arXiv subjects

Eugene Katsevich

Publications and source records attributed to Eugene Katsevich.

16 recordsLinked to original sources

arXiv2026

Power of masking methods for adaptive testing in a multivariate normal means problem

Many large-scale testing procedures learn signal structure from the data to boost power. Direct data reuse can inflate Type-I error ("double dipping"), so a common remedy is masking: withholding some information during learning and using it for testing. Sample splitting masks by withholding observations for testing, while null augmentation (e.g., knockoffs or full-conformal outlier detection) masks by appending null samples or variables and withholding their identities until testing. In many settings, little is known about how the power of masking methods compares across mechanisms, across tuning choices, or against more data-efficient non-masking alternatives. We study these questions in a stylized two-groups multivariate normal means model with an unknown signal direction learned from the data. Within this testbed, we develop a transparent, unified set of asymptotic power expressions for three parallel methods differing in masking choices: a sample splitting method, a full-conformal-style null augmentation method, and an oracle in-sample benchmark. Our main findings are: (1) the augmentation method is more powerful than the splitting method with matched tuning; (2) the power-optimal number of null samples for the augmentation method is a vanishing fraction of the number of tests, in which case its power approaches that of the in-sample benchmark; and (3) for a tractable approximation to the augmentation method, the optimal number of null samples scales as the square root of the number of tests, with empirical evidence suggesting a similar scaling for the method itself. These results characterize masking-induced power trade-offs in a tractable model and suggest qualitative lessons for other settings.

math.ST↗

arXiv2025

Location Tests with Noisy Proxies for Latent Variables

We investigate inference in a latent binary variable model where a noisy proxy of the latent variable is available, motivated by the variable perturbation effectiveness problem in single-cell CRISPR screens. The baseline approach is to ignore the perturbation effectiveness problem, while a recent proposal employs a weighted average based on the proxies. Our main goals are to determine how accurate the proxies must be in order for a weighted test to gain power over the unweighted baseline, and to develop tests that are powerful regardless of the accuracy of the proxies. To address the first goal, we compute the Pitman relative efficiency of the weighted test relative to the unweighted test, yielding an interpretable quantification of proxy quality that drives the power of the weighted test. To address the second goal, we propose two strategies. First, we propose a maximum-likelihood based approach that adapts the proxies to the data. Second, we propose an estimator of the Pitman efficiency if a "positive control outcome variable" is available (as is often the case in single-cell CRISPR screens), which facilitates an adaptive choice of whether to use the proxies at all. Our numerical simulations support the Pitman efficiency as the key quantity for determining whether the weighted test gains power over the baseline, and demonstrate that the two proposed adaptive tests can improve on both existing approaches across a range of proxy qualities.

stat.ME↗

arXiv2025

The permuted score test for robust differential expression analysis

Negative binomial (NB) regression is a popular method for identifying differentially expressed genes in genomics data, such as bulk and single-cell RNA sequencing data. However, NB regression makes stringent parametric and asymptotic assumptions, which can fail to hold in practice, leading to excess false positive and false negative results. We propose the permuted score test, a new strategy for robust regression based on permuting score test statistics. The permuted score test provably controls type-I error across a much broader range of settings than standard NB regression while nevertheless approximately matching standard NB regression with respect to power (when the assumptions of standard NB regression obtain) and computational efficiency. We accelerate the permuted score test by leveraging emerging techniques for sequential Monte-Carlo testing and novel algorithms for efficiently computing GLM score tests. We apply the permuted score test to real and simulated RNA sequencing data, finding that it substantially improves upon the error control of existing NB regression implementations, including DESeq2. The permuted score test could enhance the reliability of differential expression analysis across diverse biological contexts.

stat.ME↗

arXiv2024

Doubly robust and computationally efficient high-dimensional variable selection

Variable selection can be performed by testing conditional independence (CI) between each predictor and the response, given the other predictors. A doubly robust and powerful option for these CI tests is the projected covariance measure (PCM) test. However, directly deploying PCM for variable selection brings computational challenges: testing a single variable involves a few machine learning fits, so testing $p$ variables requires $O(p)$ fits. Inspired by model-X ideas, we observe that an estimate of the joint predictor distribution and a single response-on-all-predictors fit can be used to reconstruct all PCM fits. This yields tower PCM (tPCM), a computationally efficient extension of PCM to variable selection. When the joint predictor distribution is sufficiently tractable, as in applications like genome-wide association studies, tPCM offers a substantial speedup over PCM -- up to 130$\times$ in our simulations -- while matching its power. tPCM also improves on model-X methods like knockoffs and holdout randomization test (HRT) by returning per-variable $p$-values and improving speed, respectively. We prove that tPCM is doubly robust and asymptotically equivalent to both PCM and HRT. We thus extend the bridge between model-X and doubly robust approaches, demonstrating their independent arrival at equivalent methods and showing that this intersection is a fruitful source of new methodologies like tPCM.

stat.ME↗

arXiv2024

Saddlepoint approximations for plug-in resampling

Resampling-based procedures can improve on normal approximations in sparse, large-scale testing problems, but their computational cost can be prohibitive. We recognize that several existing procedures belong to a faster plug-in resampling subclass, fixing fitted nuisance parameters during resampling. When the resampled statistic is a sum of conditionally independent terms, the saddlepoint approximation (SPA) for the resampling $p$-value offers further acceleration, replacing resampling with an analytical tail approximation. However, standard Edgeworth-based approximation-error bounds impose regularity conditions that are hard to verify for plug-in resampling laws. We use an alternative approach to establish a finite-sample relative-error bound for the Lugannani-Rice approximation under more tractable conditions, which we apply in two contexts. In statistical genetics, we identify response resampling procedures as the targets of existing SPAs and establish guarantees in a representative setting. In conditional independence testing, we introduce spaCRT, an SPA for the distilled conditional randomization test (dCRT), which has been applied successfully in biology. Our rates quantify the effects of sparsity and signal strength, with matching lower bounds in special cases. We additionally establish asymptotic Type-I error control of the corresponding plug-in resampling procedures under growing sparsity. In simulations and single-cell CRISPR data analysis, spaCRT closely approximates dCRT $p$-values and preserves its statistical performance while accelerating computation by up to 250-fold.

stat.ME↗

arXiv2024

The saddlepoint approximation for averages of conditionally independent random variables

Motivated by the application of saddlepoint approximations to resampling-based statistical tests, we prove that the Lugannani-Rice formula has vanishing relative error when applied to approximate conditional tail probabilities of averages of conditionally independent random variables. In a departure from existing work, this result is valid under only sub-exponential assumptions on the summands, and does not require any assumptions on their smoothness or lattice structure. The derived saddlepoint approximation result can be directly applied to resampling-based hypothesis tests, including bootstrap, sign-flipping and conditional randomization tests. We exemplify this by providing the first rigorous justification of a saddlepoint approximation for the sign-flipping test of symmetry about the origin, initially proposed in 1955. On the way to our main result, we establish a conditional Berry-Esseen inequality for sums of conditionally independent random variables, which may be of independent interest.

math.ST↗

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.

stat.ME↗

arXiv2023

Reconciling model-X and doubly robust approaches to conditional independence testing

Model-X approaches to testing conditional independence between a predictor and an outcome variable given a vector of covariates usually assume exact knowledge of the conditional distribution of the predictor given the covariates. Nevertheless, model-X methodologies are often deployed with this conditional distribution learned in sample. We investigate the consequences of this choice through the lens of the distilled conditional randomization test (dCRT). We find that Type-I error control is still possible, but only if the mean of the outcome variable given the covariates is estimated well enough. This demonstrates that the dCRT is doubly robust, and motivates a comparison to the generalized covariance measure (GCM) test, another doubly robust conditional independence test. We prove that these two tests are asymptotically equivalent, and show that the GCM test is optimal against (generalized) partially linear alternatives by leveraging semiparametric efficiency theory. In an extensive simulation study, we compare the dCRT to the GCM test. These two tests have broadly similar Type-I error and power, though dCRT can have somewhat better Type-I error control but somewhat worse power in small samples or when the response is discrete. We also find that post-lasso based test statistics (as compared to lasso based statistics) can dramatically improve Type-I error control for both methods.

stat.ME↗

arXiv2022

On the power of conditional independence testing under model-X

For testing conditional independence (CI) of a response Y and a predictor X given covariates Z, the recently introduced model-X (MX) framework has been the subject of active methodological research, especially in the context of MX knockoffs and their successful application to genome-wide association studies. In this paper, we study the power of MX CI tests, yielding quantitative insights into the role of machine learning and providing evidence in favor of using likelihood-based statistics in practice. Focusing on the conditional randomization test (CRT), we find that its conditional mode of inference allows us to reformulate it as testing a point null hypothesis involving the conditional distribution of X. The Neyman-Pearson lemma then implies that a likelihood-based statistic yields the most powerful CRT against a point alternative. We also obtain a related optimality result for MX knockoffs. Switching to an asymptotic framework with arbitrarily growing covariate dimension, we derive an expression for the limiting power of the CRT against local semiparametric alternatives in terms of the prediction error of the machine learning algorithm on which its test statistic is based. Finally, we exhibit a resampling-free test with uniform asymptotic Type-I error control under the assumption that only the first two moments of X given Z are known, a significant relaxation of the MX assumption.

math.ST↗

arXiv2022

Large-scale simultaneous inference under dependence

Simultaneous inference allows for the exploration of data while deciding on criteria for proclaiming discoveries. It was recently proved that all admissible post-hoc inference methods for true discoveries must employ closed testing. In this paper, we investigate efficient closed testing with local tests of a special form: thresholding a function of sums of test scores for the individual hypotheses. Under this special design, we propose a new statistic that quantifies the cost of multiplicity adjustments, and we develop fast (mostly linear-time) algorithms for post-hoc inference. Paired with recent advances in global null tests based on generalized means, our work instantiates a series of simultaneous inference methods that can handle many dependence structures and signal compositions. We provide guidance on the method choices via theoretical investigation of the conservativeness and sensitivity for different local tests, as well as simulations that find analogous behavior for local tests and full closed testing.

math.ST↗

arXiv2021

Fast and Powerful Conditional Randomization Testing via Distillation

We consider the problem of conditional independence testing: given a response Y and covariates (X,Z), we test the null hypothesis that Y is independent of X given Z. The conditional randomization test (CRT) was recently proposed as a way to use distributional information about X|Z to exactly (non-asymptotically) control Type-I error using any test statistic in any dimensionality without assuming anything about Y|(X,Z). This flexibility in principle allows one to derive powerful test statistics from complex prediction algorithms while maintaining statistical validity. Yet the direct use of such advanced test statistics in the CRT is prohibitively computationally expensive, especially with multiple testing, due to the CRT's requirement to recompute the test statistic many times on resampled data. We propose the distilled CRT, a novel approach to using state-of-the-art machine learning algorithms in the CRT while drastically reducing the number of times those algorithms need to be run, thereby taking advantage of their power and the CRT's statistical guarantees without suffering the usual computational expense. In addition to distillation, we propose a number of other tricks like screening and recycling computations to further speed up the CRT without sacrificing its high power and exact validity. Indeed, we show in simulations that all our proposals combined lead to a test that has similar power to the most powerful existing CRT implementations but requires orders of magnitude less computation, making it a practical tool even for large data sets. We demonstrate these benefits on a breast cancer dataset by identifying biomarkers related to cancer stage.

stat.ME↗

arXiv2020

The leave-one-covariate-out conditional randomization test

Conditional independence testing is an important problem, yet provably hard without assumptions. One of the assumptions that has become popular of late is called "model-X", where we assume we know the joint distribution of the covariates, but assume nothing about the conditional distribution of the outcome given the covariates. Knockoffs is a popular methodology associated with this framework, but it suffers from two main drawbacks: only one-bit $p$-values are available for inference on each variable, and the method is randomized with significant variability across runs in practice. The conditional randomization test (CRT) is thought to be the "right" solution under model-X, but usually viewed as computationally inefficient. This paper proposes a computationally efficient leave-one-covariate-out (LOCO) CRT that addresses both drawbacks of knockoffs. LOCO CRT produces valid $p$-values that can be used to control the familywise error rate, and has nearly zero algorithmic variability. For L1 regularized M-estimators, we develop an even faster variant called L1ME CRT, which reuses computation by leveraging a novel observation about the stability of the cross-validated lasso to removing inactive variables. Last, for multivariate Gaussian covariates, we present a closed form expression for the LOCO CRT $p$-value, thus completely eliminating resampling in this important special case.

stat.ME↗

arXiv2020

Filtering the rejection set while preserving false discovery rate control

Scientific hypotheses in a variety of applications have domain-specific structures, such as the tree structure of the International Classification of Diseases (ICD), the directed acyclic graph structure of the Gene Ontology (GO), or the spatial structure in genome-wide association studies. In the context of multiple testing, the resulting relationships among hypotheses can create redundancies among rejections that hinder interpretability. This leads to the practice of filtering rejection sets obtained from multiple testing procedures, which may in turn invalidate their inferential guarantees. We propose Focused BH, a simple, flexible, and principled methodology to adjust for the application of any pre-specified filter. We prove that Focused BH controls the false discovery rate under various conditions, including when the filter satisfies an intuitive monotonicity property and the p-values are positively dependent. We demonstrate in simulations that Focused BH performs well across a variety of settings, and illustrate this method's practical utility via analyses of real datasets based on ICD and GO.

stat.ME↗

arXiv2019

Simultaneous high-probability bounds on the false discovery proportion in structured, regression, and online settings

While traditional multiple testing procedures prohibit adaptive analysis choices made by users, Goeman and Solari (2011) proposed a simultaneous inference framework that allows users such flexibility while preserving high-probability bounds on the false discovery proportion (FDP) of the chosen set. In this paper, we propose a new class of such simultaneous FDP bounds, tailored for nested sequences of rejection sets. While most existing simultaneous FDP bounds are based on closed testing using global null tests based on sorted p-values, we additionally consider the setting where side information can be leveraged to boost power, the variable selection setting where knockoff statistics can be used to order variables, and the online setting where decisions about rejections must be made as data arrives. Our finite-sample, closed form bounds are based on repurposing the FDP estimates from false discovery rate (FDR) controlling procedures designed for each of the above settings. These results establish a novel connection between the parallel literatures of simultaneous FDP bounds and FDR control methods, and use proof techniques employing martingales and filtrations that are new to both these literatures. We demonstrate the utility of our results by augmenting a recent knockoffs analysis of the UK Biobank dataset.

math.ST↗

arXiv2018

Multilayer Knockoff Filter: Controlled variable selection at multiple resolutions

We tackle the problem of selecting from among a large number of variables those that are 'important' for an outcome. We consider situations where groups of variables are also of interest in their own right. For example, each variable might be a genetic polymorphism and we might want to study how a trait depends on variability in genes, segments of DNA that typically contain multiple such polymorphisms. Or, variables might quantify various aspects of the functioning of individual internet servers owned by a company, and we might be interested in assessing the importance of each server as a whole on the average download speed for the company's customers. In this context, to discover that a variable is relevant for the outcome implies discovering that the larger entity it represents is also important. To guarantee meaningful and reproducible results, we suggest controlling the rate of false discoveries for findings at the level of individual variables and at the level of groups. Building on the knockoff construction of Barber and Candes (2015) and the multilayer testing framework of Barber and Ramdas (2016), we introduce the multilayer knockoff filter (MKF). We prove that MKF simultaneously controls the FDR at each resolution and use simulations to show that it incurs little power loss compared to methods that provide guarantees only for the discoveries of individual variables. We apply MKF to analyze a genetic dataset and find that it successfully reduces the number of false gene discoveries without a significant reduction in power.

stat.ME↗

arXiv2015

Covariance estimation using conjugate gradient for 3D classification in Cryo-EM

Classifying structural variability in noisy projections of biological macromolecules is a central problem in Cryo-EM. In this work, we build on a previous method for estimating the covariance matrix of the three-dimensional structure present in the molecules being imaged. Our proposed method allows for incorporation of contrast transfer function and non-uniform distribution of viewing angles, making it more suitable for real-world data. We evaluate its performance on a synthetic dataset and an experimental dataset obtained by imaging a 70S ribosome complex.

cs.CV↗