arXiv subjects

AmirEmad Ghassami

Publications and source records attributed to AmirEmad Ghassami.

At least 19 recordsLinked to original sources

arXiv2026

Functional Estimation under Proxy-Based Full-Law Identification

We state general conditions under which the full-data law is identified in the presence of latent variables, leveraging key observed variables ("proxies") associated with unobserved variables. These assumptions extend those used in existing examples from the literature that recover the full-data law under relatively flexible model assumptions. We first describe graphical models compatible with our assumptions, and then consider target parameters that are functionals of the full-data law, developing estimating equations that give rise to consistent M-estimators using the observed data. Our approach replaces unobserved random variables appearing in full-data estimating equations with observed variables via a proxy-based weighting scheme. This strategy can be extended to construct observed-data influence functions, giving estimators with desirable properties such as multiple robustness and $\sqrt{n}$-consistency despite slower than parametric convergence of nuisance functions.

stat.ME↗

arXiv2026

Proximal Causal Inference for Hidden Outcomes

Methods that rely on proxies, without imposing strong parametric structure, are increasingly used to deal with unobserved variables in causal inference. One influential line of this work reconstructs latent distributions used to identify the target functional by exploiting eigenvalue eigenvector structure. Within this framework, we first establish identification of the full data law in the presence of hidden outcomes, and then develop influence function based estimators for causal effects. To the best of our knowledge, this is the first work to develop influence function based estimators in this setting without relying on unbiased proxy measurements or partial observation, while achieving multiple robustness and desirable efficiency properties. We demonstrate the performance of our approach through simulation studies.

stat.ME↗

arXiv2026

Debiased Causal Mediation Analysis in Ultra-High-Dimensional Settings in the Presence of Interaction Effects

Mediation analysis is a crucial tool for uncovering the mechanisms through which a treatment affects an outcome, providing deeper causal insights and guiding effective interventions. Despite substantial advances in mediation analysis with fixed- or low-dimensional mediators and covariates, estimation and inference for mediation functionals remain limited when both mediators and covariates are ultra-high-dimensional. In this paper, we propose an estimator for the mediation functional in a high-dimensional setting that accommodates the treatment--covariate interactions in the mediator model, as well as treatment--covariate and treatment--mediator interactions in the outcome model. As the parameter of interest involves high-dimensional components from different treatment arms and regression equations, existing debiasing approaches are not directly applicable, motivating our multi-step debiasing technique for handling such structurally complex functionals. We establish that the proposed estimator is $\sqrt{n}$-consistent and asymptotically normal, enabling valid inference for natural direct and indirect effects. We evaluate our proposed methodology through extensive simulation studies and apply it to the TCGA lung cancer dataset to estimate the effect of smoking, mediated by DNA methylation, on the survival time of lung cancer patients.

stat.ME↗

arXiv2026

Partial Identification of Causal Effects Using Proxy Variables

Proximal causal inference is a framework for evaluating the causal effects in the presence of unmeasured confounding. For point identification, it leverages a pair of proxy variables to identify a bridge function that matches the dependence of potential outcomes or treatment variables on the hidden factors to corresponding functions of observed proxies. Unique identification requires that proxies are sufficiently relevant for hidden factors, a requirement that has previously been formalized as a completeness condition. However, completeness is not empirically testable, and although a bridge function may be well-defined in a given setting, lack of completeness, sometimes manifested by availability of a single type of proxy, may severely limit prospects for identification of a bridge function and thus a causal effect; therefore, potentially restricting the application of the framework. In this paper, we propose partial identification methods that do not require completeness and obviate the need for identification of a bridge function. We establish that proxies can be leveraged to obtain bounds on the causal effect even if available information does not suffice to identify either a bridge function or a corresponding causal effect of interest. Our bounds are non-smooth functionals of the underlying distribution. For inference, we employ LogSumExp approximations that yield smooth lower and upper bounds, and we derive the efficient influence functions of the resulting bound functionals which enable analytic variance estimation, while bootstrap confidence intervals remain available for regular plug-in implementations. We further establish analogous results in related settings where identification hinges upon hidden mediators for which proxies are available, however such proxies are not sufficiently rich for point identification of a bridge function or a corresponding causal effect of interest.

stat.ME↗

arXiv2026

A Sensitivity Analysis Framework for Causal Inference Under Interference

In many applications of causal inference, the treatment received by one unit may influence the outcome of another, a phenomenon referred to as interference. Although there are several frameworks for conducting causal inference in the presence of interference, practitioners often lack the data necessary to adjust for its effects. In this paper, we propose a weighting-based sensitivity analysis framework that can be used to assess the systematic bias arising from ignoring interference. Unlike most of the existing literature, we allow for the presence of unmeasured confounding, and show that the combination of interference and unmeasured confounding is a notable challenge to causal inference. We also study a third factor contributing to systematic bias: lack of transportability. Our framework enables practitioners to assess the impact of these three issues simultaneously through several easily interpretable sensitivity parameters that can reflect a wide range of intuitions about the data.

stat.ME↗

arXiv2026

Multiply Robust Causal Mediation Analysis with Continuous Treatments

In many applications, researchers are interested in the direct and indirect causal effects of a treatment or exposure on an outcome of interest. Mediation analysis offers a rigorous framework for identifying and estimating these causal effects. For binary treatments, efficient estimators for the direct and indirect effects are presented by Tchetgen Tchetgen and Shpitser (2012) based on the influence function of the parameter of interest. These estimators possess desirable properties such as multiple-robustness and asymptotic normality while allowing for slower than root-n rates of convergence for the nuisance parameters. However, in settings involving continuous treatments, these influence function-based estimators are not readily applicable without making strong parametric assumptions. In this work, utilizing a kernel smoothing approach, we propose an estimator suitable for settings with continuous treatments inspired by the influence function-based estimation strategy. Our proposed approach employs cross-fitting, relaxing the smoothness requirements on the nuisance functions and allowing them to be estimated at slower rates than the target parameter. Additionally, similar to influence function-based estimators, our proposed estimator is multiply robust and asymptotically normal, allowing for inference in settings where parametric assumptions may not be justified.

math.ST↗

arXiv2026

MediEncoder: Nonlinear Representation Learning for High-Dimensional Causal Mediation Analysis

Causal mediation analysis decomposes a treatment effect into indirect pathways through mediators and direct pathways not operating through them. Modern biomedical studies often involve high-dimensional covariates and mediators that are noisy proxies for lower-dimensional latent biological processes. Existing methods typically rely on sparsity, linear factor models, or ignore the connection among variables in the learned representations, which can be restrictive when measurements are nonlinear and covariate and mediator factors are structurally dependent. We propose MediEncoder, a representation-learning framework for nonlinear high-dimensional mediation analysis. MediEncoder jointly learns low-dimensional covariate and mediator representations using a coupled encoder-decoder architecture with a cross-factor network that links treatment and covariate representations to mediator representations. The learned features are then used in a cross-fitted efficient influence function-based estimator of natural direct and indirect effects. The resulting estimator is multiply robust and asymptotically normal under suitable regularity conditions. Simulations show that MediEncoder improves estimation accuracy over competing dimension-reduction approaches, and an application to Alzheimer's Disease Neuroimaging Initiative data illustrates its utility in high-dimensional biomedical causal mediation analysis.

stat.ME↗

arXiv2026

Causal Discovery in Structural VAR Models Under Equal Noise Variance

Causal discovery from multivariate time series is challenging when causal effects may occur both across time and within the same sampling interval. This issue is especially important in applications such as neuroscience, where the sampling rate may be coarse relative to the underlying dynamics and contemporaneous effects need not form an acyclic graph. We study causal discovery in linear Gaussian structural VAR models under an equal noise variance assumption, meaning that the structural noise terms have a common variance. Unlike the DAG-based cross-sectional equal noise variance setting, the time-series setting considered here does not generally yield point identification of a unique causal graph. Instead, multiple structural VAR parameterizations can induce the same stationary observed process law. We introduce a notion of observational equivalence tailored to this setting and show that the corresponding equivalence class is characterized by orthogonal transformations of the structural equations together with a global positive scale. This characterization leads to an equivalence-aware model discrepancy, the observational alignment discrepancy, which compares structural models modulo transformations that preserve the observed law. Building on this theory, we propose ENVAR, a sparsity-based procedure that searches over the induced observational equivalence class for a sparse normalized structural representative. We evaluate the proposed methodology on synthetic structural VAR data and on an fMRI dataset.

stat.ME↗

arXiv2026

Model-Robust Direct Effect Under Confounder-Mediator Ambiguity

Direct effect analyses usually require deciding whether a focal variable is a pre-exposure confounder or a post-exposure mediator. In observational studies, that distinction may be unclear because timing is measured coarsely or the variable reflects an evolving process. Considering the average treatment effect (ATE) and the natural direct effect (NDE) as a common notion of the direct effect when the focal variable is a confounder and a mediator, respectively, we show that, in general, no single observed-data estimand recovers both the ATE when the focal variable is a confounder and the NDE when it is a mediator. Consequently, if a practitioner applies an NDE estimator when the variable is actually pre-exposure, the resulting estimate may have no clear causal interpretation. We identify a no-additive-interaction condition under which these quantities coincide, develop sensitivity bounds for departures from that condition, and propose an alternative model-robust estimand. This estimand equals the ATE when the variable is pre-exposure and an interventional direct effect when it is post-exposure. Moreover, within a natural class of outcome-free stochastic direct effects, it is the unique observed-data functional that remains causally interpretable under both structural roles of the focal variable. We derive an efficient influence function and a doubly robust estimator, yielding robustness at two levels: the estimand is model-robust across the two causal scenarios, and the estimator is doubly robust with respect to nuisance estimation. In simulations and in an NHANES application on elevated PFAS burden, kidney function, and uric acid, mediation-based analyses yielded materially different reported estimates.

stat.ME↗

arXiv2026

Causal Discovery in Linear Models with Unobserved Variables and Measurement Error

The presence of unobserved common causes and measurement error poses two major obstacles to causal structure learning, since ignoring either source of complexity can induce spurious causal relations among variables of interest. We study causal structure learning in linear systems where both challenges may occur simultaneously. We introduce a causal model called LV-SEM-ME, which contains four types of variables: directly observed variables, variables that are not directly observed but are measured with error, the corresponding measurements, and variables that are neither observed nor measured. Under a separability condition-namely, identifiability of the mixing matrix associated with the exogenous noise terms of the observed variables-together with certain faithfulness assumptions, we characterize the extent of identifiability and the corresponding observational equivalence classes. We provide graphical characterizations of these equivalence classes and develop recovery algorithms that enumerate all models in the equivalence class of the ground truth. We also establish, via a four-node union model that subsumes instrumental variable, front-door, and negative-control-outcome settings, a form of identification robustness: the target effect remains identifiable in the broader LV-SEM-ME model even when the assumptions underlying the specialized identification formulas for the corresponding submodels need not all hold simultaneously.

cs.LG↗

arXiv2026

Bias-Targeted Nonparametric Balancing for Stable Causal Mediation Analysis

Influence function (IF)-based estimators are widely used in mediation analysis due to their modeling flexibility, but standard implementations require direct estimation of the distribution functions of the mediator and treatment variables. Since these functions appear in the denominator of IF-based estimators, they can induce significant instability, particularly with continuous mediators. In this work, we propose an alternative implementation of IF-based estimators for both single- and multiple-mediator settings, based on reparametrizations of the likelihood. The key idea is to estimate the involved nuisance functions according to their role in the bias structure of the IF-based estimators. In our approach, key nuisance functions that are potential sources of instability are estimated using a novel nonparametric weighted balancing method-which can be viewed as a nonparametric extension of covariate balancing generalized to mediation analysis-fully stabilizing the estimators. We establish consistency and multiple robustness under suitable regularity conditions, and asymptotic normality. Simulation studies demonstrate substantial reductions in bias and variance relative to existing methods for continuous mediators. We further illustrate the approach using NHANES 2013-2014 data to estimate the effect of obesity on coronary heart disease mediated by Glycohemoglobin.

stat.ME↗

arXiv2026

Causal Data Fusion for Panel Data without a Pre-Intervention Period

Traditional panel-data causal inference frameworks, such as difference-in-differences and synthetic control methods, rely on pre-intervention data to estimate counterfactual means. However, such data may be unavailable in real-world settings when interventions are implemented in response to sudden events, such as public health crises or epidemiological shocks. In this paper, we introduce two data-fusion methods for causal inference from panel data in scenarios where pre-intervention data are unavailable. These methods leverage auxiliary reference domains with related panel data to estimate causal effects in the target domain, thereby overcoming the limitations imposed by the absence of pre-intervention data. We demonstrate the efficacy of these methods by deriving bounds on the absolute bias that converge to zero under suitable conditions, as well as through simulations across a variety of panel-data settings. Our proposed methodology renders causal inference feasible in urgent and data-constrained environments where the assumptions of existing causal inference frameworks are not met. As an application of our methodology, we evaluate the effect of a community organization vaccination intervention in Chelsea, Massachusetts on COVID-19 vaccination rates.

stat.ME↗

arXiv2026

Causal Imitation Learning Under Measurement Error and Distribution Shift

We study offline imitation learning (IL) when part of the decision-relevant state is observed only through noisy measurements and the distribution may change between training and deployment. Such settings induce spurious state-action correlations, so standard behavioral cloning (BC) -- whether conditioning on raw measurements or ignoring them -- can converge to systematically biased policies under distribution shift. We propose a general framework for IL under measurement error, inspired by explicitly modeling the causal relationships among the variables, yielding a target that retains a causal interpretation and is robust to distribution shift. Building on ideas from proximal causal inference, we introduce \texttt{CausIL}, which treats noisy state observations as proxy variables, and we provide identification conditions under which the target policy is recoverable from demonstrations without rewards or interactive expert queries. We develop estimators for both discrete and continuous state spaces; for continuous settings, we use an adversarial procedure over RKHS function classes to learn the required parameters. We evaluate \texttt{CausIL} on semi-simulated longitudinal data from the PhysioNet/Computing in Cardiology Challenge 2019 cohort and demonstrate improved robustness to distribution shift compared to BC baselines.

cs.LG↗

arXiv2025

Combining Experimental and Observational Data for Identification and Estimation of Long-Term Causal Effects

We study identifying and estimating the causal effect of a treatment variable on a long-term outcome using data from an observational and an experimental domain. The observational data are subject to unobserved confounding. Furthermore, subjects in the experiment are only followed for a short period; thus, long-term effects are unobserved, though short-term effects are available. Consequently, neither data source alone suffices for causal inference on the long-term outcome, necessitating a principled fusion of the two. We propose three approaches for data fusion for the purpose of identifying and estimating the causal effect. The first assumes equal confounding bias for short-term and long-term outcomes. The second weakens this assumption by leveraging an observed confounder for which the short-term and long-term potential outcomes share the same partial additive association with this confounder. The third approach employs proxy variables of the latent confounder of the treatment-outcome relationship, extending the proximal causal inference framework to the data fusion setting. For each approach, we develop influence function-based estimators and analyze their robustness properties. We illustrate our methods by estimating the effect of class size on 8th-grade SAT scores using data from the Project STAR experiment combined with observational data from the Early Childhood Longitudinal Study.

stat.ME↗

arXiv2025

Semiparametric Triple Difference Estimators

The triple difference causal inference framework is an extension of the well-known difference-in-differences framework. It relaxes the parallel trends assumption of the difference-in-differences framework through leveraging data from an auxiliary domain. Despite being commonly applied in empirical research, the triple difference framework has received relatively limited attention in the statistics literature. Specifically, investigating the intricacies of identification and the design of robust and efficient estimators for this framework has remained largely unexplored. This work aims to address these gaps in the literature. From the identification standpoint, we present outcome regression and weighting methods to identify the average treatment effect on the treated in both panel data and repeated cross-section settings. For the latter, we relax the commonly made assumption of time-invariant composition of units. From the estimation perspective, we develop semiparametric estimators for the triple difference framework in both panel data and repeated cross-sections settings. These estimators are based on the cross-fitting technique, and flexible machine learning tools can be used to estimate the nuisance components. We characterize conditions under which our proposed estimators are efficient, doubly robust, root-n consistent and asymptotically normal. As an application of our proposed methodology, we examined the effect of mandated maternity benefits on the hourly wages of women of childbearing age and found that these mandates result in a 2.6% drop in hourly wages.

econ.EM↗

arXiv2025

Debiased Ill-Posed Regression

In various statistical settings, the goal is to estimate a function which is restricted by the statistical model only through a conditional moment restriction. Prominent examples include the nonparametric instrumental variable framework for estimating the structural function of the outcome variable, and the proximal causal inference framework for estimating the bridge functions. A common strategy in the literature is to find the minimizer of the projected mean squared error. However, this approach can be sensitive to misspecification or slow convergence rate of the estimators of the involved nuisance components. In this work, we propose a debiased estimation strategy based on the influence function of a modification of the projected error and demonstrate its finite-sample convergence rate. Our proposed estimator possesses a second-order bias with respect to the involved nuisance functions and a desirable robustness property with respect to the misspecification of one of the nuisance functions. The proposed estimator involves a hyper-parameter, for which the optimal value depends on potentially unknown features of the underlying data-generating process. Hence, we further propose a hyper-parameter selection approach based on cross-validation and derive an error bound for the resulting estimator. This analysis highlights the potential rate loss due to hyper-parameter selection and underscore the importance and advantages of incorporating debiasing in this setting. We also study the application of our approach to the estimation of regular parameters in a specific parameter class, which are linear functionals of the solutions to the conditional moment restrictions and provide sufficient conditions for achieving root-n consistency using our debiased estimator.

stat.ME↗

arXiv2024

A General Identification Algorithm For Data Fusion Problems Under Systematic Selection

Causal inference is made challenging by confounding, selection bias, and other complications. A common approach to addressing these difficulties is the inclusion of auxiliary data on the superpopulation of interest. Such data may measure a different set of variables, or be obtained under different experimental conditions than the primary dataset. Analysis based on multiple datasets must carefully account for similarities between datasets, while appropriately accounting for differences. In addition, selection of experimental units into different datasets may be systematic; similar difficulties are encountered in missing data problems. Existing methods for combining datasets either do not consider this issue, or assume simple selection mechanisms. In this paper, we provide a general approach, based on graphical causal models, for causal inference from data on the same superpopulation that is obtained under different experimental conditions. Our framework allows both arbitrary unobserved confounding, and arbitrary selection processes into different experimental regimes in our data. We describe how systematic selection processes may be organized into a hierarchy similar to censoring processes in missing data: selected completely at random (SCAR), selected at random (SAR), and selected not at random (SNAR). In addition, we provide a general identification algorithm for interventional distributions in this setting.

stat.ME↗

arXiv2024

Identification and Estimation for Nonignorable Missing Data: A Data Fusion Approach

We consider the task of identifying and estimating a parameter of interest in settings where data is missing not at random (MNAR). In general, such parameters are not identified without strong assumptions on the missing data model. In this paper, we take an alternative approach and introduce a method inspired by data fusion, where information in an MNAR dataset is augmented by information in an auxiliary dataset subject to missingness at random (MAR). We show that even if the parameter of interest cannot be identified given either dataset alone, it can be identified given pooled data, under two complementary sets of assumptions. We derive an inverse probability weighted (IPW) estimator for identified parameters, and evaluate the performance of our estimation strategies via simulation studies, and a data application.

stat.ME↗