arXiv subjects

Kathryn Roeder

Publications and source records attributed to Kathryn Roeder.

At least 19 recordsLinked to original sources

arXiv2026

Sparse group principal component analysis via double thresholding with application to multi-cellular programs

Multi-cellular programs (MCPs) are coordinated patterns of gene expression across interacting cell types that collectively drive complex biological processes such as tissue development and immune responses. While MCPs are typically estimated from high-dimensional gene expression data using methods like sparse principal component analysis or latent factor models, these approaches often suffer from high computational costs and limited statistical power. In this work, we propose Sparse Group Principal Component Analysis (SGPCA) to estimate MCPs by leveraging their inherent group and individual sparsity. We introduce an efficient double-thresholding algorithm based on power iteration. In each iteration, a group thresholding step first identifies relevant gene groups, followed by an individual thresholding step to select active cell types. This algorithm achieves a linear computational complexity of $O(np)$, making it highly efficient and scalable for large-scale genomic analyses. We establish theoretical guarantees for SGPCA, including statistical consistency and a convergence rate that surpasses competing methods. Through extensive simulations, we demonstrate that SGPCA achieves superior estimation accuracy and improved statistical power for signal detection. Furthermore, We apply SGPCA to a Lupus study, discovering differentially expressed MCPs distinguishing Lupus patients from normal subjects.

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arXiv2025

Towards Efficient Inference under Nonmonotone Missingness with General Imputation

Missing data are ubiquitous in classical survey and longitudinal studies as well as modern multi-modality data analysis. A longstanding challenge arises under nonmonotone missingness, where different units may observe arbitrary subsets of all variables. We study parameter estimation and inference problem under this setting. Semiparametric efficiency theory characterizes the efficient estimator through inversion of an operator constructed from pattern-specific conditional expectations. However, this estimator is generally not tractable due to compositions of conditional expectations across patterns. We introduce the Restricted ANOVA hierarchY (RAY), a functional decomposition that reveals an almost-eigen structure of the operator under missing completely at random. This structure yields a closed-form, computable approximation to the efficient estimator. RAY estimator is applicable to general Z-estimation problems, and it remains unbiased for arbitrary independent imputation functions. In theory, we establish verifiable sufficient conditions where RAY attains the efficiency lower bound, and offer a general bound for the efficiency gap otherwise. We further develop adaptive RAY estimator, which attains the minimal asymptotic variance within a broader class containing RAY and other existing estimators. Finally, we investigate the extension of RAY under missing at random mechanism. Simulations and a single-cell multi-omics application demonstrate the efficiency gains of the proposed estimators.

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arXiv2025

Rescuing double robustness: safe estimation under complete misspecification

Double robustness is a major selling point of semiparametric and missing data methodology. Its virtues lie in protection against partial nuisance misspecification and asymptotic semiparametric efficiency under correct nuisance specification. However, in many applications, complete nuisance misspecification should be regarded as the norm (or at the very least the expected default), and thus doubly robust estimators may behave fragilely. In fact, it has been amply verified empirically that these estimators can perform poorly when all nuisance functions are misspecified. Here, we first characterize this phenomenon of double fragility, and then propose a solution based on adaptive correction clipping (DR+ACC). We argue that our DR+ACC proposal is safe, in that it inherits the favorable properties of doubly robust estimators under correct nuisance specification, but its error is guaranteed to be bounded by a convex combination of the individual nuisance model errors, which prevents the instability caused by the compounding product of errors of doubly robust estimators. We also show that our proposal comes with no reduction in semiparametric efficiency compared to doubly robust estimators, and thus valid inference based on asymptotic normality can be conducted when nuisances are well-specified. We showcase the efficacy of our DR+ACC estimator both through extensive simulations and by applying it to the analysis of Alzheimer's disease proteomics data.

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arXiv2025

Disentangled Feature Importance

When predictors are statistically dependent, the appropriate definition of feature importance depends on the operational goal. Conditional-incremental measures are well-suited for feature selection, acquisition, and compression, where shared predictive information is treated as redundancy. For post-hoc interpretation, however, the goal is often to attribute predictive signals across correlated measurement channels. We introduce Disentangled Feature Importance (DFI), a population-level attribution framework for this setting. DFI maps covariates to an independent latent representation under a specified entropic optimal transport geometry, computes latent importance, and attributes it back to the original covariates through barycentric sensitivities. We show that broad conditional-incremental FI functionals target conditional incremental predictive value under squared-error loss, and therefore answer a different question from attribution of shared predictive signal under dependence. Under fixed transport cost, reference law, and regularization level, DFI defines a well-specified family of estimands. Latent scores admit a functional ANOVA interpretation, and in the Gaussian linear case, the attributed DFI recovers the classical $R^2$ decomposition for correlated regressors. We derive influence-function-based inference under nuisance-rate and smoothness conditions, and show in simulations and an HIV-1 neutralization-resistance analysis that DFI yields stable, interpretable, uncertainty-quantified attributions of shared predictive signal.

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arXiv2025

Adaptive Projected Two-Sample Comparisons for Single-Cell Gene Expression Data

We study high-dimensional two-sample mean comparison and address the curse of dimensionality through data-adaptive projections. Leveraging the low-dimensional and localized signal structures commonly seen in single-cell genomics data, our first proposed method identifies a sparse, informative low-dimensional subspace and then performs statistical inference restricted to this subspace. To address the double-dipping issue -- arising from using the same data for projection and inference -- we develop a debiased projected estimator using the semiparametric double-machine learning framework. The resulting inference not only has the usual frequentist validity but also provides useful information on the potential location of the signal due to the sparsity of the projection. Our second method uses a more flexible projection scheme to improve the power against the global null hypothesis and avoid the degeneracy issue commonly faced by existing methods. It is particularly useful when debiasing is practically challenging or when the informative signal is not well-captured by the subspace. Experiments on synthetic data and real datasets demonstrate the theoretical promise and interpretability of the proposed methods.

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arXiv2025

Semiparametric semi-supervised learning for general targets under distribution shift and decaying overlap

In modern scientific applications, large volumes of covariate data are readily available, while outcome labels are costly, sparse, and often subject to distribution shift. This asymmetry has spurred interest in semi-supervised (SS) learning, but most existing approaches rely on strong assumptions -- such as missing completely at random (MCAR) labeling or strict positivity -- that put substantial limitations on their practical usefulness. In this work, we introduce a general semiparametric framework for estimation, inference, and efficiency benchmarking in SS settings where labels are missing at random (MAR) and the overlap may vanish as sample size increases. Our framework, that we label D2S3, accommodates a wide range of smooth statistical targets -- including means, linear regression coefficients, quantiles, and causal effects -- and remains valid under high-dimensional nuisance estimation and distributional shift between labeled and unlabeled samples. We extend the theoretical guarantees of augmented inverse probability weighting estimators to preserve double robustness, asymptotic normality, and semiparametric efficiency under this challenging D2S3 regime. A key insight is that classical root-n convergence fails under vanishing overlap; we instead provide corrected asymptotic rates that capture the impact of the decay in overlap. We validate our theory through simulations and demonstrate practical utility in real-world applications on the internet of things and public health where labeled data are scarce.

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arXiv2025

Causal Inference for Genomic Data with Multiple Heterogeneous Outcomes

With the evolution of single-cell RNA sequencing techniques into a standard approach in genomics, it has become possible to conduct cohort-level causal inferences based on single-cell-level measurements. However, the individual gene expression levels of interest are not directly observable; instead, only repeated proxy measurements from each individual's cells are available, providing a derived outcome to estimate the underlying outcome for each of many genes. In this paper, we propose a generic semiparametric inference framework for doubly robust estimation with multiple derived outcomes, which also encompasses the usual setting of multiple outcomes when the response of each unit is available. To reliably quantify the causal effects of heterogeneous outcomes, we specialize the analysis to standardized average treatment effects and quantile treatment effects. Through this, we demonstrate the use of the semiparametric inferential results for doubly robust estimators derived from both Von Mises expansions and estimating equations. A multiple testing procedure based on Gaussian multiplier bootstrap is tailored for doubly robust estimators to control the false discovery exceedance rate. Applications in single-cell CRISPR perturbation analysis and individual-level differential expression analysis demonstrate the utility of the proposed methods and offer insights into the usage of different estimands for causal inference in genomics.

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arXiv2025

Simultaneous inference for generalized linear models with unmeasured confounders

Tens of thousands of simultaneous hypothesis tests are routinely performed in genomic studies to identify differentially expressed genes. However, due to unmeasured confounders, many standard statistical approaches may be substantially biased. This paper investigates the large-scale hypothesis testing problem for multivariate generalized linear models in the presence of confounding effects. Under arbitrary confounding mechanisms, we propose a unified statistical estimation and inference framework that harnesses orthogonal structures and integrates linear projections into three key stages. It begins by disentangling marginal and uncorrelated confounding effects to recover the latent coefficients. Subsequently, latent factors and primary effects are jointly estimated through lasso-type optimization. Finally, we incorporate projected and weighted bias-correction steps for hypothesis testing. Theoretically, we establish the identification conditions of various effects and non-asymptotic error bounds. We show effective Type-I error control of asymptotic $z$-tests as sample and response sizes approach infinity. Numerical experiments demonstrate that the proposed method controls the false discovery rate by the Benjamini-Hochberg procedure and is more powerful than alternative methods. By comparing single-cell RNA-seq counts from two groups of samples, we demonstrate the suitability of adjusting confounding effects when significant covariates are absent from the model.

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arXiv2025

Active multiple testing with proxy p-values and e-values

Researchers often lack the resources to test every hypothesis of interest directly or compute test statistics comprehensively, but often possess auxiliary data from which we can compute an estimate of the experimental outcome. We introduce a novel approach for selecting which hypotheses to query a statistic (e.g., run an experiment, perform expensive computation, etc.) in a hypothesis testing setup by leveraging estimates to compute proxy statistics. Our framework allows a scientist to propose a proxy statistic and then query the true statistic with some probability based on the value of the proxy. We make no assumptions about how the proxy is derived, and it can be arbitrarily dependent on the true statistic. If the true statistic is not queried, the proxy is used in its place. We characterize "active" methods that produce valid p-values and e-values in this setting and utilize this framework in the multiple testing setting to create procedures with false discovery rate (FDR) control. Through simulations and real data analysis of causal effects in scCRISPR screen experiments, we empirically demonstrate that our proxy framework has both high power and low resource usage when our proxies are accurate estimates of the respective true statistics.

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arXiv2025

Augmented Doubly Robust Post-Imputation Inference for Proteomic Data

Quantitative measurements produced by mass spectrometry proteomics experiments offer a direct way to explore the role of proteins in molecular mechanisms. However, analysis of such data is challenging due to the large proportion of missing values. A common strategy to address this issue is to utilize an imputed dataset, which often introduces systematic bias into downstream analyses if the imputation errors are ignored. In this paper, we propose a statistical framework inspired by doubly robust estimators that offers valid and efficient inference for proteomic data. Our framework combines powerful machine learning tools, such as variational autoencoders, to augment the imputation quality with high-dimensional peptide data, and a parametric model to estimate the propensity score for debiasing imputed outcomes. Our estimator is compatible with the double machine learning framework and has provable properties. In application to both single-cell and bulk-cell proteomic data our method utilizes the imputed data to gain additional, meaningful discoveries and yet maintains good control of false positives.

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arXiv2024

Assumption-Lean Post-Integrated Inference with Surrogate Control Outcomes

Data integration methods aim to extract low-dimensional embeddings from high-dimensional outcomes to remove unwanted variations, such as batch effects and unmeasured covariates, across heterogeneous datasets. However, multiple hypothesis testing after integration can be biased due to data-dependent processes. We introduce a robust post-integrated inference method that accounts for latent heterogeneity by utilizing control outcomes. Leveraging causal interpretations, we derive nonparametric identifiability of the direct effects using negative control outcomes. By utilizing surrogate control outcomes as an extension of negative control outcomes, we develop semiparametric inference on projected direct effect estimands, accounting for hidden mediators, confounders, and moderators. These estimands remain statistically meaningful under model misspecifications and with error-prone embeddings. We provide bias quantifications and finite-sample linear expansions with uniform concentration bounds. The proposed doubly robust estimators are consistent and efficient under minimal assumptions and potential misspecification, facilitating data-adaptive estimation with machine learning algorithms. Our proposal is evaluated using random forests through simulations and analysis of single-cell CRISPR perturbed datasets, which may contain potential unmeasured confounders.

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arXiv2024

Exponential family measurement error models for single-cell CRISPR screens

CRISPR genome engineering and single-cell RNA sequencing have accelerated biological discovery. Single-cell CRISPR screens unite these two technologies, linking genetic perturbations in individual cells to changes in gene expression and illuminating regulatory networks underlying diseases. Despite their promise, single-cell CRISPR screens present substantial statistical challenges. We demonstrate through theoretical and real data analyses that a standard method for estimation and inference in single-cell CRISPR screens -- "thresholded regression" -- exhibits attenuation bias and a bias-variance tradeoff as a function of an intrinsic, challenging-to-select tuning parameter. To overcome these difficulties, we introduce GLM-EIV ("GLM-based errors-in-variables"), a new method for single-cell CRISPR screen analysis. GLM-EIV extends the classical errors-in-variables model to responses and noisy predictors that are exponential family-distributed and potentially impacted by the same set of confounding variables. We develop a computational infrastructure to deploy GLM-EIV across hundreds of processors on clouds (e.g., Microsoft Azure) and high-performance clusters. Leveraging this infrastructure, we apply GLM-EIV to analyze two recent, large-scale, single-cell CRISPR screen datasets, yielding several novel insights.

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arXiv2023

Extrapolated cross-validation for randomized ensembles

Ensemble methods such as bagging and random forests are ubiquitous in various fields, from finance to genomics. Despite their prevalence, the question of the efficient tuning of ensemble parameters has received relatively little attention. This paper introduces a cross-validation method, ECV (Extrapolated Cross-Validation), for tuning the ensemble and subsample sizes in randomized ensembles. Our method builds on two primary ingredients: initial estimators for small ensemble sizes using out-of-bag errors and a novel risk extrapolation technique that leverages the structure of prediction risk decomposition. By establishing uniform consistency of our risk extrapolation technique over ensemble and subsample sizes, we show that ECV yields $δ$-optimal (with respect to the oracle-tuned risk) ensembles for squared prediction risk. Our theory accommodates general ensemble predictors, only requires mild moment assumptions, and allows for high-dimensional regimes where the feature dimension grows with the sample size. As a practical case study, we employ ECV to predict surface protein abundances from gene expressions in single-cell multiomics using random forests. In comparison to sample-split cross-validation and $K$-fold cross-validation, ECV achieves higher accuracy avoiding sample splitting. At the same time, its computational cost is considerably lower owing to the use of the risk extrapolation technique. Additional numerical results validate the finite-sample accuracy of ECV for several common ensemble predictors under a computational constraint on the maximum ensemble size.

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arXiv2023

Asymptotic Distribution-Free Independence Test for High Dimension Data

Test of independence is of fundamental importance in modern data analysis, with broad applications in variable selection, graphical models, and causal inference. When the data is high dimensional and the potential dependence signal is sparse, independence testing becomes very challenging without distributional or structural assumptions. In this paper, we propose a general framework for independence testing by first fitting a classifier that distinguishes the joint and product distributions, and then testing the significance of the fitted classifier. This framework allows us to borrow the strength of the most advanced classification algorithms developed from the modern machine learning community, making it applicable to high dimensional, complex data. By combining a sample split and a fixed permutation, our test statistic has a universal, fixed Gaussian null distribution that is independent of the underlying data distribution. Extensive simulations demonstrate the advantages of the newly proposed test compared with existing methods. We further apply the new test to a single-cell data set to test the independence between two types of single-cell sequencing measurements, whose high dimensionality and sparsity make existing methods hard to apply.

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arXiv2022

From local to global gene co-expression estimation using single-cell RNA-seq data

In genomics studies, the investigation of the gene relationship often brings important biological insights. Currently, the large heterogeneous datasets impose new challenges for statisticians because gene relationships are often local. They change from one sample point to another, may only exist in a subset of the sample, and can be non-linear or even non-monotone. Most previous dependence measures do not specifically target local dependence relationships, and the ones that do are computationally costly. In this paper, we explore a state-of-the-art network estimation technique that characterizes gene relationships at the single-cell level, under the name of cell-specific gene networks. We first show that averaging the cell-specific gene relationship over a population gives a novel univariate dependence measure that can detect any non-linear, non-monotone relationship. Together with a consistent nonparametric estimator, we establish its robustness on both the population and empirical levels. Simulations and real data analysis show that this measure outperforms existing independence measures like Pearson, Kendall's $τ$, $τ^\star$, distance correlation, HSIC, Hoeffding's D, HHG, and MIC, on various tasks.

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arXiv2020

The huge Package for High-dimensional Undirected Graph Estimation in R

We describe an R package named huge which provides easy-to-use functions for estimating high dimensional undirected graphs from data. This package implements recent results in the literature, including Friedman et al. (2007), Liu et al. (2009, 2012) and Liu et al. (2010). Compared with the existing graph estimation package glasso, the huge package provides extra features: (1) instead of using Fortan, it is written in C, which makes the code more portable and easier to modify; (2) besides fitting Gaussian graphical models, it also provides functions for fitting high dimensional semiparametric Gaussian copula models; (3) more functions like data-dependent model selection, data generation and graph visualization; (4) a minor convergence problem of the graphical lasso algorithm is corrected; (5) the package allows the user to apply both lossless and lossy screening rules to scale up large-scale problems, making a tradeoff between computational and statistical efficiency.

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arXiv2020

Covariance-based sample selection for heterogeneous data: Applications to gene expression and autism risk gene detection

Risk for autism can be influenced by genetic mutations in hundreds of genes. Based on findings showing that genes with highly correlated gene expressions are functionally interrelated, "guilt by association" methods such as DAWN have been developed to identify these autism risk genes. Previous research analyzes the BrainSpan dataset, which contains gene expression of brain tissues from varying regions and developmental periods. Since the spatiotemporal properties of brain tissue is known to affect the gene expression's covariance, previous research have focused only on a specific subset of samples to avoid the issue of heterogeneity. This leads to a potential loss of power when detecting risk genes. In this article, we develop a new method called COBS (COvariance-Based sample Selection) to find a larger and more homogeneous subset of samples that share the same population covariance matrix for the downstream DAWN analysis. To demonstrate COBS's effectiveness, we utilize genetic risk scores from two sequential data freezes obtained in 2014 and 2019. We show COBS improves DAWN's ability to predict risk genes detected in the newer data freeze when utilizing the risk scores of the older data freeze as input.

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arXiv2019

Gradient-based Sparse Principal Component Analysis with Extensions to Online Learning

Sparse principal component analysis (PCA) is an important technique for dimensionality reduction of high-dimensional data. However, most existing sparse PCA algorithms are based on non-convex optimization, which provide little guarantee on the global convergence. Sparse PCA algorithms based on a convex formulation, for example the Fantope projection and selection (FPS), overcome this difficulty, but are computationally expensive. In this work we study sparse PCA based on the convex FPS formulation, and propose a new algorithm that is computationally efficient and applicable to large and high-dimensional data sets. Nonasymptotic and explicit bounds are derived for both the optimization error and the statistical accuracy, which can be used for testing and inference problems. We also extend our algorithm to online learning problems, where data are obtained in a streaming fashion. The proposed algorithm is applied to high-dimensional gene expression data for the detection of functional gene groups.

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