arXiv subjects

Changliang Zou

Publications and source records attributed to Changliang Zou.

51 records · Page 3Linked to original sources

arXiv2024

Prediction De-Correlated Inference: A safe approach for post-prediction inference

In modern data analysis, it is common to use machine learning methods to predict outcomes on unlabeled datasets and then use these pseudo-outcomes in subsequent statistical inference. Inference in this setting is often called post-prediction inference. We propose a novel assumption-lean framework for statistical inference under post-prediction setting, called Prediction De-Correlated Inference (PDC). Our approach is safe, in the sense that PDC can automatically adapt to any black-box machine-learning model and consistently outperform the supervised counterparts. The PDC framework also offers easy extensibility for accommodating multiple predictive models. Both numerical results and real-world data analysis demonstrate the superiority of PDC over the state-of-the-art methods.

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arXiv2024

Model-free controlled variable selection via data splitting

Addressing the simultaneous identification of contributory variables while controlling the false discovery rate (FDR) in high-dimensional data is a crucial statistical challenge. In this paper, we propose a novel model-free variable selection procedure in sufficient dimension reduction framework via a data splitting technique. The variable selection problem is first converted to a least squares procedure with several response transformations. We construct a series of statistics with global symmetry property and leverage the symmetry to derive a data-driven threshold aimed at error rate control. Our approach demonstrates the capability for achieving finite-sample and asymptotic FDR control under mild theoretical conditions. Numerical experiments confirm that our procedure has satisfactory FDR control and higher power compared with existing methods.

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arXiv2024

Covariance Regression with High-Dimensional Predictors

In the high-dimensional landscape, addressing the challenges of covariance regression with high-dimensional covariates has posed difficulties for conventional methodologies. This paper addresses these hurdles by presenting a novel approach for high-dimensional inference with covariance matrix outcomes. The proposed methodology is illustrated through its application in elucidating brain coactivation patterns observed in functional magnetic resonance imaging (fMRI) experiments and unraveling complex associations within anatomical connections between brain regions identified through diffusion tensor imaging (DTI). In the pursuit of dependable statistical inference, we introduce an integrative approach based on penalized estimation. This approach combines data splitting, variable selection, aggregation of low-dimensional estimators, and robust variance estimation. It enables the construction of reliable confidence intervals for covariate coefficients, supported by theoretical confidence levels under specified conditions, where asymptotic distributions are provided. Through various types of simulation studies, the proposed approach performs well for covariance regression in the presence of high-dimensional covariates. This innovative approach is applied to the Lifespan Human Connectome Project (HCP) Aging Study, which aims to uncover a typical aging trajectory and variations in the brain connectome among mature and older adults. The proposed approach effectively identifies brain networks and associated predictors of white matter integrity, aligning with established knowledge of the human brain.

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arXiv2024

Selective conformal inference with false coverage-statement rate control

Conformal inference is a popular tool for constructing prediction intervals (PI). We consider here the scenario of post-selection/selective conformal inference, that is PIs are reported only for individuals selected from an unlabeled test data. To account for multiplicity, we develop a general split conformal framework to construct selective PIs with the false coverage-statement rate (FCR) control. We first investigate the Benjamini and Yekutieli (2005)'s FCR-adjusted method in the present setting, and show that it is able to achieve FCR control but yields uniformly inflated PIs. We then propose a novel solution to the problem, named as Selective COnditional conformal Predictions (SCOP), which entails performing selection procedures on both calibration set and test set and construct marginal conformal PIs on the selected sets by the aid of conditional empirical distribution obtained by the calibration set. Under a unified framework and exchangeable assumptions, we show that the SCOP can exactly control the FCR. More importantly, we provide non-asymptotic miscoverage bounds for a general class of selection procedures beyond exchangeablity and discuss the conditions under which the SCOP is able to control the FCR. As special cases, the SCOP with quantile-based selection or conformal p-values-based multiple testing procedures enjoys valid coverage guarantee under mild conditions. Numerical results confirm the effectiveness and robustness of SCOP in FCR control and show that it achieves more narrowed PIs over existing methods in many settings.

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arXiv2023

Uncertainty Quantification for Data-Driven Change-Point Learning via Cross-Validation

Accurately detecting multiple change-points is critical for various applications, but determining the optimal number of change-points remains a challenge. Existing approaches based on information criteria attempt to balance goodness-of-fit and model complexity, but their performance varies depending on the model. Recently, data-driven selection criteria based on cross-validation has been proposed, but these methods can be prone to slight overfitting in finite samples. In this paper, we introduce a method that controls the probability of overestimation and provides uncertainty quantification for learning multiple change-points via cross-validation. We frame this problem as a sequence of model comparison problems and leverage high-dimensional inferential procedures. We demonstrate the effectiveness of our approach through experiments on finite-sample data, showing superior uncertainty quantification for overestimation compared to existing methods. Our approach has broad applicability and can be used in diverse change-point models.

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arXiv2023

Leverage classifier: Another look at support vector machine

Support vector machine (SVM) is a popular classifier known for accuracy, flexibility, and robustness. However, its intensive computation has hindered its application to large-scale datasets. In this paper, we propose a new optimal leverage classifier based on linear SVM under a nonseparable setting. Our classifier aims to select an informative subset of the training sample to reduce data size, enabling efficient computation while maintaining high accuracy. We take a novel view of SVM under the general subsampling framework and rigorously investigate the statistical properties. We propose a two-step subsampling procedure consisting of a pilot estimation of the optimal subsampling probabilities and a subsampling step to construct the classifier. We develop a new Bahadur representation of the SVM coefficients and derive unconditional asymptotic distribution and optimal subsampling probabilities without giving the full sample. Numerical results demonstrate that our classifiers outperform the existing methods in terms of estimation, computation, and prediction.

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arXiv2023

Zipper: Addressing degeneracy in algorithm-agnostic inference

The widespread use of black box prediction methods has sparked an increasing interest in algorithm/model-agnostic approaches for quantifying goodness-of-fit, with direct ties to specification testing, model selection and variable importance assessment. A commonly used framework involves defining a predictiveness criterion, applying a cross-fitting procedure to estimate the predictiveness, and utilizing the difference in estimated predictiveness between two models as the test statistic. However, even after standardization, the test statistic typically fails to converge to a non-degenerate distribution under the null hypothesis of equal goodness, leading to what is known as the degeneracy issue. To addresses this degeneracy issue, we present a simple yet effective device, Zipper. It draws inspiration from the strategy of additional splitting of testing data, but encourages an overlap between two testing data splits in predictiveness evaluation. Zipper binds together the two overlapping splits using a slider parameter that controls the proportion of overlap. Our proposed test statistic follows an asymptotically normal distribution under the null hypothesis for any fixed slider value, guaranteeing valid size control while enhancing power by effective data reuse. Finite-sample experiments demonstrate that our procedure, with a simple choice of the slider, works well across a wide range of settings.

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arXiv2023

Statistical Inference for Ultrahigh Dimensional Location Parameter Based on Spatial Median

Motivated by the widely used geometric median-of-means estimator in machine learning, this paper studies statistical inference for ultrahigh dimensionality location parameter based on the sample spatial median under a general multivariate model, including simultaneous confidence intervals construction, global tests, and multiple testing with false discovery rate control. To achieve these goals, we derive a novel Bahadur representation of the sample spatial median with a maximum-norm bound on the remainder term, and establish Gaussian approximation for the sample spatial median over the class of hyperrectangles. In addition, a multiplier bootstrap algorithm is proposed to approximate the distribution of the sample spatial median. The approximations are valid when the dimension diverges at an exponentially rate of the sample size, which facilitates the application of the spatial median in the ultrahigh dimensional region. The proposed approaches are further illustrated by simulations and analysis of a genomic dataset from a microarray study.

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arXiv2022

Model-Free Statistical Inference on High-Dimensional Data

This paper aims to develop an effective model-free inference procedure for high-dimensional data. We first reformulate the hypothesis testing problem via sufficient dimension reduction framework. With the aid of new reformulation, we propose a new test statistic and show that its asymptotic distribution is $χ^2$ distribution whose degree of freedom does not depend on the unknown population distribution. We further conduct power analysis under local alternative hypotheses. In addition, we study how to control the false discovery rate of the proposed $χ^2$ tests, which are correlated, to identify important predictors under a model-free framework. To this end, we propose a multiple testing procedure and establish its theoretical guarantees. Monte Carlo simulation studies are conducted to assess the performance of the proposed tests and an empirical analysis of a real-world data set is used to illustrate the proposed methodology.

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arXiv2021

Multi-Kink Quantile Regression for Longitudinal Data with Application to the Progesterone Data Analysis

Motivated by investigating the relationship between progesterone and the days in a menstrual cycle in a longitudinal study, we propose a multi-kink quantile regression model for longitudinal data analysis. It relaxes the linearity condition and assumes different regression forms in different regions of the domain of the threshold covariate. In this paper, we first propose a multi-kink quantile regression for longitudinal data. Two estimation procedures are proposed to estimate the regression coefficients and the kink points locations: one is a computationally efficient profile estimator under the working independence framework while the other one considers the within-subject correlations by using the unbiased generalized estimation equation approach. The selection consistency of the number of kink points and the asymptotic normality of two proposed estimators are established. Secondly, we construct a rank score test based on partial subgradients for the existence of kink effect in longitudinal studies. Both the null distribution and the local alternative distribution of the test statistic have been derived. Simulation studies show that the proposed methods have excellent finite sample performance. In the application to the longitudinal progesterone data, we identify two kink points in the progesterone curves over different quantiles and observe that the progesterone level remains stable before the day of ovulation, then increases quickly in five to six days after ovulation and then changes to stable again or even drops slightly

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arXiv2021

Dynamic statistical inference in massive datastreams

Modern technological advances have expanded the scope of applications requiring analysis of large-scale datastreams that comprise multiple indefinitely long time series. There is an acute need for statistical methodologies that perform online inference and continuously revise the model to reflect the current status of the underlying process. In this manuscript, we propose a dynamic statistical inference framework--named dynamic tracking and screening (DTS)--that is not only able to provide accurate estimates of the underlying parameters in a dynamic statistical model, but also capable of rapidly identifying irregular individual streams whose behavioral patterns deviate from the majority. Concretely, by fully exploiting the sequential feature of datastreams, we develop a robust estimation approach under a framework of varying coefficient model. The procedure naturally accommodates unequally-spaced design points and updates the coefficient estimates as new data arrive without the need to store historical data. A data-driven choice of an optimal smoothing parameter is accordingly proposed. Furthermore, we suggest a new multiple testing procedure tailored to the streaming environment. The resulting DTS scheme is able to adapt time-varying structures appropriately, track changes in the underlying models, and hence maintain high accuracy in detecting time periods during which individual streams exhibit irregular behavior. Moreover, we derive rigorous statistical guarantees of the procedure and investigate its finite-sample performance through simulation studies. We demonstrate the proposed methods through a mobile health example to estimate the timings when subjects' sleep and physical activities have unusual influence upon their mood.

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arXiv2021

False Discovery Rate Control Under General Dependence By Symmetrized Data Aggregation

We develop a new class of distribution--free multiple testing rules for false discovery rate (FDR) control under general dependence. A key element in our proposal is a symmetrized data aggregation (SDA) approach to incorporating the dependence structure via sample splitting, data screening and information pooling. The proposed SDA filter first constructs a sequence of ranking statistics that fulfill global symmetry properties, and then chooses a data--driven threshold along the ranking to control the FDR. The SDA filter substantially outperforms the knockoff method in power under moderate to strong dependence, and is more robust than existing methods based on asymptotic $p$-values. We first develop finite--sample theory to provide an upper bound for the actual FDR under general dependence, and then establish the asymptotic validity of SDA for both the FDR and false discovery proportion (FDP) control under mild regularity conditions. The procedure is implemented in the R package \texttt{SDA}. Numerical results confirm the effectiveness and robustness of SDA in FDR control and show that it achieves substantial power gain over existing methods in many settings.

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arXiv2020

A New Procedure for Controlling False Discovery Rate in Large-Scale t-tests

This paper is concerned with false discovery rate (FDR) control in large-scale multiple testing problems. We first propose a new data-driven testing procedure for controlling the FDR in large-scale t-tests for one-sample mean problem. The proposed procedure achieves exact FDR control in finite sample settings when the populations are symmetric no matter the number of tests or sample sizes. Comparing with the existing bootstrap method for FDR control, the proposed procedure is computationally efficient. We show that the proposed method can control the FDR asymptotically for asymmetric populations even when the test statistics are not independent. We further show that the proposed procedure with a simple correction is as accurate as the bootstrap method to the second-order degree, and could be much more effective than the existing normal calibration. We extend the proposed procedure to two-sample mean problem. Empirical results show that the proposed procedures have better FDR control than existing ones when the proportion of true alternative hypotheses is not too low, while maintaining reasonably good detection ability.

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arXiv2014

Nonparametric maximum likelihood approach to multiple change-point problems

In multiple change-point problems, different data segments often follow different distributions, for which the changes may occur in the mean, scale or the entire distribution from one segment to another. Without the need to know the number of change-points in advance, we propose a nonparametric maximum likelihood approach to detecting multiple change-points. Our method does not impose any parametric assumption on the underlying distributions of the data sequence, which is thus suitable for detection of any changes in the distributions. The number of change-points is determined by the Bayesian information criterion and the locations of the change-points can be estimated via the dynamic programming algorithm and the use of the intrinsic order structure of the likelihood function. Under some mild conditions, we show that the new method provides consistent estimation with an optimal rate. We also suggest a prescreening procedure to exclude most of the irrelevant points prior to the implementation of the nonparametric likelihood method. Simulation studies show that the proposed method has satisfactory performance of identifying multiple change-points in terms of estimation accuracy and computation time.

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arXiv2012

Coordinate-independent sparse sufficient dimension reduction and variable selection

Sufficient dimension reduction (SDR) in regression, which reduces the dimension by replacing original predictors with a minimal set of their linear combinations without loss of information, is very helpful when the number of predictors is large. The standard SDR methods suffer because the estimated linear combinations usually consist of all original predictors, making it difficult to interpret. In this paper, we propose a unified method - coordinate-independent sparse estimation (CISE) - that can simultaneously achieve sparse sufficient dimension reduction and screen out irrelevant and redundant variables efficiently. CISE is subspace oriented in the sense that it incorporates a coordinate-independent penalty term with a broad series of model-based and model-free SDR approaches. This results in a Grassmann manifold optimization problem and a fast algorithm is suggested. Under mild conditions, based on manifold theories and techniques, it can be shown that CISE would perform asymptotically as well as if the true irrelevant predictors were known, which is referred to as the oracle property. Simulation studies and a real-data example demonstrate the effectiveness and efficiency of the proposed approach.

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