arXiv subjects

Melody Huang

Publications and source records attributed to Melody Huang.

14 recordsLinked to original sources

arXiv2026

Seeing the Forest for the Trees: The Gaussian Process Limit of BART

Bayesian Additive Regression Trees (BART) have shown state-of-the-art performance in both prediction and causal inference problems. Previous theoretical work has attempted to explain BART's superior performance by establishing posterior contraction rates for standard BART models, but these rates depend strongly on the number of covariates. Here, we take a different approach and study the behavior of BART as the number of trees grows towards infinity. We show that in this regime, BART converges to a Gaussian process (GP) with a particular kernel. The kernel and its corresponding reproducing kernel Hilbert space (RKHS) have favorable inferential properties that help explain BART's excellent performance. We introduce random tree features as an approximation to this limiting GP, and establish minimax-optimal learning rates for ridge regression on these random features that depend only logarithmically on dimension. In addition to providing insight into the empirical success of BART, random tree features offer a computational benefit over traditional MCMC estimation. The random-features approximation also allows practitioners to easily incorporate BART into any model which has a linear predictor, expanding the applicability and flexibility of BART.

math.ST↗

arXiv2026

Estimating Consensus Ideal Points Using Multi-Source Data

In the advent of big data and machine learning, researchers now have a wealth of congressional candidate ideal point estimates at their disposal for theory testing. Weak relationships raise questions about the extent to which they capture a shared quantity -- rather than idiosyncratic, domain-specific factors -- yet different measures are used interchangeably in most substantive analyses. Moreover, questions central to the study of American politics implicate relationships between candidate ideal points and other variables derived from the same data sources, introducing endogeneity. We propose a method, consensus multidimensional scaling (CoMDS), which better aligns with how applied scholars use ideal points in practice. CoMDS captures the shared, stable associations of a set of underlying ideal point estimates and can be interpreted as their common spatial representation. We illustrate the utility of our approach for assessing relationships within domains of existing measures and provide a suite of diagnostic tools to aid in practical usage.

stat.AP↗

arXiv2025

Relative Bias Under Imperfect Identification in Observational Causal Inference

To conduct causal inference in observational settings, researchers must rely on certain identifying assumptions. In practice, these assumptions are unlikely to hold exactly. This paper considers the bias of selection-on-observables, instrumental variables, and proximal inference estimates under violations of their identifying assumptions. We develop bias expressions for IV and proximal inference that show how violations of their respective assumptions are amplified by any unmeasured confounding in the outcome variable. We propose a set of sensitivity tools that quantify the sensitivity of different identification strategies, and an augmented bias contour plot visualizes the relationship between these strategies. We argue that the act of choosing an identification strategy implicitly expresses a belief about the degree of violations that must be present in alternative identification strategies. Even when researchers intend to conduct an IV or proximal analysis, a sensitivity analysis comparing different identification strategies can help to better understand the implications of each set of assumptions. Throughout, we compare the different approaches on a re-analysis of the impact of state surveillance on the incidence of protest in Communist Poland.

stat.ME↗

arXiv2025

Generalizing causal effects with noncompliance: Application to deep canvassing experiments

Standard approaches in generalizability often focus on generalizing the intent-to-treat (ITT). However, in practice, a more policy-relevant quantity is the generalized impact of an intervention across compliers. While instrumental variable (IV) methods are commonly used to estimate the complier average causal effect (CACE) within samples, standard approaches cannot be applied to a target population with a different distribution from the study sample. This paper makes several key contributions. First, we introduce a new set of identifying assumptions in the form of a population-level exclusion restriction that allows for identification of the target complier average causal effect (T-CACE) in both randomized experiments and observational studies. This allows researchers to identify the T-CACE without relying on standard principal ignorability assumptions. Second, we propose a class of inverse-weighted estimators for the T-CACE and derive their asymptotic properties. We provide extensions for settings in which researchers have access to auxiliary compliance information across the target population. Finally, we introduce a sensitivity analysis for researchers to evaluate the robustness of the estimators in the presence of unmeasured confounding and extend existing tests to evaluate instrument validity in this context. We illustrate our proposed method through extensive simulations and a study evaluating the impact of deep canvassing on reducing exclusionary attitudes.

stat.ME↗

arXiv2025

Sensitivity Analysis for Clustered Observational Studies with an Application to the Effectiveness of Magnet Nursing Hospitals

In a clustered observational study, treatment is assigned to groups and all units within the group are exposed to the treatment. Here, we use a clustered observational study (COS) design to estimate the effectiveness of Magnet Nursing certificates for emergency surgery patients. Recent research has introduced specialized weighting estimators for the COS design that balance baseline covariates at the unit and cluster level. These methods allow researchers to adjust for observed confounders, but are sensitive to unobserved confounding. In this paper, we develop new sensitivity analysis methods tailored to weighting estimators for COS designs. We provide several key contributions. First, we introduce a key bias decomposition, tailored to the specific confounding structure that arises in a COS. Second, we develop a sensitivity framework for weighted COS designs that constrain the error in the underlying weights. We introduce both a marginal sensitivity model and a variance-based sensitivity model, and extend both to accommodate multiple estimands. Finally, we propose amplification and benchmarking methods to better interpret the results. Throughout, we illustrate our proposed methods by analyzing the effectiveness of Magnet nursing hospitals.

stat.ME↗

arXiv2025

Distilling heterogeneous treatment effects: Stable subgroup estimation in causal inference

Recent methodological developments have introduced new black-box approaches to better estimate heterogeneous treatment effects; however, these methods fall short of providing interpretable characterizations of the underlying individuals who may be most at risk or benefit most from receiving the treatment, thereby limiting their practical utility. In this work, we introduce causal distillation trees (CDT) to estimate interpretable subgroups. CDT allows researchers to fit any machine learning model to estimate heterogeneous treatment effects, and then leverages a simple, second-stage tree-based model to "distill" the estimated treatment effects into meaningful subgroups. As a result, CDT inherits the improvements in predictive performance from black-box machine learning models while preserving the interpretability of a simple decision tree. We derive theoretical guarantees for the consistency of the estimated subgroups using CDT, and introduce stability-driven diagnostics for researchers to evaluate the quality of the estimated subgroups. We illustrate our proposed method on a randomized controlled trial of antiretroviral treatment for HIV from the AIDS Clinical Trials Group Study 175 and show that CDT out-performs state-of-the-art approaches in constructing stable, clinically relevant subgroups.

stat.ME↗

arXiv2024

Minimax Regret Estimation for Generalizing Heterogeneous Treatment Effects with Multisite Data

To test scientific theories and develop individualized treatment rules, researchers often wish to learn heterogeneous treatment effects that can be consistently found across diverse populations and contexts. We consider the problem of generalizing heterogeneous treatment effects (HTE) based on data from multiple sites. A key challenge is that a target population may differ from the source sites in unknown and unobservable ways. This means that the estimates from site-specific models lack external validity, and a simple pooled analysis risks bias. We develop a robust CATE (conditional average treatment effect) estimation methodology with multisite data from heterogeneous populations. We propose a minimax-regret framework that learns a generalizable CATE model by minimizing the worst-case regret over a class of target populations whose CATE can be represented as convex combinations of site-specific CATEs. Using robust optimization, the proposed methodology accounts for distribution shifts in both individual covariates and treatment effect heterogeneity across sites. We show that the resulting CATE model has an interpretable closed-form solution, expressed as a weighted average of site-specific CATE models. Thus, researchers can utilize a flexible CATE estimation method within each site and aggregate site-specific estimates to produce the final model. Through simulations and a real-world application, we show that the proposed methodology improves the robustness and generalizability of existing approaches.

stat.ME↗

arXiv2024

Does AI help humans make better decisions? A statistical evaluation framework for experimental and observational studies

The use of Artificial Intelligence (AI), or more generally data-driven algorithms, has become ubiquitous in today's society. Yet, in many cases and especially when stakes are high, humans still make final decisions. The critical question, therefore, is whether AI helps humans make better decisions compared to a human-alone or AI-alone system. We introduce a new methodological framework to empirically answer this question with a minimal set of assumptions. We measure a decision maker's ability to make correct decisions using standard classification metrics based on the baseline potential outcome. We consider a single-blinded and unconfounded treatment assignment, where the provision of AI-generated recommendations is assumed to be randomized across cases with humans making final decisions. Under this study design, we show how to compare the performance of three alternative decision-making systems--human-alone, human-with-AI, and AI-alone. Importantly, the AI-alone system includes any individualized treatment assignment, including those that are not used in the original study. We also show when AI recommendations should be provided to a human-decision maker, and when one should follow such recommendations. We apply the proposed methodology to our own randomized controlled trial evaluating a pretrial risk assessment instrument. We find that the risk assessment recommendations do not improve the classification accuracy of a judge's decision to impose cash bail. Furthermore, we find that replacing a human judge with algorithms--the risk assessment score and a large language model in particular--leads to a worse classification performance.

cs.AI↗

arXiv2024

Design Sensitivity and Its Implications for Weighted Observational Studies

Sensitivity to unmeasured confounding is not typically a primary consideration in designing treated-control comparisons in observational studies. We introduce a framework allowing researchers to optimize robustness to omitted variable bias at the design stage using a measure called design sensitivity. Design sensitivity, which describes the asymptotic power of a sensitivity analysis, allows transparent assessment of the impact of different estimation strategies on sensitivity. We apply this general framework to two commonly-used sensitivity models, the marginal sensitivity model and the variance-based sensitivity model. By comparing design sensitivities, we interrogate how key features of weighted designs, including choices about trimming of weights and model augmentation, impact robustness to unmeasured confounding, and how these impacts may differ for the two different sensitivity models. We illustrate the proposed framework on a study examining drivers of support for the 2016 Colombian peace agreement.

stat.ME↗

arXiv2024

Overlap violations in external validity

Estimating externally valid causal effects is a foundational problem in the social and biomedical sciences. Generalizing or transporting causal estimates from an experimental sample to a target population of interest relies on an overlap assumption between the experimental sample and the target population--i.e., all units in the target population must have a non-zero probability of being included in the experiment. In practice, having full overlap between an experimental sample and a target population can be implausible. In the following paper, we introduce a framework for considering external validity in the presence of overlap violations. We introduce a novel bias decomposition that parameterizes the bias from an overlap violation into two components: (1) the proportion of units omitted, and (2) the degree to which omitting the units moderates the treatment effect. The bias decomposition offers an intuitive and straightforward approach to conducting sensitivity analysis to assess robustness to overlap violations. Furthermore, we introduce a suite of sensitivity tools in the form of summary measures and benchmarking, which help researchers consider the plausibility of the overlap violations. We apply the proposed framework on an experiment evaluating the impact of a cash transfer program in Northern Uganda.

stat.ME↗

arXiv2023

Variance-based sensitivity analysis for weighting estimators result in more informative bounds

Weighting methods are popular tools for estimating causal effects; assessing their robustness under unobserved confounding is important in practice. In the following paper, we introduce a new set of sensitivity models called "variance-based sensitivity models". Variance-based sensitivity models characterize the bias from omitting a confounder by bounding the distributional differences that arise in the weights from omitting a confounder, with several notable innovations over existing approaches. First, the variance-based sensitivity models can be parameterized with respect to a simple $R^2$ parameter that is both standardized and bounded. We introduce a formal benchmarking procedure that allows researchers to use observed covariates to reason about plausible parameter values in an interpretable and transparent way. Second, we show that researchers can estimate valid confidence intervals under a set of variance-based sensitivity models, and provide extensions for researchers to incorporate their substantive knowledge about the confounder to help tighten the intervals. Last, we highlight the connection between our proposed approach and existing sensitivity analyses, and demonstrate both, empirically and theoretically, that variance-based sensitivity models can provide improvements on both the stability and tightness of the estimated confidence intervals over existing methods. We illustrate our proposed approach on a study examining blood mercury levels using the National Health and Nutrition Examination Survey (NHANES).

stat.ME↗

arXiv2023

Sensitivity Analysis for Survey Weights

Survey weighting allows researchers to account for bias in survey samples, due to unit nonresponse or convenience sampling, using measured demographic covariates. Unfortunately, in practice, it is impossible to know whether the estimated survey weights are sufficient to alleviate concerns about bias due to unobserved confounders or incorrect functional forms used in weighting. In the following paper, we propose two sensitivity analyses for the exclusion of important covariates: (1) a sensitivity analysis for partially observed confounders (i.e., variables measured across the survey sample, but not the target population), and (2) a sensitivity analysis for fully unobserved confounders (i.e., variables not measured in either the survey or the target population). We provide graphical and numerical summaries of the potential bias that arises from such confounders, and introduce a benchmarking approach that allows researchers to quantitatively reason about the sensitivity of their results. We demonstrate our proposed sensitivity analyses using state-level 2020 U.S. Presidential Election polls.

stat.ME↗

arXiv2022

Sensitivity Analysis in the Generalization of Experimental Results

Randomized controlled trials (RCT's) allow researchers to estimate causal effects in an experimental sample with minimal identifying assumptions. However, to generalize or transport a causal effect from an RCT to a target population, researchers must adjust for a set of treatment effect moderators. In practice, it is impossible to know whether the set of moderators has been properly accounted for. In the following paper, I propose a three parameter sensitivity analysis for generalizing or transporting experimental results using weighted estimators, with several advantages over existing methods. First, the framework does not require assumptions on the underlying data generating process for either the experimental sample selection mechanism or treatment effect heterogeneity. Second, I show that the sensitivity parameters are guaranteed to be bounded and propose several tools researchers can use to perform sensitivity analysis: (1) graphical and numerical summaries for researchers to assess how robust a point estimate is to killer confounders; (2) an extreme scenario analysis; and (3) a formal benchmarking approach for researchers to estimate potential sensitivity parameter values using existing data. Finally, I demonstrate that the proposed framework can be easily extended to the class of doubly robust, augmented weighted estimators. The sensitivity analysis framework is applied to a set of Jobs Training Program experiments.

stat.ME↗

arXiv2021

Leveraging Population Outcomes to Improve the Generalization of Experimental Results

Generalizing causal estimates in randomized experiments to a broader target population is essential for guiding decisions by policymakers and practitioners in the social and biomedical sciences. While recent papers developed various weighting estimators for the population average treatment effect (PATE), many of these methods result in large variance because the experimental sample often differs substantially from the target population, and estimated sampling weights are extreme. To improve efficiency in practice, we propose post-residualized weighting in which we use the outcome measured in the observational population data to build a flexible predictive model (e.g., machine learning methods) and residualize the outcome in the experimental data before using conventional weighting methods. We show that the proposed PATE estimator is consistent under the same assumptions required for existing weighting methods, importantly without assuming the correct specification of the predictive model. We demonstrate the efficiency gains from this approach through simulations and our application based on a set of job training experiments.

stat.ME↗