arXiv subjects

Yumou Qiu

Publications and source records attributed to Yumou Qiu.

At least 19 recordsLinked to original sources

arXiv2026

A Tutorial on Bregman Projection in Statistics

A single geometric operation -- projecting a reference onto a constrained family under a Bregman divergence -- underlies a striking range of statistical methods. This tutorial develops the operation first as pure convex geometry, with no statistics attached. A strictly convex generator $G$ and its conjugate $F$ furnish two coordinate systems, a projection theorem with existence and uniqueness, and a Pythagorean {theorem}; the Pythagorean theorem itself produces {two} dual projections -- the information (e-) projection onto moment-constrained families and the moment (m-) projection onto exponential families -- exchanged by the conjugacy $G\leftrightarrow F$, so a single theorem governs both. Part~II reads off the statistics. The generalized linear model is treated in detail as the concrete carrier of the two projections: {under the canonical link,} the score equation is exactly the Pythagorean orthogonality, and the fit is simultaneously an e-projection in the natural coordinate and an m-projection in the mean coordinate. Maximum entropy, survey calibration, over-identified moment models, the EM algorithm, variational inference, autoencoders, and expectation propagation then fall into place as instances of the same construction -- exactly where the underlying families are flat, and as controlled approximations or neighboring-divergence analogies where they are not. The mathematics of Part~I is self-contained; the statistical sections presume only familiarity with the methods being unified.

math.ST↗

arXiv2026

Bregman projection for calibration estimation in Survey Sampling

Calibration weighting is a fundamental tool in survey sampling for incorporating auxiliary population information into design-based estimators. Classical formulations measure distance between calibrated and design weights on the multiplicative ratio scale. We develop a unified framework based on Bregman divergence defined directly on the weight vector. The framework reveals a primal--dual symmetry in which both the weight-space and multiplier-space optimization problems are themselves Bregman projections, and the calibrated weights satisfy a generalized Pythagorean decomposition with respect to the constraint manifold. The resulting estimator is asymptotically equivalent to a debiased prediction estimator whose regression coefficient depends explicitly on the Bregman generator, in contrast to the generalized regression estimator equivalent of classical calibration. Exploiting this dependence, we identify a contrast-entropy generator that achieves design-optimality under Poisson sampling. Two extensions are developed: cross-fitted estimation under non-probability sampling, yielding doubly robust inference under standard product-rate conditions; and a regularized extension whose Lagrangian dual produces a H\"older-conjugate penalty for soft balance under high-dimensional auxiliary variables. Simulations and an analysis of National Oceanic and Atmospheric Administration (NOAA)'s Large Pelagics Intercept Survey illustrate the framework.

stat.ME↗

arXiv2026

Localization Estimator for High Dimensional Tensor Covariance Matrices

This paper considers covariance matrix estimation of tensor data under high dimensionality. A multi-bandable covariance class is established to accommodate the need for complex covariance structures of multi-layer lattices and general covariance decay patterns. We propose a high dimensional covariance localization estimator for tensor data, which regulates the sample covariance matrix through a localization function. The statistical properties of the proposed estimator are studied by deriving the minimax rates of convergence under the spectral and the Frobenius norms. Numerical experiments and real data analysis on ocean eddy data are carried out to illustrate the utility of the proposed method in practice.

stat.ME↗

arXiv2025

Multi-source Learning for Target Population by High-dimensional Calibration

Multi-source learning is an emerging area of research in statistics, where information from multiple datasets with heterogeneous distributions is combined to estimate the parameter of interest for a target population without observed responses. We propose a high-dimensional debiased calibration (HDC) method and a multi-source HDC (MHDC) estimator for general estimating equations. The HDC method uses a novel approach to achieve Neyman orthogonality for the target parameter via high-dimensional covariate balancing on an augmented set of covariates. It avoids the augmented inverse probability weighting formulation and leads to an easier optimization algorithm for the target parameter in estimating equations and M-estimation. The proposed MHDC estimator integrates multi-source data while supporting flexible specifications for both density ratio and outcome regression models, achieving multiple robustness against model misspecification. Its asymptotic normality is established, and a specification test is proposed to examine the transferability condition for the multi-source data. Compared to the linear combination of single-source HDC estimators, the MHDC estimator improves efficiency by jointly utilizing all data sources. Through simulation studies, we show that the MHDC estimator accommodates multiple sources and multiple working models effectively and performs better than the existing doubly robust estimators for multi-source learning. An empirical analysis of a meteorological dataset demonstrates the utility of the proposed method in practice.

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arXiv2025

A General Approach for Calibration Weighting under Missing at Random

We propose a unified class of calibration weighting methods based on weighted generalized entropy to handle missing at random (MAR) data with improved stability and efficiency. The proposed generalized entropy calibration (GEC) formulates weight construction as a convex optimization program that unifies entropy-based approaches and generalized regression weighting. Double robustness is achieved by augmenting standard covariate balancing with a debiasing constraint tied to the propensity score model and a Neyman-orthogonal constraint that removes first-order sensitivity to nuisance estimation. Selection of the weights on the entropy function can lead to the optimal calibration estimator under a correctly specified outcome regression model. The proposed GEC weighting ha a nice geometric characterization: the GEC solution is the Bregman projection of the initial weights onto a constraint set, which yields a generalized Pythagorean identity and a nested decomposition that quantifies the incremental distance paid for additional constraints. We also develop a high-dimensional extension with soft calibration and a projection calibration constraint that preserves doubly robust inference. Two simulation studies are presented to compare the performance of the proposed method with the existing methods.

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arXiv2025

Collaborative Indirect Treatment Comparisons with Multiple Distributed Single-arm Trials

When randomized controlled trials are impractical or unethical to simultaneously compare multiple treatments, indirect treatment comparisons using single-arm trials offer valuable evidence for health technology assessments, especially for rare diseases and early-phase drug development. In practice, each sponsor conducts a single-arm trial on its own drug with restricted data-sharing and targets effects in its trial population, which can lead to unfair comparisons. This motivates methods for fair treatment comparisons across a range of target populations in distributed networks of single-arm trials sharing only aggregated data. Existing federated methods, which assume at least one site contains all treatments and allow pooling of treatment groups within the same site, cannot address this problem. We propose a novel distributed augmented calibration weighting (DAC) method to simultaneously estimate the pairwise average treatment effects (ATEs) across all trial population combinations in a distributed network of multiple single-arm trials. Using two communication rounds, DAC estimators balance covariates via calibration weighting, incorporate flexible nuisance parameter estimation, achieve doubly robust consistency, and yield results identical to pooled-data analysis. When nuisance parameters are estimated parametrically, DAC estimators are enhanced to achieve doubly robust inference with minimal squared first-order asymptotic bias. Simulations and a real-data application show good performance.

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arXiv2025

Multiply Robust Inference of Average Treatment Effects by High-dimensional Empirical Likelihood

In this paper, we develop a multiply robust inference procedure of the average treatment effect (ATE) for data with high-dimensional covariates. We consider the case where it is difficult to correctly specify a single parametric model for the propensity scores (PS). For example, the target population is formed from heterogeneous sources with different treatment assignment mechanisms. We propose a novel high-dimensional empirical likelihood weighting method under soft covariate balancing constraints to combine multiple working PS models. An extended set of calibration functions is used, and a regularized augmented outcome regression is developed to correct the bias due to non-exact covariate balancing. Those two approaches provide a new way to construct the Neyman orthogonal score of the ATE. The proposed confidence interval for the ATE achieves asymptotically valid nominal coverage under high-dimensional covariates if any of the PS models, their linear combination, or the outcome regression model is correctly specified. The proposed method is extended to generalized linear models for the outcome variable. Specifically, we consider estimating the ATE for data with unknown clusters, where multiple working PS models can be fitted based on the estimated clusters. Our proposed approach enables robust inference of the ATE for clustered data. We demonstrate the advantages of the proposed approach over the existing doubly robust inference methods under high-dimensional covariates via simulation studies. We analyzed the right heart catheterization dataset, initially collected from five medical centers and two different phases of studies, to demonstrate the effectiveness of the proposed method in practice.

stat.ME↗

arXiv2025

Radial Neighborhood Smoothing Recommender System

Recommender systems inherently exhibit a low-rank structure in latent space. A key challenge is to define meaningful and measurable distances in the latent space to capture user-user, item-item, user-item relationships effectively. In this work, we establish that distances in the latent space can be systematically approximated using row-wise and column-wise distances in the observed matrix, providing a novel perspective on distance estimation. To refine the distance estimation, we introduce the correction based on empirical variance estimator to account for noise-induced non-centrality. The novel distance estimation enables a more structured approach to constructing neighborhoods, leading to the Radial Neighborhood Estimator (RNE), which constructs neighborhoods by including both overlapped and partially overlapped user-item pairs and employs neighborhood smoothing via localized kernel regression to improve imputation accuracy. We provide the theoretical asymptotic analysis for the proposed estimator. We perform evaluations on both simulated and real-world datasets, demonstrating that RNE achieves superior performance compared to existing collaborative filtering and matrix factorization methods. While our primary focus is on distance estimation in latent space, we find that RNE also mitigates the ``cold-start'' problem.

cs.LG↗

arXiv2025

Permutation-Based Rank Test in the Presence of Discretization and Application in Causal Discovery with Mixed Data

Recent advances have shown that statistical tests for the rank of cross-covariance matrices play an important role in causal discovery. These rank tests include partial correlation tests as special cases and provide further graphical information about latent variables. Existing rank tests typically assume that all the continuous variables can be perfectly measured, and yet, in practice many variables can only be measured after discretization. For example, in psychometric studies, the continuous level of certain personality dimensions of a person can only be measured after being discretized into order-preserving options such as disagree, neutral, and agree. Motivated by this, we propose Mixed data Permutation-based Rank Test (MPRT), which properly controls the statistical errors even when some or all variables are discretized. Theoretically, we establish the exchangeability and estimate the asymptotic null distribution by permutations; as a consequence, MPRT can effectively control the Type I error in the presence of discretization while previous methods cannot. Empirically, our method is validated by extensive experiments on synthetic data and real-world data to demonstrate its effectiveness as well as applicability in causal discovery.

cs.LG↗

arXiv2025

A Sample Efficient Conditional Independence Test in the Presence of Discretization

In many real-world scenarios, interested variables are often represented as discretized values due to measurement limitations. Applying Conditional Independence (CI) tests directly to such discretized data, however, can lead to incorrect conclusions. To address this, recent advancements have sought to infer the correct CI relationship between the latent variables through binarizing observed data. However, this process inevitably results in a loss of information, which degrades the test's performance. Motivated by this, this paper introduces a sample-efficient CI test that does not rely on the binarization process. We find that the independence relationships of latent continuous variables can be established by addressing an over-identifying restriction problem with Generalized Method of Moments (GMM). Based on this insight, we derive an appropriate test statistic and establish its asymptotic distribution correctly reflecting CI by leveraging nodewise regression. Theoretical findings and Empirical results across various datasets demonstrate that the superiority and effectiveness of our proposed test. Our code implementation is provided in https://github.com/boyangaaaaa/DCT

cs.AI↗

arXiv2025

Generalized entropy calibration for analyzing voluntary survey data

Statistical analysis of voluntary survey data is an important area of research in survey sampling. We consider a unified approach to voluntary survey data analysis under the assumption that the sampling mechanism is ignorable. Generalized entropy calibration is introduced as a unified tool for calibration weighting to control the selection bias. We first establish the relationship between the generalized calibration weighting and its dual expression for regression estimation. The dual relationship is critical in identifying the implied regression model and developing model selection for calibration weighting. Also, if a linear regression model for an important study variable is available, then two-step calibration method can be used to smooth the final weights and achieve the statistical efficiency. Asymptotic properties of the proposed estimator are investigated. Results from a limited simulation study are also presented.

stat.ME↗

arXiv2025

Debiased calibration estimation using generalized entropy in survey sampling

Incorporating the auxiliary information into the survey estimation is a fundamental problem in survey sampling. Calibration weighting is a popular tool for incorporating the auxiliary information. The calibration weighting method of Deville and Sarndal (1992) uses a distance measure between the design weights and the final weights to solve the optimization problem with calibration constraints. This paper introduces a novel framework that leverages generalized entropy as the objective function for optimization, where design weights play a role in the constraints to ensure design consistency, rather than being part of the objective function. This innovative calibration framework is particularly attractive due to its generality and its ability to generate more efficient calibration weights compared to traditional methods based on Deville and Sarndal (1992). Furthermore, we identify the optimal choice of the generalized entropy function that achieves the minimum variance across various choices of the generalized entropy function under the same constraints. Asymptotic properties, such as design consistency and asymptotic normality, are presented rigorously. The results from a limited simulation study are also presented. We demonstrate a real-life application using agricultural survey data collected from Kynetec, Inc.

stat.ME↗

arXiv2025

High-dimensional Clustering and Signal Recovery under Block Signals

This paper studies computationally efficient methods and their minimax optimality for high-dimensional clustering and signal recovery under block signal structures. We propose two sets of methods, cross-block feature aggregation PCA (CFA-PCA) and moving average PCA (MA-PCA), designed for sparse and dense block signals, respectively. Both methods adaptively utilize block signal structures, applicable to non-Gaussian data with heterogeneous variances and non-diagonal covariance matrices. Specifically, the CFA method utilizes a block-wise U-statistic to aggregate and select block signals non-parametrically from data with unknown cluster labels. We show that the proposed methods are consistent for both clustering and signal recovery under mild conditions and weaker signal strengths than the existing methods without considering block structures of signals. Furthermore, we derive both statistical and computational minimax lower bounds (SMLB and CMLB) for high-dimensional clustering and signal recovery under block signals, where the CMLBs are restricted to algorithms with polynomial computation complexity. The minimax boundaries partition signals into regions of impossibility and possibility. No algorithm (or no polynomial time algorithm) can achieve consistent clustering or signal recovery if the signals fall into the statistical (or computational) region of impossibility. We show that the proposed CFA-PCA and MA-PCA methods can achieve the CMLBs for the sparse and dense block signal regimes, respectively, indicating the proposed methods are computationally minimax optimal. A tuning parameter selection method is proposed based on post-clustering signal recovery results. Simulation studies are conducted to evaluate the proposed methods. A case study on global temperature change demonstrates their utility in practice.

stat.ME↗

arXiv2025

A Conditional Independence Test in the Presence of Discretization

Testing conditional independence has many applications, such as in Bayesian network learning and causal discovery. Different test methods have been proposed. However, existing methods generally can not work when only discretized observations are available. Specifically, consider $X_1$, $\tilde{X}_2$ and $X_3$ are observed variables, where $\tilde{X}_2$ is a discretization of latent variables $X_2$. Applying existing test methods to the observations of $X_1$, $\tilde{X}_2$ and $X_3$ can lead to a false conclusion about the underlying conditional independence of variables $X_1$, $X_2$ and $X_3$. Motivated by this, we propose a conditional independence test specifically designed to accommodate the presence of such discretization. To achieve this, we design the bridge equations to recover the parameter reflecting the statistical information of the underlying latent continuous variables. An appropriate test statistic and its asymptotic distribution under the null hypothesis of conditional independence have also been derived. Both theoretical results and empirical validation have been provided, demonstrating the effectiveness of our test methods.

stat.ML↗

arXiv2025

Versatile Differentially Private Learning for General Loss Functions

This paper aims to provide a versatile privacy-preserving release mechanism along with a unified approach for subsequent parameter estimation and statistical inference. We propose the ZIL privacy mechanism based on zero-inflated symmetric multivariate Laplace noise, which requires no prior specification of subsequent analysis tasks, allows for general loss functions under minimal conditions, imposes no limit on the number of analyses, and is adaptable to the increasing data volume in online scenarios. We derive the trade-off function for the proposed ZIL mechanism that characterizes its privacy protection level. Within the M-estimation framework, we propose a novel doubly random corrected loss (DRCL) for the ZIL mechanism, which provides consistent and asymptotic normal M-estimates for the parameters of the target population under differential privacy constraints. The proposed approach is easy to compute without numerical integration and differentiation for noisy data. It is applicable for a general class of loss functions, including non-smooth loss functions like check loss and hinge loss. Simulation studies, including logistic regression and quantile regression, are conducted to evaluate the performance of the proposed method.

stat.ME↗

arXiv2019

Multi-level Thresholding Test for High Dimensional Covariance Matrices

We consider testing the equality of two high-dimensional covariance matrices by carrying out a multi-level thresholding procedure, which is designed to detect sparse and faint differences between the covariances. A novel U-statistic composition is developed to establish the asymptotic distribution of the thresholding statistics in conjunction with the matrix blocking and the coupling techniques. We propose a multi-thresholding test that is shown to be powerful in detecting sparse and weak differences between two covariance matrices. The test is shown to have attractive detection boundary and to attain the optimal minimax rate in the signal strength under different regimes of high dimensionality and the sparsity of the signal. Simulation studies are conducted to demonstrate the utility of the proposed test.

math.ST↗

arXiv2018

Confidence regions for entries of a large precision matrix

Precision matrices play important roles in many practical applications. Motivated by temporally dependent multivariate data in modern social and scientific studies, we consider the statistical inference of precision matrices for high-dimensional time dependent observations. Specifically, we propose a data-driven procedure to construct a class of simultaneous confidence regions for the precision coefficients within an index set of interest. The confidence regions can be applied to test for specific structures of a precision matrix and to recover its nonzero components. We first construct an estimator of the underlying precision matrix via penalized node-wise regressions, and then develope the Gaussian approximation results on the maximal difference between the estimated and true precision matrices. A computationally feasible parametric bootstrap algorithm is developed to implement the proposed procedure. Theoretical results indicate that the proposed procedure works well without the second order cross-time stationary assumption on the data and sparse structure conditions on the long-run covariance of the estimates. Simulation studies and a real example on S&P 500 stock return data confirm the performance of the proposed approach.

stat.ME↗

arXiv2018

A Neighborhood-Assisted Hotelling's $T^2$ Test for High-Dimensional Means

Many tests have been proposed to remedy the classical Hotelling's $T^2$ test in the "large $p$, small $n$" paradigm, but the existence of an optimal sum-of-squares type test has not been explored. This paper shows that under certain conditions, the population Hotelling's $T^2$ test with the known $Σ^{-1}$ attains the best power among all the $L_2$-norm based tests with the data transformation by $Σ^η$ for $η\in (-\infty, \infty)$. To extend the result to the case of unknown $Σ^{-1}$, we propose a Neighborhood-Assisted Hotelling's $T^2$ statistic obtained by replacing the inverse of sample covariance matrix in the classical Hotelling's $T^2$ statistic with a regularized covariance estimator. Utilizing a regression model, we establish its asymptotic normality under mild conditions. We show that the proposed test is able to match the performance of the population Hotelling's $T^2$ test under certain conditions, and thus possesses certain optimality. Moreover, it can adaptively attain the best power by empirically choosing a neighborhood size to maximize its signal-to-noise ratio. Simulation experiments and case studies are given to demonstrate the empirical performance of the proposed test.

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