arXiv subjects

Xianyang Zhang

Publications and source records attributed to Xianyang Zhang.

At least 37 records · Page 2Linked to original sources

arXiv2024

Powerful Spatial Multiple Testing via Borrowing Neighboring Information

Clustered effects are often encountered in multiple hypothesis testing of spatial signals. In this paper, we propose a new method, termed \textit{two-dimensional spatial multiple testing} (2d-SMT) procedure, to control the false discovery rate (FDR) and improve the detection power by exploiting the spatial information encoded in neighboring observations. The proposed method provides a novel perspective of utilizing spatial information by gathering signal patterns and spatial dependence into an auxiliary statistic. 2d-SMT rejects the null when a primary statistic at the location of interest and the auxiliary statistic constructed based on nearby observations are greater than their corresponding cutoffs. 2d-SMT can also be combined with different variants of the weighted BH procedures to improve the detection power further. A fast algorithm is developed to accelerate the search for optimal cutoffs in 2d-SMT. In theory, we establish the asymptotic FDR control of 2d-SMT under weak spatial dependence. Extensive numerical experiments demonstrate that the 2d-SMT method combined with various weighted BH procedures achieves the most competitive performance in FDR and power trade-off.

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arXiv2024

Soft-constrained Schrodinger Bridge: a Stochastic Control Approach

Schrödinger bridge can be viewed as a continuous-time stochastic control problem where the goal is to find an optimally controlled diffusion process whose terminal distribution coincides with a pre-specified target distribution. We propose to generalize this problem by allowing the terminal distribution to differ from the target but penalizing the Kullback-Leibler divergence between the two distributions. We call this new control problem soft-constrained Schrödinger bridge (SSB). The main contribution of this work is a theoretical derivation of the solution to SSB, which shows that the terminal distribution of the optimally controlled process is a geometric mixture of the target and some other distribution. This result is further extended to a time series setting. One application is the development of robust generative diffusion models. We propose a score matching-based algorithm for sampling from geometric mixtures and showcase its use via a numerical example for the MNIST data set.

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arXiv2024

fastcpd: Fast Change Point Detection in R

Change point analysis is concerned with detecting and locating structure breaks in the underlying model of a sequence of observations ordered by time, space or other variables. A widely adopted approach for change point analysis is to minimize an objective function with a penalty term on the number of change points. This framework includes several well-established procedures, such as the penalized log-likelihood using the (modified) Bayesian information criterion (BIC) or the minimum description length (MDL). The resulting optimization problem can be solved in polynomial time by dynamic programming or its improved version, such as the Pruned Exact Linear Time (PELT) algorithm (Killick, Fearnhead, and Eckley 2012). However, existing computational methods often suffer from two primary limitations: (1) methods based on direct implementation of dynamic programming or PELT are often time-consuming for long data sequences due to repeated computation of the cost value over different segments of the data sequence; (2) state-of-the-art R packages do not provide enough flexibility for users to handle different change point settings and models. In this work, we present the fastcpd package, aiming to provide an efficient and versatile framework for change point detection in several commonly encountered settings. The core of our algorithm is built upon PELT and the sequential gradient descent method recently proposed by Zhang and Dawn (2023). We illustrate the usage of the fastcpd package through several examples, including mean/variance changes in a (multivariate) Gaussian sequence, parameter changes in regression models, structural breaks in ARMA/GARCH/VAR models, and changes in user-specified models.

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arXiv2023

Batch effect correction with sample remeasurement in highly confounded case-control studies

Batch effects are pervasive in biomedical studies. One approach to address the batch effects is repeatedly measuring a subset of samples in each batch. These remeasured samples are used to estimate and correct the batch effects. However, rigorous statistical methods for batch effect correction with remeasured samples are severely under-developed. In this study, we developed a framework for batch effect correction using remeasured samples in highly confounded case-control studies. We provided theoretical analyses of the proposed procedure, evaluated its power characteristics, and provided a power calculation tool to aid in the study design. We found that the number of samples that need to be remeasured depends strongly on the between-batch correlation. When the correlation is high, remeasuring a small subset of samples is possible to rescue most of the power.

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arXiv2023

Joint Mirror Procedure: Controlling False Discovery Rate for Identifying Simultaneous Signals

In many applications, the process of identifying a specific feature of interest often involves testing multiple hypotheses for their joint statistical significance. Examples include mediation analysis which simultaneously examines the existence of the exposure-mediator and the mediator-outcome effects, and replicability analysis aiming to identify simultaneous signals that exhibit statistical significance across multiple independent experiments. In this study, we present a new approach called joint mirror (JM) procedure that effectively detects such features while maintaining false discovery rate (FDR) control in finite samples. The JM procedure employs an iterative method that gradually shrinks the rejection region based on progressively revealed information until a conservative estimate of the false discovery proportion (FDP) is below the target FDR level. Additionally, we introduce a more stringent error measure, known as the modified FDR (mFDR), which assigns weights to each false discovery based on its number of null components. We demonstrate that, under appropriate assumptions, the JM procedure controls the mFDR in finite samples. To implement the JM procedure, we propose an efficient algorithm that can incorporate partial ordering information. Through extensive simulations, we demonstrate that our procedure effectively controls the mFDR and enhances statistical power across various scenarios. Finally, we showcase the utility of our method by applying it to real-world mediation and replicability analyses.

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arXiv2023

Adaptive Testing for Alphas in High-dimensional Factor Pricing Models

This paper proposes a new procedure to validate the multi-factor pricing theory by testing the presence of alpha in linear factor pricing models with a large number of assets. Because the market's inefficient pricing is likely to occur to a small fraction of exceptional assets, we develop a testing procedure that is particularly powerful against sparse signals. Based on the high-dimensional Gaussian approximation theory, we propose a simulation-based approach to approximate the limiting null distribution of the test. Our numerical studies show that the new procedure can deliver a reasonable size and achieve substantial power improvement compared to the existing tests under sparse alternatives, and especially for weak signals.

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arXiv2023

Structure Adaptive Elastic-Net

Penalized linear regression is of fundamental importance in high-dimensional statistics and has been routinely used to regress a response on a high-dimensional set of predictors. In many scientific applications, there exists external information that encodes the predictive power and sparsity structure of the predictors. In this article, we propose the Structure Adaptive Elastic-Net (SA-Enet), which provides a new framework for incorporating potentially useful side information into a penalized regression. The basic idea is to translate the external information into different penalization strengths for the regression coefficients. We particularly focus on group and covariate-dependent structures and study the risk properties of the resulting estimator. To this, we generalize the state evolution framework recently introduced for the analysis of the approximate message-passing algorithm to the SA-Enet framework. We show that the finite sample risk of the SA-Enet estimator is consistent with the theoretical risk predicted by the state evolution equation. Our theory suggests that the SA-Enet with an informative group or covariate structure can outperform the Lasso, Adaptive Lasso, Sparse Group Lasso, Feature-weighted Elastic-Net, and Graper. This evidence is further confirmed in our numerical studies. We also demonstrate the usefulness and the superiority of our method for leukemia data from molecular biology and precision medicine.

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arXiv2023

High Dimensional Analysis of Variance in Multivariate Linear Regression

In this paper, we develop a systematic theory for high dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new \emph{U}~type test statistic to test linear hypotheses and establish a high dimensional Gaussian approximation result under fairly mild moment assumptions. Our general framework and theory can be applied to deal with the classical one-way multivariate ANOVA and the nonparametric one-way MANOVA in high dimensions. To implement the test procedure in practice, we introduce a sample-splitting based estimator of the second moment of the error covariance and discuss its properties. A simulation study shows that our proposed test outperforms some existing tests in various settings.

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arXiv2022

Sequential Gradient Descent and Quasi-Newton's Method for Change-Point Analysis

One common approach to detecting change-points is minimizing a cost function over possible numbers and locations of change-points. The framework includes several well-established procedures, such as the penalized likelihood and minimum description length. Such an approach requires finding the cost value repeatedly over different segments of the data set, which can be time-consuming when (i) the data sequence is long and (ii) obtaining the cost value involves solving a non-trivial optimization problem. This paper introduces a new sequential method (SE) that can be coupled with gradient descent (SeGD) and quasi-Newton's method (SeN) to find the cost value effectively. The core idea is to update the cost value using the information from previous steps without re-optimizing the objective function. The new method is applied to change-point detection in generalized linear models and penalized regression. Numerical studies show that the new approach can be orders of magnitude faster than the Pruned Exact Linear Time (PELT) method without sacrificing estimation accuracy.

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arXiv2022

A General Framework for Powerful Confounder Adjustment in Omics Association Studies

Genomic data are subject to various sources of confounding, such as demographic variables, biological heterogeneity, and batch effects. To identify genomic features associated with a variable of interest in the presence of confounders, the traditional approach involves fitting a confounder-adjusted regression model to each genomic feature, followed by multiplicity correction. This study shows that the traditional approach was sub-optimal and proposes a new two-dimensional false discovery rate control framework (2dFDR+) that provides significant power improvement over the conventional method and applies to a wide range of settings. 2dFDR+ uses marginal independence test statistics as auxiliary information to filter out less promising features, and FDR control is performed based on conditional independence test statistics in the remaining features. 2dFDR+ provides (asymptotically) valid inference from samples in settings where the conditional distribution of the genomic variables given the covariate of interest and the confounders is arbitrary and completely unknown. To achieve this goal, our method requires the conditional distribution of the covariate given the confounders to be known or can be estimated from the data. We develop a new procedure to simultaneously select the two cutoff values for the marginal and conditional independence test statistics. 2dFDR+ is proved to offer asymptotic FDR control and dominate the power of the traditional procedure. Promising finite sample performance is demonstrated via extensive simulations and real data applications.

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arXiv2022

LinDA: linear models for differential abundance analysis of microbiome compositional data

Differential abundance analysis is at the core of statistical analysis of microbiome data. The compositional nature of microbiome sequencing data makes false positive control challenging. Here, we show that the compositional effects can be addressed by a simple, yet highly flexible and scalable, approach. The proposed method, LinDA, only requires fitting linear regression models on the centered log-ratio transformed data, and correcting the bias due to compositional effects. We show that LinDA enjoys asymptotic FDR control and can be extended to mixed-effect models for correlated microbiome data. Using simulations and real examples, we demonstrate the effectiveness of LinDA.

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arXiv2021

Optimal False Discovery Rate Control for Large Scale Multiple Testing with Auxiliary Information

Large-scale multiple testing is a fundamental problem in high dimensional statistical inference. It is increasingly common that various types of auxiliary information, reflecting the structural relationship among the hypotheses, are available. Exploiting such auxiliary information can boost statistical power. To this end, we propose a framework based on a two-group mixture model with varying probabilities of being null for different hypotheses a priori, where a shape-constrained relationship is imposed between the auxiliary information and the prior probabilities of being null. An optimal rejection rule is designed to maximize the expected number of true positives when average false discovery rate is controlled. Focusing on the ordered structure, we develop a robust EM algorithm to estimate the prior probabilities of being null and the distribution of $p$-values under the alternative hypothesis simultaneously. We show that the proposed method has better power than state-of-the-art competitors while controlling the false discovery rate, both empirically and theoretically. Extensive simulations demonstrate the advantage of the proposed method. Datasets from genome-wide association studies are used to illustrate the new methodology.

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arXiv2021

Kernel-Distance-Based Covariate Balancing

A common concern in observational studies focuses on properly evaluating the causal effect, which usually refers to the average treatment effect or the average treatment effect on the treated. In this paper, we propose a data preprocessing method, the Kernel-distance-based covariate balancing, for observational studies with binary treatments. This proposed method yields a set of unit weights for the treatment and control groups, respectively, such that the reweighted covariate distributions can satisfy a set of pre-specified balance conditions. This preprocessing methodology can effectively reduce confounding bias of subsequent estimation of causal effects. We demonstrate the implementation and performance of Kernel-distance-based covariate balancing with Monte Carlo simulation experiments and a real data analysis.

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arXiv2020

Covariate Adaptive Family-wise Error Rate Control for Genome-Wide Association Studies

The family-wise error rate (FWER) has been widely used in genome-wide association studies. With the increasing availability of functional genomics data, it is possible to increase the detection power by leveraging these genomic functional annotations. Previous efforts to accommodate covariates in multiple testing focus on the false discovery rate control while covariate-adaptive FWER-controlling procedures remain under-developed. Here we propose a novel covariate-adaptive FWER-controlling procedure that incorporates external covariates which are potentially informative of either the statistical power or the prior null probability. An efficient algorithm is developed to implement the proposed method. We prove its asymptotic validity and obtain the rate of convergence through a perturbation-type argument. Our numerical studies show that the new procedure is more powerful than competing methods and maintains robustness across different settings. We apply the proposed approach to the UK Biobank data and analyze 27 traits with 9 million single-nucleotide polymorphisms tested for associations. Seventy-five genomic annotations are used as covariates. Our approach detects more genome-wide significant loci than other methods in 21 out of the 27 traits.

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arXiv2020

Covariate Adaptive False Discovery Rate Control with Applications to Omics-Wide Multiple Testing

Conventional multiple testing procedures often assume hypotheses for different features are exchangeable. However, in many scientific applications, additional covariate information regarding the patterns of signals and nulls are available. In this paper, we introduce an FDR control procedure in large-scale inference problem that can incorporate covariate information. We develop a fast algorithm to implement the proposed procedure and prove its asymptotic validity even when the underlying model is misspecified and the p-values are weakly dependent (e.g., strong mixing). Extensive simulations are conducted to study the finite sample performance of the proposed method and we demonstrate that the new approach improves over the state-of-the-art approaches by being flexible, robust, powerful and computationally efficient. We finally apply the method to several omics datasets arising from genomics studies with the aim to identify omics features associated with some clinical and biological phenotypes. We show that the method is overall the most powerful among competing methods, especially when the signal is sparse. The proposed Covariate Adaptive Multiple Testing procedure is implemented in the R package CAMT.

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arXiv2019

A New Framework for Distance and Kernel-based Metrics in High Dimensions

The paper presents new metrics to quantify and test for (i) the equality of distributions and (ii) the independence between two high-dimensional random vectors. We show that the energy distance based on the usual Euclidean distance cannot completely characterize the homogeneity of two high-dimensional distributions in the sense that it only detects the equality of means and the traces of covariance matrices in the high-dimensional setup. We propose a new class of metrics which inherits the desirable properties of the energy distance and maximum mean discrepancy/(generalized) distance covariance and the Hilbert-Schmidt Independence Criterion in the low-dimensional setting and is capable of detecting the homogeneity of/completely characterizing independence between the low-dimensional marginal distributions in the high dimensional setup. We further propose t-tests based on the new metrics to perform high-dimensional two-sample testing/independence testing and study their asymptotic behavior under both high dimension low sample size (HDLSS) and high dimension medium sample size (HDMSS) setups. The computational complexity of the t-tests only grows linearly with the dimension and thus is scalable to very high dimensional data. We demonstrate the superior power behavior of the proposed tests for homogeneity of distributions and independence via both simulated and real datasets.

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arXiv2019

Distance-based and RKHS-based Dependence Metrics in High Dimension

In this paper, we study distance covariance, Hilbert-Schmidt covariance (aka Hilbert-Schmidt independence criterion [Gretton et al. (2008)]) and related independence tests under the high dimensional scenario. We show that the sample distance/Hilbert-Schmidt covariance between two random vectors can be approximated by the sum of squared componentwise sample cross-covariances up to an asymptotically constant factor, which indicates that the distance/Hilbert-Schmidt covariance based test can only capture linear dependence in high dimension. As a consequence, the distance correlation based t-test developed by Szekely and Rizzo (2013) for independence is shown to have trivial limiting power when the two random vectors are nonlinearly dependent but component-wisely uncorrelated. This new and surprising phenomenon, which seems to be discovered for the first time, is further confirmed in our simulation study. As a remedy, we propose tests based on an aggregation of marginal sample distance/Hilbert-Schmidt covariances and show their superior power behavior against their joint counterparts in simulations. We further extend the distance correlation based t-test to those based on Hilbert-Schmidt covariance and marginal distance/Hilbert-Schmidt covariance. A novel unified approach is developed to analyze the studentized sample distance/Hilbert-Schmidt covariance as well as the studentized sample marginal distance covariance under both null and alternative hypothesis. Our theoretical and simulation results shed light on the limitation of distance/Hilbert-Schmidt covariance when used jointly in the high dimensional setting and suggest the aggregation of marginal distance/Hilbert-Schmidt covariance as a useful alternative.

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arXiv2018

High Dimensional Robust Inference for Cox Regression Models

We consider high-dimensional inference for potentially misspecified Cox proportional hazard models based on low dimensional results by Lin and Wei [1989]. A de-sparsified Lasso estimator is proposed based on the log partial likelihood function and shown to converge to a pseudo-true parameter vector. Interestingly, the sparsity of the true parameter can be inferred from that of the above limiting parameter. Moreover, each component of the above (non-sparse) estimator is shown to be asymptotically normal with a variance that can be consistently estimated even under model misspecifications. In some cases, this asymptotic distribution leads to valid statistical inference procedures, whose empirical performances are illustrated through numerical examples.

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