Razieh Nabi

Yue Yu, Xuan Kan, Hejie Cui et al. · cmu

Functional magnetic resonance imaging (fMRI) has become one of the most common imaging modalities for brain function analysis. Recently, graph neural networks (GNN) have been adopted for fMRI analysis with superior performance. Unfortunately, traditional functional brain networks are mainly constructed based on similarities among region of interests (ROI), which are noisy and agnostic to the downstream prediction tasks and can lead to inferior results for GNN-based models. To better adapt GNNs for fMRI analysis, we propose TBDS, an end-to-end framework based on \underline{T}ask-aware \underline{B}rain connectivity \underline{D}AG (short for Directed Acyclic Graph) \underline{S}tructure generation for fMRI analysis. The key component of TBDS is the brain network generator which adopts a DAG learning approach to transform the raw time-series into task-aware brain connectivities. Besides, we design an additional contrastive regularization to inject task-specific knowledge during the brain network generation process. Comprehensive experiments on two fMRI datasets, namely Adolescent Brain Cognitive Development (ABCD) and Philadelphia Neuroimaging Cohort (PNC) datasets demonstrate the efficacy of TBDS. In addition, the generated brain networks also highlight the prediction-related brain regions and thus provide unique interpretations of the prediction results. Our implementation will be published to https://github.com/yueyu1030/TBDS upon acceptance.

Razieh Nabi, Rohit Bhattacharya, Ilya Shpitser et al.

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.

Rohit Bhattacharya, Razieh Nabi

The front-door criterion can be used to identify and compute causal effects despite the existence of unmeasured confounders between a treatment and outcome. However, the key assumptions -- (i) the existence of a variable (or set of variables) that fully mediates the effect of the treatment on the outcome, and (ii) which simultaneously does not suffer from similar issues of confounding as the treatment-outcome pair -- are often deemed implausible. This paper explores the testability of these assumptions. We show that under mild conditions involving an auxiliary variable, the assumptions encoded in the front-door model (and simple extensions of it) may be tested via generalized equality constraints a.k.a Verma constraints. We propose two goodness-of-fit tests based on this observation, and evaluate the efficacy of our proposal on real and synthetic data. We also provide theoretical and empirical comparisons to instrumental variable approaches to handling unmeasured confounding.

Razieh Nabi, David Benkeser

This paper introduces a framework for estimating fair optimal predictions using machine learning where the notion of fairness can be quantified using path-specific causal effects. We use a recently developed approach based on Lagrange multipliers for infinite-dimensional functional estimation to derive closed-form solutions for constrained optimization based on mean squared error and cross-entropy risk criteria. The theoretical forms of the solutions are analyzed in detail and described as nuanced adjustments to the unconstrained minimizer. This analysis highlights important trade-offs between risk minimization and achieving fairnes. The theoretical solutions are also used as the basis for construction of flexible semiparametric estimation strategies for these nuisance components. We describe the robustness properties of our estimators in terms of achieving the optimal constrained risk, as well as in terms of controlling the value of the constraint. We study via simulation the impact of using robust estimators of pathway-specific effects to validate our theory. This work advances the discourse on algorithmic fairness by integrating complex causal considerations into model training, thus providing strategies for implementing fair models in real-world applications.

Anna Guo, Razieh Nabi

The identification theory for causal effects in directed acyclic graphs (DAGs) with hidden variables is well established, but methods for estimating and inferring functionals that extend beyond the g-formula remain underdeveloped. Previous studies have introduced semiparametric estimators for such functionals in a broad class of DAGs with hidden variables. While these estimators exhibit desirable statistical properties such as double robustness in certain cases, they also face significant limitations. Notably, they encounter substantial computational challenges, particularly involving density estimation and numerical integration for continuous variables, and their estimates may fall outside the parameter space of the target estimand. Additionally, the asymptotic properties of these estimators is underexplored, especially when integrating flexible statistical and machine learning models for nuisance functional estimations. This paper addresses these challenges by introducing novel one-step corrected plug-in and targeted minimum loss-based estimators of causal effects for a class of hidden variable DAGs that go beyond classical back-door and front-door criteria (known as the treatment primal fixability criterion in prior literature). These estimators leverage data-adaptive machine learning algorithms to minimize modeling assumptions while ensuring key statistical properties including double robustness, efficiency, boundedness within the target parameter space, and asymptotic linearity under $L^2(P)$-rate conditions for nuisance functional estimates that yield root-n consistent causal effect estimates. To ensure our estimation methods are accessible in practice, we provide the flexCausal package in R.

Qi Zhang, Harsh Parikh, Ashley Naimi et al.

Method validation and study design in causal inference rely on synthetic data with known counterfactuals. Existing simulators trade off distributional realism, the ability to capture mixed-type and multimodal tabular data, against causal controllability, including explicit control over overlap, unmeasured confounding, and treatment effect heterogeneity. We introduce CausalMix, a variational generative framework that closes this gap by coupling a mixture of Gaussian latent priors with data-type-specific decoders for continuous, binary, and categorical variables. The model incorporates explicit causal controls: an overlap regularizer shaping propensity-score distributions, alongside direct parameterizations of confounding strength and effect heterogeneity. This unified objective preserves fidelity to the observed data while enabling factorial manipulation of causal mechanisms, allowing overlap, confounding strength, and treatment effect heterogeneity to be varied independently at design time. Across benchmarks, CausalMix achieves state-of-the-art distributional metrics on mixed-type tables while providing stable, fine-grained causal control. We demonstrate practical utility in a comparative safety study of metastatic castration-resistant prostate cancer treatments, using CausalMix to compare estimators under calibrated data-generating processes, tune hyperparameters, and conduct simulation-based power analyses under targeted treatment effect heterogeneity scenarios.

Xiaxian Ou, Razieh Nabi

A class of causal effect functionals requires integration over conditional densities of continuous variables, as in mediation effects and nonparametric identification in causal graphical models. Estimating such densities and evaluating the resulting integrals can be statistically and computationally demanding. A common workaround is to discretize the variable and replace integrals with finite sums. Although convenient, discretization alters the population-level functional and can induce non-negligible approximation bias, even under correct identification. Under smoothness conditions, we show that this coarsening bias is first order in the bin width and arises at the level of the target functional, distinct from statistical estimation error. We propose a simple bias-reduced functional that evaluates the outcome regression at within-bin conditional means, eliminating the leading term and yielding a second-order approximation error. We derive plug-in and one-step estimators for the bias-reduced functional. Simulations demonstrate substantial bias reduction and near-nominal confidence interval coverage, even under coarse binning. Our results provide a simple framework for controlling the impact of variable discretization on parameter approximation and estimation.

Lydia T. Liu, Inioluwa Deborah Raji, Angela Zhou et al.

Many automated decision systems (ADS) are designed to solve prediction problems -- where the goal is to learn patterns from a sample of the population and apply them to individuals from the same population. In reality, these prediction systems operationalize holistic policy interventions in deployment. Once deployed, ADS can shape impacted population outcomes through an effective policy change in how decision-makers operate, while also being defined by past and present interactions between stakeholders and the limitations of existing organizational, as well as societal, infrastructure and context. In this work, we consider the ways in which we must shift from a prediction-focused paradigm to an interventionist paradigm when considering the impact of ADS within social systems. We argue this requires a new default problem setup for ADS beyond prediction, to instead consider predictions as decision support, final decisions, and outcomes. We highlight how this perspective unifies modern statistical frameworks and other tools to study the design, implementation, and evaluation of ADS systems, and point to the research directions necessary to operationalize this paradigm shift. Using these tools, we characterize the limitations of focusing on isolated prediction tasks, and lay the foundation for a more intervention-oriented approach to developing and deploying ADS.

Razieh Nabi, Nima S. Hejazi, Mark J. van der Laan et al.

We develop a general framework for estimating function-valued parameters under equality or inequality constraints in infinite-dimensional statistical models. Such constrained learning problems are common across many areas of statistics and machine learning, where estimated parameters must satisfy structural requirements such as moment restrictions, policy benchmarks, calibration criteria, or fairness considerations. To address these problems, we characterize the solution as the minimizer of a penalized population risk using a Lagrange-type formulation, and analyze it through a statistical functional lens. Central to our approach is a constraint-specific path through the unconstrained parameter space that defines the constrained solutions. For a broad class of constraint-risk pairs, this path admits closed-form expressions and reveals how constraints shape optimal adjustments. When closed forms are unavailable, we derive recursive representations that support tractable estimation. Our results also suggest natural estimators of the constrained parameter, constructed by combining estimates of unconstrained components of the data-generating distribution. Thus, our procedure can be integrated with any statistical learning approach and implemented using standard software. We provide general conditions under which the resulting estimators achieve optimal risk and constraint satisfaction, and we demonstrate the flexibility and effectiveness of the proposed method through various examples, simulations, and real-data applications.

Razieh Nabi, Rohit Bhattacharya, Ilya Shpitser et al.

We are grateful to the discussants, Levis and Kennedy [2025], Luo and Geng [2025], Wang and van der Laan [2025], and Yang and Kim [2025], for their thoughtful comments on our paper (Nabi et al., 2025). In this rejoinder, we summarize our main contributions and respond to each discussion in turn.

Muralikrishnna G. Sethuraman, Razieh Nabi, Faramarz Fekri · gatech

Causal discovery in real-world systems, such as biological networks, is often complicated by feedback loops and incomplete data. Standard algorithms, which assume acyclic structures or fully observed data, struggle with these challenges. To address this gap, we propose MissNODAG, a differentiable framework for learning both the underlying cyclic causal graph and the missingness mechanism from partially observed data, including data missing not at random. Our framework integrates an additive noise model with an expectation-maximization procedure, alternating between imputing missing values and optimizing the observed data likelihood, to uncover both the cyclic structures and the missingness mechanism. We demonstrate the effectiveness of MissNODAG through synthetic experiments and an application to real-world gene perturbation data.

Razieh Nabi, Rohit Bhattacharya

Significant progress has been made in developing identification and estimation techniques for missing data problems where modeling assumptions can be described via a directed acyclic graph. The validity of results using such techniques rely on the assumptions encoded by the graph holding true; however, verification of these assumptions has not received sufficient attention in prior work. In this paper, we provide new insights on the testable implications of three broad classes of missing data graphical models, and design goodness-of-fit tests for them. The classes of models explored are: sequential missing-at-random and missing-not-at-random models which can be used for modeling longitudinal studies with dropout/censoring, and a no self-censoring model which can be applied to cross-sectional studies and surveys.

Razieh Nabi, Joel Pfeiffer, Murat Ali Bayir et al.

In classical causal inference, inferring cause-effect relations from data relies on the assumption that units are independent and identically distributed. This assumption is violated in settings where units are related through a network of dependencies. An example of such a setting is ad placement in sponsored search advertising, where the clickability of a particular ad is potentially influenced by where it is placed and where other ads are placed on the search result page. In such scenarios, confounding arises due to not only the individual ad-level covariates but also the placements and covariates of other ads in the system. In this paper, we leverage the language of causal inference in the presence of interference to model interactions among the ads. Quantification of such interactions allows us to better understand the click behavior of users, which in turn impacts the revenue of the host search engine and enhances user satisfaction. We illustrate the utility of our formalization through experiments carried out on the ad placement system of the Bing search engine.

Numair Sani, Jaron Lee, Razieh Nabi et al.

Black box models in machine learning have demonstrated excellent predictive performance in complex problems and high-dimensional settings. However, their lack of transparency and interpretability restrict the applicability of such models in critical decision-making processes. In order to combat this shortcoming, we propose a novel approach to trading off interpretability and performance in prediction models using ideas from semiparametric statistics, allowing us to combine the interpretability of parametric regression models with performance of nonparametric methods. We achieve this by utilizing a two-piece model: the first piece is interpretable and parametric, to which a second, uninterpretable residual piece is added. The performance of the overall model is optimized using methods from the sufficient dimension reduction literature. Influence function based estimators are derived and shown to be doubly robust. This allows for use of approaches such as double Machine Learning in estimating our model parameters. We illustrate the utility of our approach via simulation studies and a data application based on predicting the length of stay in the intensive care unit among surgery patients.

Razieh Nabi, Rohit Bhattacharya, Ilya Shpitser

Missing data has the potential to affect analyses conducted in all fields of scientific study, including healthcare, economics, and the social sciences. Several approaches to unbiased inference in the presence of non-ignorable missingness rely on the specification of the target distribution and its missingness process as a probability distribution that factorizes with respect to a directed acyclic graph. In this paper, we address the longstanding question of the characterization of models that are identifiable within this class of missing data distributions. We provide the first completeness result in this field of study -- necessary and sufficient graphical conditions under which, the full data distribution can be recovered from the observed data distribution. We then simultaneously address issues that may arise due to the presence of both missing data and unmeasured confounding, by extending these graphical conditions and proofs of completeness, to settings where some variables are not just missing, but completely unobserved.

Rohit Bhattacharya, Razieh Nabi, Ilya Shpitser

Identification theory for causal effects in causal models associated with hidden variable directed acyclic graphs (DAGs) is well studied. However, the corresponding algorithms are underused due to the complexity of estimating the identifying functionals they output. In this work, we bridge the gap between identification and estimation of population-level causal effects involving a single treatment and a single outcome. We derive influence function based estimators that exhibit double robustness for the identified effects in a large class of hidden variable DAGs where the treatment satisfies a simple graphical criterion; this class includes models yielding the adjustment and front-door functionals as special cases. We also provide necessary and sufficient conditions under which the statistical model of a hidden variable DAG is nonparametrically saturated and implies no equality constraints on the observed data distribution. Further, we derive an important class of hidden variable DAGs that imply observed data distributions observationally equivalent (up to equality constraints) to fully observed DAGs. In these classes of DAGs, we derive estimators that achieve the semiparametric efficiency bounds for the target of interest where the treatment satisfies our graphical criterion. Finally, we provide a sound and complete identification algorithm that directly yields a weight based estimation strategy for any identifiable effect in hidden variable causal models.

Razieh Nabi, Daniel Malinsky, Ilya Shpitser

Recently there has been sustained interest in modifying prediction algorithms to satisfy fairness constraints. These constraints are typically complex nonlinear functionals of the observed data distribution. Focusing on the path-specific causal constraints proposed by Nabi and Shpitser (2018), we introduce new theoretical results and optimization techniques to make model training easier and more accurate. Specifically, we show how to reparameterize the observed data likelihood such that fairness constraints correspond directly to parameters that appear in the likelihood, transforming a complex constrained optimization objective into a simple optimization problem with box constraints. We also exploit methods from empirical likelihood theory in statistics to improve predictive performance by constraining baseline covariates, without requiring parametric models. We combine the merits of both proposals to optimize a hybrid reparameterized likelihood. The techniques presented here should be applicable more broadly to fair prediction proposals that impose constraints on predictive models.

Rohit Bhattacharya, Razieh Nabi, Ilya Shpitser et al.

Missing data is a pervasive problem in data analyses, resulting in datasets that contain censored realizations of a target distribution. Many approaches to inference on the target distribution using censored observed data, rely on missing data models represented as a factorization with respect to a directed acyclic graph. In this paper we consider the identifiability of the target distribution within this class of models, and show that the most general identification strategies proposed so far retain a significant gap in that they fail to identify a wide class of identifiable distributions. To address this gap, we propose a new algorithm that significantly generalizes the types of manipulations used in the ID algorithm, developed in the context of causal inference, in order to obtain identification.

Razieh Nabi, Phyllis Kanki, Ilya Shpitser

The goal of personalized decision making is to map a unit's characteristics to an action tailored to maximize the expected outcome for that unit. Obtaining high-quality mappings of this type is the goal of the dynamic regime literature. In healthcare settings, optimizing policies with respect to a particular causal pathway may be of interest as well. For example, we may wish to maximize the chemical effect of a drug given data from an observational study where the chemical effect of the drug on the outcome is entangled with the indirect effect mediated by differential adherence. In such cases, we may wish to optimize the direct effect of a drug, while keeping the indirect effect to that of some reference treatment. [16] shows how to combine mediation analysis and dynamic treatment regime ideas to defines policies associated with causal pathways and counterfactual responses to these policies. In this paper, we derive a variety of methods for learning high quality policies of this type from data, in a causal model corresponding to a longitudinal setting of practical importance. We illustrate our methods via a dataset of HIV patients undergoing therapy, gathered in the Nigerian PEPFAR program.

Razieh Nabi, Daniel Malinsky, Ilya Shpitser

Systematic discriminatory biases present in our society influence the way data is collected and stored, the way variables are defined, and the way scientific findings are put into practice as policy. Automated decision procedures and learning algorithms applied to such data may serve to perpetuate existing injustice or unfairness in our society. In this paper, we consider how to make optimal but fair decisions, which "break the cycle of injustice" by correcting for the unfair dependence of both decisions and outcomes on sensitive features (e.g., variables that correspond to gender, race, disability, or other protected attributes). We use methods from causal inference and constrained optimization to learn optimal policies in a way that addresses multiple potential biases which afflict data analysis in sensitive contexts, extending the approach of (Nabi and Shpitser 2018). Our proposal comes equipped with the theoretical guarantee that the chosen fair policy will induce a joint distribution for new instances that satisfies given fairness constraints. We illustrate our approach with both synthetic data and real criminal justice data.

Razieh Nabi, Ilya Shpitser

In this paper, we consider the problem of fair statistical inference involving outcome variables. Examples include classification and regression problems, and estimating treatment effects in randomized trials or observational data. The issue of fairness arises in such problems where some covariates or treatments are "sensitive," in the sense of having potential of creating discrimination. In this paper, we argue that the presence of discrimination can be formalized in a sensible way as the presence of an effect of a sensitive covariate on the outcome along certain causal pathways, a view which generalizes (Pearl, 2009). A fair outcome model can then be learned by solving a constrained optimization problem. We discuss a number of complications that arise in classical statistical inference due to this view and provide workarounds based on recent work in causal and semi-parametric inference.