Kathryn Roeder

Jin-Hong Du, Larry Wasserman, Kathryn Roeder

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.

Jin-Hong Du, Kathryn Roeder, Larry Wasserman

Feature importance quantification faces a fundamental challenge: when predictors are correlated, standard methods systematically underestimate their contributions. We prove that major existing approaches target identical population functionals under squared-error loss, revealing why they share this correlation-induced bias. To address this limitation, we introduce \emph{Disentangled Feature Importance (DFI)}, a nonparametric generalization of the classical $R^2$ decomposition via optimal transport. DFI transforms correlated features into independent latent variables using a transport map, eliminating correlation distortion. Importance is computed in this disentangled space and attributed back through the transport map's sensitivity. DFI provides a principled decomposition of importance scores that sum to the total predictive variability for latent additive models and to interaction-weighted functional ANOVA variances more generally, under arbitrary feature dependencies. We develop a comprehensive semiparametric theory for DFI. For general transport maps, we establish root-$n$ consistency and asymptotic normality of importance estimators in the latent space, which extends to the original feature space for the Bures-Wasserstein map. Notably, our estimators achieve second-order estimation error, which vanishes if both regression function and transport map estimation errors are $o_{\mathbb{P}}(n^{-1/4})$. By design, DFI avoids the computational burden of repeated submodel refitting and the challenges of conditional covariate distribution estimation, thereby achieving computational efficiency.

Tuo Zhao, Han Liu, Kathryn Roeder et al.

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.

Yixuan Qiu, Jing Lei, Kathryn Roeder

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.