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Anpeng Wu

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14 papers

2 author rows

AAAI Conference 2026 Conference Paper

Uplift Modeling with Delayed Feedback: Identifiability and Algorithms

Chunyuan Zheng
Anpeng Wu
Chuan Zhou
Taojun Hu
Qingying Chen
Hongyi Liu
Chenxi Li
Huiyou Jiang

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.

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ICLR Conference 2025 Conference Paper

Causal Graph Transformer for Treatment Effect Estimation Under Unknown Interference

Anpeng Wu
Haiyi Qiu
Zhengming Chen 0002
Zijian Li 0001
Ruoxuan Xiong
Fei Wu 0001
Kun Zhang 0001

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.

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ICML Conference 2025 Conference Paper

Generalizing Causal Effects from Randomized Controlled Trials to Target Populations across Diverse Environments

Baohong Li
Yingrong Wang
Anpeng Wu
Ming Ma
Ruoxuan Xiong
Kun Kuang 0001

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.

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ICML Conference 2025 Conference Paper

Invariant Deep Uplift Modeling for Incentive Assignment in Online Marketing via Probability of Necessity and Sufficiency

Zexu Sun
Qiyu Han
Hao Yang 0045
Anpeng Wu
Minqin Zhu
Dugang Liu
Chen Ma 0001
Yunpeng Weng

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 I nvariant D eep U plift M odeling, 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.

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ICML Conference 2025 Conference Paper

Rethinking Causal Ranking: A Balanced Perspective on Uplift Model Evaluation

Minqin Zhu
Zexu Sun
Ruoxuan Xiong
Anpeng Wu
Baohong Li
Caizhi Tang
Jun Zhou 0011
Fei Wu 0001

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.

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ICML Conference 2024 Conference Paper

A Generative Approach for Treatment Effect Estimation under Collider Bias: From an Out-of-Distribution Perspective

Baohong Li
Haoxuan Li 0001
Anpeng Wu
Minqin Zhu
Shiyuan Peng
Qingyu Cao
Kun Kuang 0001

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.

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AAAI Conference 2024 Conference Paper

Contrastive Balancing Representation Learning for Heterogeneous Dose-Response Curves Estimation

Minqin Zhu
Anpeng Wu
Haoxuan Li
Ruoxuan Xiong
Bo Li
Xiaoqing Yang
Xuan Qin
Peng Zhen

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.

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ICML Conference 2024 Conference Paper

Learning Causal Relations from Subsampled Time Series with Two Time-Slices

Anpeng Wu
Haoxuan Li 0001
Kun Kuang 0001
Keli Zhang
Fei Wu 0001

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.

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NeurIPS Conference 2024 Conference Paper

Learning Discrete Latent Variable Structures with Tensor Rank Conditions

Zhengming Chen
Ruichu Cai
Feng Xie
Jie Qiao
Anpeng Wu
Zijian Li
Zhifeng Hao
Kun Zhang

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.

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ICML Conference 2024 Conference Paper

Learning Shadow Variable Representation for Treatment Effect Estimation under Collider Bias

Baohong Li
Haoxuan Li 0001
Ruoxuan Xiong
Anpeng Wu
Fei Wu 0001
Kun Kuang 0001

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.

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ICML Conference 2024 Conference Paper

Two-Stage Shadow Inclusion Estimation: An IV Approach for Causal Inference under Latent Confounding and Collider Bias

Baohong Li
Anpeng Wu
Ruoxuan Xiong
Kun Kuang 0001

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.

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AAAI Conference 2023 Conference Paper

Learning Instrumental Variable from Data Fusion for Treatment Effect Estimation

Anpeng Wu
Kun Kuang
Ruoxuan Xiong
Minqin Zhu
Yuxuan Liu
Bo Li
Furui Liu
Zhihua Wang

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.

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ICML Conference 2023 Conference Paper

Stable Estimation of Heterogeneous Treatment Effects

Anpeng Wu
Kun Kuang 0001
Ruoxuan Xiong
Bo Li 0064
Fei Wu 0001

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.

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ICML Conference 2022 Conference Paper

Instrumental Variable Regression with Confounder Balancing

Anpeng Wu
Kun Kuang 0001
Bo Li 0064
Fei Wu 0001

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.

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