arXiv subjects

Zhi Geng

Publications and source records attributed to Zhi Geng.

At least 19 recordsLinked to original sources

arXiv2026

Testing the Validity of Instrumental Variable Sets in Causal Additive Models with Non-Constant Effects

Instrumental variable (IV) methods are powerful for causal effect estimation with unmeasured confounding, but in practice researchers often face a set of candidate IVs whose validity is difficult to determine from observational data. This paper studies the problem of testing the validity of IV sets under Causal Additive Models with Non-Constant Effects (CAM-NCE). To address this problem, we propose a testable condition, termed the Cross Auxiliary-based independence Test (CAT) condition, for assessing IV set validity from observational data. We show that, under the completeness condition, if the CAT condition is violated, the corresponding set cannot be a valid IV set. Furthermore, under a cross distributional non-degeneracy condition, we establish that the CAT condition becomes both necessary and sufficient for characterizing valid IV sets under CAM-NCE. We then extend the CAT condition to settings with covariates and develop a practical finite-sample algorithm for testing the validity of candidate IV sets. Extensive experiments on synthetic data and three real-world datasets demonstrate the effectiveness and practical utility of the proposed method.

stat.ME↗

arXiv2026

Mediation Analysis with Multiple Mediators Subject to Missing Not at Random

Causal mediation analysis serves as a key tool for uncovering the mediating mechanisms linking treatments to outcomes. Existing methods for mediation analysis with multiple mediators typically assume complete observations or missing-at-random and may yield biased estimation when mediator values are missing not at random (MNAR). This paper studies the identification and estimation of causal mediation effects with multiple mediators subject to MNAR missingness. We consider a broad class of MNAR mechanisms in which missingness may depend on unobserved mediators, treatment, covariates, and outcomes. Under a series of increasingly general MNAR mechanisms, we establish identified natural direct and indirect effects, effectively generalizing existing mediation analysis to handle nonignorable missing mediators. Based on the proposed identification framework, we develop estimation procedures for causal mediation effects and evaluate their finite-sample performance through simulation studies. The results demonstrate satisfactory performance across a range of missingness scenarios. An application to data from the National Health and Nutrition Examination Survey(NHANES) illustrates the practical utility of the proposed methodology for investigating mediation pathways in the presence of nonignorable missing data.

stat.ME↗

arXiv2026

Apportioning Causal Responsibility of Two Risk Factors for an Adverse Outcome via Counterfactual Attribution

Unlike traditional causal inference, which prospectively evaluates the effects of causes, apportioning causal responsibility requires a retrospective assessment to deduce the causes of an outcome that has already occurred. This paper proposes a quantitative framework for apportioning causal responsibility between two binary risk factors that jointly contribute to a realized adverse outcome. Ideally, knowing the individual's latent causal type, defined by the potential outcomes under all possible exposure combinations, would allow precise apportionment; however, these potential outcomes cannot be simultaneously observed. We therefore define the average causal responsibility of each risk factor as its expected responsibility over the distribution of latent causal types. Under the assumptions of no confounding and monotonicity, we establish nonparametric identification of this metric when the type-specific responsibilities satisfy a structural balance condition, and derive sharp bounds otherwise. We illustrate the proposed framework using the classic example of lung cancer attributable to smoking and asbestos exposures.

stat.ME↗

arXiv2026

Probability of Root Cause: A Counterfactual Definition and Its Identification

Attributing an observed outcome to its root cause is a central task in domains ranging from medical diagnosis to engineering fault diagnosis. Existing approaches either equate the root cause with a root node of the causal graph, as in causal-discovery-based root cause analysis, or target causes more broadly and thereby favour proximate ones, as with the probability of causation and posterior causal effects. We argue that this issue stems from the absence of a formal definition of a root cause, which has led to methods designed for other purposes being applied to root cause attribution by default. We address this by giving a formal, individual-level definition of a root cause within the potential outcomes framework, based on the notion of an individual cause and a counterfactual root condition motivated by mediation analysis. Building on this definition, we propose the probability of root cause (PRC), which quantifies how probable it is that a candidate variable set is the root cause of a given outcome, conditional on observed evidence. Under standard assumptions, we establish the identifiability of the PRC and derive an explicit identification formula. Two numerical examples illustrate the approach.

stat.ME↗

arXiv2026

Universal rapid machine learning models for predicting unconvoluted and convoluted X-ray Absorption Spectra

X-ray absorption near edge structure (XANES) is an essential tool for elucidating the atomic-scale, local three-dimensional (3D) structure of given materials and molecules. The rapid computation of XANES based on molecular 3D structures constitutes a vital element of quantitative XANES analysis. Here, we present an XANES prediction model. It takes 3D structures as input and generates either unconvoluted XANES or convoluted spectra as output, demonstrating excellent generalizability across diverse instrumental broadening. This model has validated its predictive capability for both hard X-ray XAS (exemplified by K-edges of 3d 4d metals and lanthanides) and soft X-ray XAS (using S K-edge as examples). Adopting the model, XANES spectra of multiple elements can be predicted using a single unified model. A highly efficient 3D structure fitting algorithm based on this unconvoluted XANES prediction model, aiming to serve as an online data analysis method suitable for XAS beamlines.

physics.chem-ph↗

arXiv2026

Assessing Interactive Causes of an Occurred Outcome Due to Two Binary Exposures

In contrast to evaluating treatment effects, causal attribution analysis focuses on identifying the key factors responsible for an observed outcome. For two binary exposure variables and a binary outcome variable, researchers need to assess not only the likelihood that an observed outcome was caused by a particular exposure, but also the likelihood that it resulted from the interaction between the two exposures. For example, in the case of a male worker who smoked, was exposed to asbestos, and developed lung cancer, researchers aim to explore whether the cancer resulted from smoking, asbestos exposure, or their interaction. Even in randomized controlled trials, widely regarded as the gold standard for causal inference, identifying and evaluating retrospective causal interactions between two exposures remains challenging. In this paper, we define posterior probabilities to characterize the interactive causes of an observed outcome. We establish the identifiability of posterior probabilities by using a secondary outcome variable that may appear after the primary outcome. We apply the proposed method to the classic case of smoking and asbestos exposure. Our results indicate that for lung cancer patients who smoked and were exposed to asbestos, the disease is primarily attributable to the synergistic effect between smoking and asbestos exposure.

stat.AP↗

arXiv2025

Pseudo-strata learning via maximizing misclassification reward

Online advertising aims to increase user engagement and maximize revenue, but users respond heterogeneously to ad exposure. Some users purchase only when exposed to ads, while others purchase regardless of exposure, and still others never purchase. This heterogeneity can be characterized by latent response types, commonly referred to as principal strata, defined by users' joint potential outcomes under exposure and non-exposure. However, users' true strata are unobserved, making direct analysis infeasible. In this article, instead of learning the true strata, we propose a novel approach that learns users' pseudo-strata by leveraging information from an outcome (revenue) observed after the response (purchase). We construct pseudo-strata to classify users and introduce misclassification rewards to quantify the expected revenue gain of pseudo-strata-based policies relative to true strata. Within a Bayesian classification framework, we learn the pseudo-strata by optimizing the expected revenue. To implement these procedures, we introduce identification assumptions and estimation methods, and establish their large-sample properties. Simulation studies show that the proposed method achieves more accurate strata classification and substantially higher revenue than baselines. We further illustrate the method using a large-scale industrial dataset from the Criteo Predictive Search Platform.

stat.ME↗

arXiv2025

Covariate Balancing Value Estimation for Optimal Individualized Treatment Rules

Learning an optimal individualized treatment rule depends on reliable value comparisons across the candidate class. Standard doubly robust estimators are consistent when either the propensity score or outcome regression model is correctly specified, but they do not directly control the remaining bias in value estimation when both models are misspecified. In this paper, we propose a covariate balancing doubly robust estimator that combines propensity score estimation based on covariate balancing with an outcome regression component selected using an empirical variance criterion based on the influence function. Using prespecified covariate functions, the balancing procedure induces an effective balancing space to which the weighted propensity score error is orthogonal. Consequently, the proposed value estimator is consistent if either the propensity score model is correct or the rule-relevant outcome regression error lies in this space. The latter condition does not require a correctly specified outcome regression model and can hold even when both working models are misspecified. Under correct propensity score specification, the estimator has the smallest asymptotic variance within the proposed covariate balancing doubly robust class. Simulations evaluate value estimation in finite samples and the regret of learned rules, and an application to a leukemia dataset illustrates the proposed method in practice.

stat.ME↗

arXiv2025

Confounded Causal Imitation Learning with Instrumental Variables

Imitation learning from demonstrations usually suffers from the confounding effects of unmeasured variables (i.e., unmeasured confounders) on the states and actions. If ignoring them, a biased estimation of the policy would be entailed. To break up this confounding gap, in this paper, we take the best of the strong power of instrumental variables (IV) and propose a Confounded Causal Imitation Learning (C2L) model. This model accommodates confounders that influence actions across multiple timesteps, rather than being restricted to immediate temporal dependencies. We develop a two-stage imitation learning framework for valid IV identification and policy optimization. In particular, in the first stage, we construct a testing criterion based on the defined pseudo-variable, with which we achieve identifying a valid IV for the C2L models. Such a criterion entails the sufficient and necessary identifiability conditions for IV validity. In the second stage, with the identified IV, we propose two candidate policy learning approaches: one is based on a simulator, while the other is offline. Extensive experiments verified the effectiveness of identifying the valid IV as well as learning the policy.

cs.LG↗

arXiv2025

Safe Individualized Treatment Rules with Controllable Harm Rates

Estimating individualized treatment rules (ITRs) is crucial for tailoring interventions in precision medicine. Typical ITR estimation methods rely on conditional average treatment effects (CATEs) to guide treatment assignments. However, such methods overlook individual-level harm within covariate-specific subpopulations, potentially leading many individuals to experience worse outcomes under CATE-based ITRs. In this article, we aim to estimate ITRs that maximize the reward while ensuring that the harm rate induced by the ITR remains below a pre-specified threshold. We first derive the explicit form of the oracle ITR. However, the oracle ITR is not achievable without strong assumptions, as the harm rate is generally unidentifiable due to its dependence on the joint distribution of potential outcomes. To address this, we propose two strategies for estimating ITRs with a harm rate constraint under partial identification and establish their large-sample properties. By accounting for both reward and harm, our method provides a reliable solution for developing ITRs in high-stakes domains where harm is a critical consideration. Extensive simulations demonstrate the effectiveness of the proposed methods in controlling harm rates. We apply the proposed method to analyze two real-world datasets from a new perspective, assessing the potential reduction in harm rate compared with historical interventions.

stat.ME↗

arXiv2024

Local Learning for Covariate Selection in Nonparametric Causal Effect Estimation with Latent Variables

Estimating causal effects from nonexperimental data is a fundamental problem in many fields of science. A key component of this task is selecting an appropriate set of covariates for confounding adjustment to avoid bias. Most existing methods for covariate selection often assume the absence of latent variables and rely on learning the global network structure among variables. However, identifying the global structure can be unnecessary and inefficient, especially when our primary interest lies in estimating the effect of a treatment variable on an outcome variable. To address this limitation, we propose a novel local learning approach for covariate selection in nonparametric causal effect estimation, which accounts for the presence of latent variables. Our approach leverages testable independence and dependence relationships among observed variables to identify a valid adjustment set for a target causal relationship, ensuring both soundness and completeness under standard assumptions. We validate the effectiveness of our algorithm through extensive experiments on both synthetic and real-world data.

cs.LG↗

arXiv2024

Testability of Instrumental Variables in Additive Nonlinear, Non-Constant Effects Models

We address the issue of the testability of instrumental variables derived from observational data. Most existing testable implications are centered on scenarios where the treatment is a discrete variable, e.g., instrumental inequality (Pearl, 1995), or where the effect is assumed to be constant, e.g., instrumental variables condition based on the principle of independent mechanisms (Burauel, 2023). However, treatments can often be continuous variables, such as drug dosages or nutritional content levels, and non-constant effects may occur in many real-world scenarios. In this paper, we consider an additive nonlinear, non-constant effects model with unmeasured confounders, in which treatments can be either discrete or continuous, and propose an Auxiliary-based Independence Test (AIT) condition to test whether a variable is a valid instrument. We first show that, under the completeness condition, if the candidate instrument is valid, then the AIT condition holds. Moreover, we illustrate the implications of the AIT condition and demonstrate that, under certain additional conditions, the AIT condition is necessary and sufficient to detect all invalid IVs. We also extend the AIT condition to include covariates and introduce a practical testing algorithm. Experimental results on both synthetic and three different real-world datasets show the effectiveness of our proposed condition.

stat.ME↗

arXiv2024

Identifying and bounding the probability of necessity for causes of effects with ordinal outcomes

Although the existing causal inference literature focuses on the forward-looking perspective by estimating effects of causes, the backward-looking perspective can provide insights into causes of effects. In backward-looking causal inference, the probability of necessity measures the probability that a certain event is caused by the treatment given the observed treatment and outcome. Most existing results focus on binary outcomes. Motivated by applications with ordinal outcomes, we propose a general definition of the probability of necessity. However, identifying the probability of necessity is challenging because it involves the joint distribution of the potential outcomes. We propose a novel assumption of monotonic incremental treatment effect to identify the probability of necessity with ordinal outcomes. We also discuss the testable implications of this key identification assumption. When it fails, we derive explicit formulas of the sharp large-sample bounds on the probability of necessity.

math.ST↗

arXiv2024

On the Comparative Analysis of Average Treatment Effects Estimation via Data Combination

There is growing interest in exploring causal effects in target populations via data combination. However, most approaches are tailored to specific settings and lack comprehensive comparative analyses. In this article, we focus on a typical scenario involving a source dataset and a target dataset. We first design six settings under covariate shift and conduct a comparative analysis by deriving the semiparametric efficiency bounds for the ATE in the target population. We then extend this analysis to six new settings that incorporate both covariate shift and posterior drift. Our study uncovers the key factors that influence efficiency gains and the ``effective sample size" when combining two datasets, with a particular emphasis on the roles of the variance ratio of potential outcomes between datasets and the derivatives of the posterior drift function. To the best of our knowledge, this is the first paper that explicitly explores the role of the posterior drift functions in causal inference. Additionally, we also propose novel methods for conducting sensitivity analysis to address violations of transportability between the two datasets. We empirically validate our findings by constructing locally efficient estimators and conducting extensive simulations. We demonstrate the proposed methods in two real-world applications.

stat.ME↗

arXiv2024

Identification and multiply robust estimation of causal effects via instrumental variables from an auxiliary population

Estimating causal effects in a target population with unmeasured confounders is challenging, especially when instrumental variables (IVs) are unavailable. However, IVs from auxiliary populations with similar problems can help infer causal effects in the target population. While the homogeneous conditional average treatment effect assumption has been widely used for effect transportability, it has not been explored in IV-based data fusion. We include it as a basic approach, though it may be biased when treatment effect heterogeneity exists. As an alternative approach, we introduce the equi-confounding assumption that the unmeasured confounding bias remains the same after adjusting for observed covariates, while allowing conditional average treatment effects to differ across populations. This allows us to identify the confounding bias in the auxiliary population and remove it from the treatment-outcome association in the target population to recover the causal effect. We develop multiply robust estimators under both approaches and demonstrate them through simulation studies and a real data application.

stat.ME↗

arXiv2024

Identification and Estimation of the Bi-Directional MR with Some Invalid Instruments

We consider the challenging problem of estimating causal effects from purely observational data in the bi-directional Mendelian randomization (MR), where some invalid instruments, as well as unmeasured confounding, usually exist. To address this problem, most existing methods attempt to find proper valid instrumental variables (IVs) for the target causal effect by expert knowledge or by assuming that the causal model is a one-directional MR model. As such, in this paper, we first theoretically investigate the identification of the bi-directional MR from observational data. In particular, we provide necessary and sufficient conditions under which valid IV sets are correctly identified such that the bi-directional MR model is identifiable, including the causal directions of a pair of phenotypes (i.e., the treatment and outcome). Moreover, based on the identification theory, we develop a cluster fusion-like method to discover valid IV sets and estimate the causal effects of interest. We theoretically demonstrate the correctness of the proposed algorithm. Experimental results show the effectiveness of our method for estimating causal effects in bi-directional MR.

stat.ME↗

arXiv2024

Causal Inference with Outcomes Truncated by Death and Missing Not at Random

In clinical trials, principal stratification analysis is commonly employed to address the issue of truncation by death, where a subject dies before the outcome can be measured. However, in practice, many survivor outcomes may remain uncollected or be missing not at random, posing a challenge to standard principal stratification analyses. In this paper, we explore the identification, estimation, and bounds of the average treatment effect within a subpopulation of individuals who would potentially survive under both treatment and control conditions. We show that the causal parameter of interest can be identified by introducing a proxy variable that affects the outcome only through the principal strata, while requiring that the treatment variable does not directly affect the missingness mechanism. Subsequently, we propose an approach for estimating causal parameters and derive nonparametric bounds in cases where identification assumptions are violated. We illustrate the performance of the proposed method through simulation studies and a real dataset obtained from a Human Immunodeficiency Virus (HIV) study.

stat.ME↗

arXiv2024

Generalized Independent Noise Condition for Estimating Causal Structure with Latent Variables

We investigate the task of learning causal structure in the presence of latent variables, including locating latent variables and determining their quantity, and identifying causal relationships among both latent and observed variables. To this end, we propose a Generalized Independent Noise (GIN) condition for linear non-Gaussian acyclic causal models that incorporate latent variables, which establishes the independence between a linear combination of certain measured variables and some other measured variables. Specifically, for two observed random vectors $\bf{Y}$ and $\bf{Z}$, GIN holds if and only if $ω^{\intercal}\mathbf{Y}$ and $\mathbf{Z}$ are independent, where $ω$ is a non-zero parameter vector determined by the cross-covariance between $\mathbf{Y}$ and $\mathbf{Z}$. We then give necessary and sufficient graphical criteria of the GIN condition in linear non-Gaussian acyclic models. Roughly speaking, GIN implies the existence of a set $\mathcal{S}$ such that $\mathcal{S}$ is causally earlier (w.r.t. the causal ordering) than $\mathbf{Y}$, and that every active (collider-free) path between $\mathbf{Y}$ and $\mathbf{Z}$ must contain a node from $\mathcal{S}$. Interestingly, we find that the independent noise condition (i.e., if there is no confounder, causes are independent of the residual derived from regressing the effect on the causes) can be seen as a special case of GIN. With such a connection between GIN and latent causal structures, we further leverage the proposed GIN condition, together with a well-designed search procedure, to efficiently estimate Linear, Non-Gaussian Latent Hierarchical Models (LiNGLaHs), where latent confounders may also be causally related and may even follow a hierarchical structure. We show that the causal structure of a LiNGLaH is identifiable in light of GIN conditions. Experimental results show the effectiveness of the proposed method.

cs.LG↗