable, causal relationships between features and outcomes. The deep auto-encoder model is designed to reduce the dimensionality of the feature space, thus making global balancing easier. We show, both theoretically and with empirical experiments, that our algorithm can make stable predictions across unknown environments. Our experiments on both synthetic and real datasets demonstrate that our algorithm outperforms the state-of-the-art methods for stable prediction across unknown environments.