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Ilya Shpitser

Publications and source records attributed to Ilya Shpitser.

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.

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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.

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arXiv2026

A Characterization of the Orthocomplement of the Tangent Space of Semiparametric Markov Models

Graphical models are ubiquitous in social and empirical science as they are intuitive and easy to use. These models belong to the broader class of Markov models, defined using solely conditional independence (CI) restrictions. In order to estimate finite-dimensional target parameters in such models efficiently, semi-parametric theory provides a principled framework for constructing regular and asymptotically linear estimators via influence functions (IFs). These estimators are asymptotically normal and root-$n$ consistent. Characterizing the class of all influence functions for a target parameter is crucial for statistically efficient inference in these models. For models that are Markov relative to directed acyclic graphs (DAGs), the orthogonal complement of the tangent space is known, implying that for any target the class of all influence functions can be derived once an influence function is obtained. On the other hand, for Markov models not equivalent to a DAG model -- such as ordinary Markov models associated with undirected graphs, chain graphs, or acyclic directed mixed graphs -- the orthogonal complement has not been characterized, impeding semi-parametric inference in these models. We derive closed form expressions for the orthogonal complement of the tangent space for general Markov models and illustrate our results by characterizing the class of influence functions for the conditional mean parameter in several graphical models.

stat.ME↗
arXiv2026

Proximal Identification and Estimation in Front-Door Causal Structures with Unobserved Confounding of the Mediator

Unobserved confounding is a fundamental obstacle in causal inference problems. In the graphical modeling literature, a general theory has been developed that allows identification in the presence of hidden variables, with some limitations. In particular, Pearl's celebrated front-door criterion allows nonparametric identification in the presence of unobserved common causes of the treatment and the outcome, however it requires the presence of an unconfounded variable that mediates all causal influence from the treatment to the outcome. This stringent requirement limits the applicability of the front-door criterion. We propose proximal generalizations of the front-door criterion, allowing both arbitrary treatment/outcome confounding, and unobserved confounders of the mediator, provided informative proxies for the latter type of confounders are observed. In addition to deriving three new identification strategies in this setting, we provide plug-in and influence function-based estimation strategies for the resulting functionals, and evaluate their performance through simulations.

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

Exploiting independence constraints for efficient estimation of bounds on causal effects in the presence of unmeasured confounding

Causal graphs may inform covariate adjustment for estimating causal effects and improve estimation efficiency by exploiting the graphical structure. In many applications, however, the target causal parameter may not be point-identified due to the presence of unmeasured confounding. Sensitivity analysis methods address this challenge by characterizing bounds on the causal parameter under varying assumptions about the magnitude or form of unmeasured confounding. We focus on semiparametric efficient estimation of causal effects in non-identifiable settings, assuming a known (or hypothesized) causal graph. We propose an influence function projection approach that exploits the conditional independence constraints implied by the graph to improve the efficiency of semiparametric estimators of upper and lower bounds on the average causal effect under a given sensitivity analysis model. Our approach applies across multiple sensitivity analysis frameworks and causal estimands, thereby connecting knowledge of graphical structure with the sensitivity analysis literature. We illustrate our approach through simulations and real data examples thought to be affected by unmeasured confounding, including the effect of labor training program on post-intervention earnings, and the effect of low ejection fraction on heart failure death.

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arXiv2026

Comparing Two Proxy Methods for Causal Identification

Identifying causal effects in the presence of unmeasured variables is a fundamental challenge in causal inference, for which proxy variable methods have emerged as a powerful solution. We contrast two major approaches in this framework: (1) bridge equation methods, which leverage solutions to integral equations to recover causal targets, and (2) array decomposition methods, which recover latent factors used to identify counterfactual quantities via eigendecomposition tasks. We compare the model restrictions underlying these two approaches and provide insight into implications of the underlying assumptions, clarifying the scope of applicability for each method.

stat.ME↗
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

Explaining the Behavior of Black-Box Prediction Algorithms with Causal Learning

Causal approaches to post-hoc explainability for black-box prediction models (e.g., deep neural networks trained on image pixel data) have become increasingly popular. However, existing approaches have two important shortcomings: (i) the "explanatory units" are micro-level inputs into the relevant prediction model, e.g., image pixels, rather than interpretable macro-level features that are more useful for understanding how to possibly change the algorithm's behavior, and (ii) existing approaches assume there exists no unmeasured confounding between features and target model predictions, which fails to hold when the explanatory units are macro-level variables. Our focus is on the important setting where the analyst has no access to the inner workings of the target prediction algorithm, rather only the ability to query the output of the model in response to a particular input. To provide causal explanations in such a setting, we propose to learn causal graphical representations that allow for arbitrary unmeasured confounding among features. We demonstrate the resulting graph can differentiate between interpretable features that causally influence model predictions versus those that are merely associated with model predictions due to confounding. Our approach is motivated by a counterfactual theory of causal explanation wherein good explanations point to factors that are "difference-makers" in an interventionist sense.

cs.LG↗
arXiv2025

Recursive Equations For Imputation Of Missing Not At Random Data With Sparse Pattern Support

A common approach for handling missing values in data analysis pipelines is multiple imputation via software packages such as MICE (Van Buuren and Groothuis-Oudshoorn, 2011) and Amelia (Honaker et al., 2011). These packages typically assume the data are missing at random (MAR), and impose parametric or smoothing assumptions upon the imputing distributions in a way that allows imputation to proceed even if not all missingness patterns have support in the data. Such assumptions are unrealistic in practice, and induce model misspecification bias on any analysis performed after such imputation. In this paper, we provide a principled alternative. Specifically, we develop a new characterization for the full data law in graphical models of missing data. This characterization is constructive, is easily adapted for the calculation of imputation distributions for both MAR and MNAR (missing not at random) mechanisms, and is able to handle lack of support for certain patterns of missingness. We use this characterization to develop a new imputation algorithm -- Multivariate Imputation via Supported Pattern Recursion (MISPR) -- which uses Gibbs sampling, by analogy with the Multivariate Imputation with Chained Equations (MICE) algorithm, but which is consistent under both MAR and MNAR settings, and is able to handle missing data patterns with no support without imposing additional assumptions beyond those already imposed by the missing data model itself. In simulations, we show MISPR obtains comparable results to MICE when data are MAR, and superior, less biased results when data are MNAR. Our characterization and imputation algorithm based on it are a step towards making principled missing data methods more practical in applied settings, where the data are likely both MNAR and sufficiently high dimensional to yield missing data patterns with no support at available sample sizes.

stat.ME↗
arXiv2025

Evaluation of Active Feature Acquisition Methods for Time-varying Feature Settings

Machine learning methods often assume that input features are available at no cost. However, in domains like healthcare, where acquiring features could be expensive or harmful, it is necessary to balance a feature's acquisition cost against its predictive value. The task of training an AI agent to decide which features to acquire is called active feature acquisition (AFA). By deploying an AFA agent, we effectively alter the acquisition strategy and trigger a distribution shift. To safely deploy AFA agents under this distribution shift, we present the problem of active feature acquisition performance evaluation (AFAPE). We examine AFAPE under i) a no direct effect (NDE) assumption, stating that acquisitions do not affect the underlying feature values; and ii) a no unobserved confounding (NUC) assumption, stating that retrospective feature acquisition decisions were only based on observed features. We show that one can apply missing data methods under the NDE assumption and offline reinforcement learning under the NUC assumption. When NUC and NDE hold, we propose a novel semi-offline reinforcement learning framework. This framework requires a weaker positivity assumption and introduces three new estimators: A direct method (DM), an inverse probability weighting (IPW), and a double reinforcement learning (DRL) estimator.

stat.ML↗
arXiv2024

Causal and Counterfactual Views of Missing Data Models

It is often said that the fundamental problem of causal inference is a missing data problem -- the comparison of responses to two hypothetical treatment assignments is made difficult because for every experimental unit only one potential response is observed. In this paper, we consider the implications of the converse view: that missing data problems are a form of causal inference. We make explicit how the missing data problem of recovering the complete data law from the observed law can be viewed as identification of a joint distribution over counterfactual variables corresponding to values had we (possibly contrary to fact) been able to observe them. Drawing analogies with causal inference, we show how identification assumptions in missing data can be encoded in terms of graphical models defined over counterfactual and observed variables. We review recent results in missing data identification from this viewpoint. In doing so, we note interesting similarities and differences between missing data and causal identification theories.

stat.ME↗
arXiv2024

Modeling Interference Via Symmetric Treatment Decomposition

Classical causal inference assumes treatments meant for a given unit do not have an effect on other units. This assumption is violated in interference problems, where new types of spillover causal effects arise, and causal inference becomes much more difficult. In addition, interference introduces a unique complication where variables may transmit treatment influences to each other, which is a relationship that has some features of a causal one, but is symmetric. In this paper, we develop a new approach to decomposing the spillover effect into unit-specific components that extends the DAG based treatment decomposition approach to mediation of Robins and Richardson to causal models that admit stable symmetric relationships among variables in a network. We discuss two interpretations of such models: a network structural model interpretation, and an interpretation based on equilibrium of structural equation models discussed in (Lauritzen and Richardson, 2002). We show that both interpretations yield identical identification theory, and give conditions for components of the spillover effect to be identified. We discuss statistical inference for identified components of the spillover effect, including a maximum likelihood estimator, and a doubly robust estimator for the special case of two interacting outcomes. We verify consistency and robustness of our estimators via a simulation study, and illustrate our method by assessing the causal effect of education attainment on depressive symptoms using the data on households from the Wisconsin Longitudinal Study.

stat.ME↗
arXiv2024

Markov-Restricted Analysis of Randomized Trials with Non-Monotone Missing Binary Outcomes

Scharfstein et al. (2021) developed a sensitivity analysis model for analyzing randomized trials with repeatedly measured binary outcomes that are subject to nonmonotone missingness. Their approach becomes computationally intractable when the number of measurements is large (e.g., greater than 15). In this paper, we repair this problem by introducing mth-order Markovian restrictions. We establish identification results for the joint distribution of the binary outcomes by representing the model as a directed acyclic graph (DAG). We develop a novel estimation strategy for a smooth functional of the joint distribution. We illustrate our methodology in the context of a randomized trial designed to evaluate a web-delivered psychosocial intervention to reduce substance use, assessed by evaluating abstinence twice weekly for 12 weeks, among patients entering outpatient addiction treatment.

stat.ME↗
arXiv2024

Zero Inflation as a Missing Data Problem: a Proxy-based Approach

A common type of zero-inflated data has certain true values incorrectly replaced by zeros due to data recording conventions (rare outcomes assumed to be absent) or details of data recording equipment (e.g. artificial zeros in gene expression data). Existing methods for zero-inflated data either fit the observed data likelihood via parametric mixture models that explicitly represent excess zeros, or aim to replace excess zeros by imputed values. If the goal of the analysis relies on knowing true data realizations, a particular challenge with zero-inflated data is identifiability, since it is difficult to correctly determine which observed zeros are real and which are inflated. This paper views zero-inflated data as a general type of missing data problem, where the observability indicator for a potentially censored variable is itself unobserved whenever a zero is recorded. We show that, without additional assumptions, target parameters involving a zero-inflated variable are not identified. However, if a proxy of the missingness indicator is observed, a modification of the effect restoration approach of Kuroki and Pearl allows identification and estimation, given the proxy-indicator relationship is known. If this relationship is unknown, our approach yields a partial identification strategy for sensitivity analysis. Specifically, we show that only certain proxy-indicator relationships are compatible with the observed data distribution. We give an analytic bound for this relationship in cases with a categorical outcome, which is sharp in certain models. For more complex cases, sharp numerical bounds may be computed using methods in Duarte et al.[2023]. We illustrate our method via simulation studies and a data application on central line-associated bloodstream infections (CLABSIs).

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.

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