Uplift modeling has obtained significant attention, with broad applications in medicine, economics, and marketing. For example, in a push notification scenario, accurately estimating the uplift of different push frequencies on user activation and notification switch close rate is critical for balancing user experience and business goals. Existing methods only use binary labels, i.e., convert or not within the observational window. However, they ignore time information (e.g., users who convert on day 1 vs. day 14 reflect different sensitivities) and fail to model potential closures outside the window, i.e., due to treatments always taking time to manifest causal impacts on outcomes, the potential outcomes of interest cannot be observed promptly and accurately. Failing to account for these issues can result in skewed uplift modeling. To address this gap, this work examines how observation timing influences the assessment of uplift by explicitly modeling the potential response time. Theoretical analysis establishes the conditions for identifiability under delayed feedback scenarios. We introduce CFR-DF (Counterfactual Regression with Delayed Feedback), a systematic framework that jointly learns both the latent response times and the underlying potential outcomes. Empirical evaluations on synthetic and real-world datasets, including an A/B test with over 1 billion users for 14 days, validate the approach, demonstrating its ability to handle temporal delays and improve estimation accuracy compared to previous uplift modeling methods.

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/

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.

In online platforms, incentives (e.g., discounts, coupons) are used to boost user engagement and revenue. Uplift modeling methods are developed to estimate user responses from observational data, often incorporating distribution balancing to address selection bias. However, these methods are limited by in-distribution testing data, which mirrors the training data distribution. In reality, user features change continuously due to time, geography, and other factors, especially on complex online marketing platforms. Thus, effective uplift modeling method for out-of-distribution data is crucial. To address this, we propose a novel uplift modeling method Invariant Deep Uplift Modeling, namely IDUM, which uses invariant learning to enhance out-of-distribution generalization by identifying causal factors that remain consistent across domains. IDUM further refines these features into necessary and sufficient factors and employs a masking component to reduce computational costs by selecting the most informative invariant features. A balancing discrepancy component is also introduced to mitigate selection bias in observational data. We conduct extensive experiments on public and real-world datasets to demonstrate IDUM’s effectiveness in both in-distribution and out-of-distribution scenarios in online marketing. Furthermore, we also provide theoretical analysis and related proofs to support our IDUM’s generalizability.

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.

Heterogeneous treatment effect (HTE) estimation is vital for understanding the change of treatment effect across individuals or subgroups. Most existing HTE estimation methods focus on addressing selection bias induced by imbalanced distributions of confounders between treated and control units, but ignore distribution shifts across populations. Thereby, their applicability has been limited to the in-distribution (ID) population, which shares a similar distribution with the training dataset. In real-world applications, where population distributions are subject to continuous changes, there is an urgent need for stable HTE estimation across out-of-distribution (OOD) populations, which, however, remains an open problem. As pioneers in resolving this problem, we propose a novel Stable Balanced Representation Learning with Hierarchical-Attention Paradigm (SBRL-HAP) framework, which consists of 1) Balancing Regularizer for eliminating selection bias, 2) Independence Regularizer for addressing the distribution shift issue, 3) Hierarchical-Attention Paradigm for coordination between balance and independence. In this way, SBRL- HAP regresses counterfactual outcomes using ID data, while ensuring the resulting HTE estimation can be successfully generalized to out-of-distribution scenarios, thereby enhancing the model's applicability in real-world settings. Extensive experiments conducted on synthetic and real-world datasets demonstrate the effectiveness of our SBRL-HAP in achieving stable HTE estimation across OOD populations, with an average 10% reduction in the error metric PEHE and 11% decrease in the ATE bias, compared to the SOTA methods.

Resulting from non-random sample selection caused by both the treatment and outcome, collider bias poses a unique challenge to treatment effect estimation using observational data whose distribution differs from that of the target population. In this paper, we rethink collider bias from an out-of-distribution (OOD) perspective, considering that the entire data space of the target population consists of two different environments: The observational data selected from the target population belongs to a seen environment labeled with $S=1$ and the missing unselected data belongs to another unseen environment labeled with $S=0$. Based on this OOD formulation, we utilize small-scale representative data from the entire data space with no environmental labels and propose a novel method, i.e., Coupled Counterfactual Generative Adversarial Model (C$^2$GAM), to simultaneously generate the missing $S=0$ samples in observational data and the missing $S$ labels in the small-scale representative data. With the help of C$^2$GAM, collider bias can be addressed by combining the generated $S=0$ samples and the observational data to estimate treatment effects. Extensive experiments on synthetic and real-world data demonstrate that plugging C$^2$GAM into existing treatment effect estimators achieves significant performance improvements.

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.

This paper studies the causal relations from subsampled time series, in which measurements are sparse and sampled at a coarser timescale than the causal timescale of the underlying system. In such data, because there are numerous missing time-slices (i.e., cross-sections at each time point) between two consecutive measurements, conventional causal discovery methods designed for standard time series data would produce significant errors. To learn causal relations from subsampled time series, a typical solution is to conduct different interventions and then make a comparison. However, full interventions are often expensive, unethical, or even infeasible, particularly in fields such as health and social science. In this paper, we first explore how readily available two-time-slices data can replace intervention data to improve causal ordering, and propose a novel Descendant Hierarchical Topology algorithm with Conditional Independence Test (DHT-CIT) to learn causal relations from subsampled time series using only two time-slices. Specifically, we develop a conditional independence criterion that can be applied iteratively to test each node from time series and identify all of its descendant nodes. Empirical results on both synthetic and real-world datasets demonstrate the superiority of our DHT-CIT algorithm.

Unobserved discrete data are ubiquitous in many scientific disciplines, and how to learn the causal structure of these latent variables is crucial for uncovering data patterns. Most studies focus on the linear latent variable model or impose strict constraints on latent structures, which fail to address cases in discrete data involving non-linear relationships or complex latent structures. To achieve this, we explore a tensor rank condition on contingency tables for an observed variable set $\mathbf{X}_p$, showing that the rank is determined by the minimum support of a specific conditional set (not necessary in $\mathbf{X}_p$) that d-separates all variables in $\mathbf{X}_p$. By this, one can locate the latent variable through probing the rank on different observed variables set, and further identify the latent causal structure under some structure assumptions. We present the corresponding identification algorithm and conduct simulated experiments to verify the effectiveness of our method. In general, our results elegantly extend the identification boundary for causal discovery with discrete latent variables and expand the application scope of causal discovery with latent variables.

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.

In observational studies, confounder separation and balancing are the fundamental problems of treatment effect estimation. Most of the previous methods focused on addressing the problem of confounder balancing by treating all observed pre-treatment variables as confounders, ignoring confounder separation. In general, not all the observed pre-treatment variables are confounders that refer to the common causes of the treatment and the outcome, some variables only contribute to the treatment (i.e., instrumental variables) and some only contribute to the outcome (i.e., adjustment variables). Balancing those non-confounders, including instrumental variables and adjustment variables, would generate additional bias for treatment effect estimation. By modeling the different causal relations among observed pre-treatment variables, treatment variables and outcome variables, we propose a synergistic learning framework to i) separate confounders by learning decomposed representations of both confounders and non-confounders, ii) balance confounder with sample re-weighting technique, and simultaneously iii) estimate the treatment effect in observational studies via counterfactual inference. Empirical results on synthetic and real-world datasets demonstrate that the proposed method can precisely decompose confounders and achieve a more precise estimation of treatment effect than baselines.

Influenced by the great success of deep learning via cloud computing and the rapid development of edge chips, research in artificial intelligence (AI) has shifted to both of the computing paradigms, i.e., cloud computing and edge computing. In recent years, we have witnessed significant progress in developing more advanced AI models on cloud servers that surpass traditional deep learning models owing to model innovations (e.g., Transformers, Pretrained families), explosion of training data and soaring computing capabilities. However, edge computing, especially edge and cloud collaborative computing, are still in its infancy to announce their success due to the resource-constrained IoT scenarios with very limited algorithms deployed. In this survey, we conduct a systematic review for both cloud and edge AI. Specifically, we are the first to set up the collaborative learning mechanism for cloud and edge modeling with a thorough review of the architectures that enable such mechanism. We also discuss potentials and practical experiences of some on-going advanced edge AI topics including pretraining models, graph neural networks and reinforcement learning. Finally, we discuss the promising directions and challenges in this field.

This paper considers the challenge of estimating treatment effects from observational data in the presence of unmeasured confounders. A popular way to address this challenge is to utilize an instrumental variable (IV) for two-stage regression, i.e., 2SLS and variants, but limited to the linear setting. Recently, many nonlinear IV regression variants were proposed to overcome it by regressing the treatment with IVs and observed confounders in stage 1, leading to the imbalance of the observed confounders in stage 2. In this paper, we propose a Confounder Balanced IV Regression (CB-IV) algorithm to jointly remove the bias from the unmeasured confounders and balance the observed confounders. To the best of our knowledge, this is the first work to combine confounder balancing in IV regression for treatment effect estimation. Theoretically, we re-define and solve the inverse problems for the response-outcome function. Experiments show that our algorithm outperforms the existing approaches.

Learning individualized causal effect (ICE) plays a vital role in various fields of big data analysis, ranging from fine-grained policy evaluation to personalized treatment development. However, the presence of unmeasured confounders increases the difficulty of estimating ICE in real-world scenarios. A wide range of methods have been proposed to address the unmeasured confounders with the aid of instrument variable (IV), which sources from the treatment randomization. The performance of these methods relies on the well-predefined IVs that satisfy the unconfounded instruments assumption (i.e., the IVs are independent with the unmeasured confounders given observed covariates), which is untestable and leads to finding a valid IV becomes an art rather than science. In this paper, we focus on estimating the ICE with confounded instruments that violate the unconfounded instruments assumption. By considering the conditional independence between the set of confounded instruments and the outcome variable, we propose a novel method, named CVAE-IV, to generate a substitute of the unmeasured confounder with a conditional variational autoencoder. Our theoretical analysis guarantees that the generated confounder substitute will identify unbiased ICE. Extensive experiments on bias demand prediction and Mendelian randomization analysis verify the effectiveness of our method.

Instrumental variables (IVs), sources of treatment randomization that are conditionally independent of the outcome, play an important role in causal inference with unobserved confounders. However, the existing IV-based counterfactual prediction methods need well-predefined IVs, while it’s an art rather than science to find valid IVs in many real-world scenes. Moreover, the predefined hand-made IVs could be weak or erroneous by violating the conditions of valid IVs. These thorny facts hinder the application of the IV-based counterfactual prediction methods. In this article, we propose a novel Automatic Instrumental Variable decomposition (AutoIV) algorithm to automatically generate representations serving the role of IVs from observed variables (IV candidates). Specifically, we let the learned IV representations satisfy the relevance condition with the treatment and exclusion condition with the outcome via mutual information maximization and minimization constraints, respectively. We also learn confounder representations by encouraging them to be relevant to both the treatment and the outcome. The IV and confounder representations compete for the information with their constraints in an adversarial game, which allows us to get valid IV representations for IV-based counterfactual prediction. Extensive experiments demonstrate that our method generates valid IV representations for accurate IV-based counterfactual prediction.