arXiv subjects

Liping Zhu

Publications and source records attributed to Liping Zhu.

At least 19 recordsLinked to original sources

arXiv2026

Distributed Prediction under Heterogeneity with Unidentifiable Parameter

Predicting a response based on covariates is a fundamental problem in statistics and machine learning. However, profound difficulties arise when the underlying low-dimensional structural parameters are unidentifiable, as typified in dimension reduction contexts. Specifically,estimating these non-identifiable parameters inherently introduces severe nonconvexity. In distributed settings, this difficulty is further compounded by the challenges of data heterogeneity and communication cost. To overcome these intertwined barriers, we propose a novel distributed semiparametric framework. We formulate an adaptive homogeneity pursuit utilizing a trace-similarity penalty to effectively address data heterogeneity. To resolve the ensuing severe nonconvexity and communication bottlenecks, we introduce an invex relaxation technique coupled with a multi-step local update algorithm, ensuring stable convergence to global optimality with significantly reduced communication overhead. Theoretically, we establish a non-asymptotic model-free prediction error bound and prove that our estimator achieves a two-phase minimax optimal convergence rate and an sharper model-free prediction error bound. Furthermore, we provide theoretical guarantees for algorithmic convergence and communication efficiency. Extensive simulations and a real-world multi-center medical application validate the superiority of our method.

stat.ME↗

arXiv2026

Sparse Rank Regression for Restricted-Access Economic Data

Empirical research in economics increasingly relies on restricted-access data held by multiple firms or agencies, making it impossible to construct the estimator of interest on the pooled sample. At the same time, heavy-tailed distributions are pervasive in economics and finance outcomes such as prices, expenditures and loan sizes. We study sparse, robust estimation in the restricted-access setting. The infeasible pooled benchmark is convoluted rank regression (CRR), a smooth rank-based estimator designed for heavy-tailed outcomes. Because the CRR criterion is a non-additive U-statistic, existing communication-efficient methods built for additive empirical losses do not directly apply. We propose distributed convoluted rank regression (DCRR), a surrogate criterion built from a single local CRR loss and an aggregated gradient correction, and show that it shares the same population minimizer as the pooled CRR objective. Building on this surrogate, we develop a two-stage sparse procedure: an iterative $l_1$- penalized stage followed by a folded-concave refinement. For the resulting estimator, we establish non-asymptotic error bounds, a distributed strong oracle property, and a distributed criterion for consistent model selection. Simulations and an application to used-car prices show that DCRR closely approximates pooled CRR and improves on naive divide-and-conquer, particularly under heavy-tailed errors.

stat.ME↗

arXiv2026

Distributed Convoluted Rank Regression for Non-Shareable Data under Non-Additive Losses

We study high-dimensional rank regression when data are distributed across multiple machines and the loss is a non-additive U-statistic, as in convoluted rank regression (CRR). Classical communication-efficient surrogate likelihood (CSL) methods crucially rely on the additivity of the empirical loss and therefore break down for CRR, whose global loss couples all sample pairs across machines. We propose a distributed convoluted rank regression (DCRR) framework that constructs a similar surrogate loss and demonstrate its validity under the non-additive losses. We show that this surrogate shares the same population minimizer as the full-data CRR loss and yields estimators that are statistically equivalent to centralized CRR. Building on this, we develop a two-stage sparse DCRR procedure -- an iterative $\ell_1$-penalized stage followed by a folded-concave refinement -- and establish non-asymptotic error bounds, a distributed strong oracle property, and a DHBIC-type criterion for consistent model selection. A scaling result shows that the number of machines may diverge as $M = o({N/(s^2\log p)})$ while achieving centralized oracle rates with only $O(\log N)$ communication rounds. Simulations and a large-scale real data example demonstrate substantial gains over naive divide-and-conquer, particularly under heavy-tailed errors.

stat.ME↗

arXiv2025

From Conditional to Unconditional Independence: Testing Conditional Independence via Transport Maps

Testing conditional independence between two random vectors given a third is a fundamental and challenging problem in statistics, particularly in multivariate nonparametric settings due to the complexity of conditional structures. We propose a novel method for testing conditional independence by transforming it to an unconditional independence test problem. We achieve this by constructing two transport maps that transform conditional independence into unconditional independence, this substantially simplifies the problem. These transport maps are estimated from data using conditional continuous normalizing flow models. Within this framework, we derive a test statistic and prove its asymptotic validity under both the null and alternative hypotheses. A permutation-based procedure is employed to evaluate the significance of the test. We validate the proposed method through extensive simulations and real-data analysis. Our numerical studies demonstrate the practical effectiveness of the proposed method for conditional independence

stat.ML↗

arXiv2025

Do more observations bring more information in rare events?

It is generally believed that more observations provide more information. However, we observe that in the independence test for rare events, the power of the test is, surprisingly, determined by the number of rare events rather than the total sample size. Moreover, the correlations tend to shrink to zero even as the total sample size increases, as long as the proportion of rare events decreases. We demonstrate this phenomenon in both fixed and high-dimensional settings. To address these issues, we first rescale the covariances to account for the presence of rare events. We then propose a boosted procedure that uses only a small subset of non-rare events, yet achieves nearly the same power as using the full set of observations. As a result, computational complexity is significantly reduced. The theoretical properties, including asymptotic distribution and local power analysis, are carefully derived for both the rescaled statistic based on the full sample and the boosted test statistic based on subsampling. Furthermore, we extend the theory to multi-class rare events. Extensive simulations and real-world data analyses confirm the effectiveness and computational efficiency of the proposed approach.

stat.ME↗

arXiv2025

An alternative measure for quantifying the heterogeneity in meta-analysis

Quantifying the heterogeneity is an important issue in meta-analysis, and among the existing measures, the $I^2$ statistic is most commonly used. In this paper, we first illustrate with a simple example that the $I^2$ statistic is heavily dependent on the study sample sizes, mainly because it is used to quantify the heterogeneity between the observed effect sizes. To reduce the influence of sample sizes, we introduce an alternative measure that aims to directly measure the heterogeneity between the study populations involved in the meta-analysis. We further propose a new estimator, namely the $I_A^2$ statistic, to estimate the newly defined measure of heterogeneity. For practical implementation, the exact formulas of the $I_A^2$ statistic are also derived under two common scenarios with the effect size as the mean difference (MD) or the standardized mean difference (SMD). Simulations and real data analysis demonstrate that the $I_A^2$ statistic provides an asymptotically unbiased estimator for the absolute heterogeneity between the study populations, and it is also independent of the study sample sizes as expected. To conclude, our newly defined $I_A^2$ statistic can be used as a supplemental measure of heterogeneity to monitor the situations where the study effect sizes are indeed similar with little biological difference. In such scenario, the fixed-effect model can be appropriate; nevertheless, when the sample sizes are sufficiently large, the $I^2$ statistic may still increase to 1 and subsequently suggest the random-effects model for meta-analysis.

stat.ME↗

arXiv2025

Distributed Reconstruction from Compressive Measurements: Nonconvexity and Heterogeneity

The compressive sensing (CS) and 1-bit CS demonstrate superior efficiency in signal acquisition and resource conservation, while 1-bit CS achieves maximum resource efficiency through sign-only measurements. With the emergence of massive data, the distributed signal aggregation under CS and 1-bit CS measurements introduces many challenges, including nonconvexity and heterogeneity. The nonconvexity originates from the unidentifiability of signal magnitude under finite-precision measurements. The heterogeneity arises from the signal and noisy measurement on each node. To address these challenges, we propose a framework with a squared cosine similarity penalty. We address nonconvexity by an novel invex relaxation formulation to ensure the uniqueness of the global optimality. For heterogeneous signals and noisy measurements, the proposed estimate adaptively debiases through correction guided by similarity and signal-to-noise ratio (SNR) information. Our method achieves a high probability minimax-optimal convergence rate under sufficient node counts and similarity conditions, improving from $O\{(p\log{p}/n_j)^{1/2}\}$ to $O\{(p\log{p}/N)^{1/2}+p^{1/2}/n_j\}$, with signal dimension $p$, local and total sizes $n_j$ and $N$. Extensive simulations validate the method's effectiveness and performance gains in reconstructing heterogeneous signals from 1-bit CS measurements. The proposed framework maintains applicability to CS measurements while reducing communication overhead in distributed setting.

stat.ME↗

arXiv2025

Efficient Distributed Learning over Decentralized Networks with Convoluted Support Vector Machine

This paper addresses the problem of efficiently classifying high-dimensional data over decentralized networks. Penalized support vector machines (SVMs) are widely used for high-dimensional classification tasks. However, the double nonsmoothness of the objective function poses significant challenges in developing efficient decentralized learning methods. Many existing procedures suffer from slow, sublinear convergence rates. To overcome this limitation, we consider a convolution-based smoothing technique for the nonsmooth hinge loss function. The resulting loss function remains convex and smooth. We then develop an efficient generalized alternating direction method of multipliers (ADMM) algorithm for solving penalized SVM over decentralized networks. Our theoretical contributions are twofold. First, we establish that our generalized ADMM algorithm achieves provable linear convergence with a simple implementation. Second, after a sufficient number of ADMM iterations, the final sparse estimator attains near-optimal statistical convergence and accurately recovers the true support of the underlying parameters. Extensive numerical experiments on both simulated and real-world datasets validate our theoretical findings.

stat.ML↗

arXiv2025

Statistical inference for high-dimensional convoluted rank regression

High-dimensional penalized rank regression is a powerful tool for modeling high-dimensional data due to its robustness and estimation efficiency. However, the non-smoothness of the rank loss brings great challenges to the computation. To solve this critical issue, high-dimensional convoluted rank regression has been recently proposed, introducing penalized convoluted rank regression estimators. However, these developed estimators cannot be directly used to make inference. In this paper, we investigate the statistical inference problem of high-dimensional convoluted rank regression. The use of U-statistic in convoluted rank loss function presents challenges for the analysis. We begin by establishing estimation error bounds of the penalized convoluted rank regression estimators under weaker conditions on the predictors. Building on this, we further introduce a debiased estimator and provide its Bahadur representation. Subsequently, a high-dimensional Gaussian approximation for the maximum deviation of the debiased estimator is derived, which allows us to construct simultaneous confidence intervals. For implementation, a novel bootstrap procedure is proposed and its theoretical validity is also established. Finally, simulation and real data analysis are conducted to illustrate the merits of our proposed methods.

stat.ME↗

arXiv2024

Distributed Estimation and Gap-Free Analysis of Canonical Correlations

Massive data analysis calls for distributed algorithms and theories. We design a multi-round distributed algorithm for canonical correlation analysis. We construct principal directions through the convex formulation of canonical correlation analysis and use the shift-and-invert preconditioning iteration to expedite the convergence rate. This distributed algorithm is communication-efficient. The resultant estimate achieves the same convergence rate as if all observations were pooled together, but does not impose stringent restrictions on the number of machines. We take a gap-free analysis to bypass the widely used yet unrealistic assumption of an explicit gap between the successive canonical correlations in the canonical correlation analysis. Extensive simulations and applications to three benchmark image data are conducted to demonstrate the empirical performance of our proposed algorithms and theories.

stat.CO↗

arXiv2024

Non-hermitian magnonic knobbing between electromagnetically induced reflection and transparancy

Manipulation of wave propagation through open resonant systems has attracted tremendous interest. When accessible to the open system, the system under study is prone to tempering to out of equilibrium, and a lack of reciprocity is the rule rather than the exception. Open systems correspond to non-hermitian Hamiltonians with very unique properties such as resulting exceptional points and ideal isolation. Here, we have found a highly sensitive modulation for the intersection of resonant patch antennas with respect to cavity magnonic coupling by means of an open coupling system of three resonant modes. Two types of crossings are implemented in this study: the first type of crossing remotely controls the sharp switching of the transmission line 's transmittance, while regulating the repulsive behavior of its zero-reflection states. The second type of crossing corresponds to the modulation of non-reciprocal phase transitions, which enables a more desirable isolation effect. Three different coupling models are realized by a non-Hermitian scattering Hamiltonian, revealing distinct spatial overlaps between modes. This elucidates that dissipative coupling of at least two modes to the environment is crucial for non-reciprocal transport. Our work not only reveals the versatility of cavity magnonic systems but also provides a way to design functional devices for general wave optics using patch antenna crossings.

physics.app-ph↗

arXiv2024

Reducing multivariate independence testing to two bivariate means comparisons

Testing for independence between two random vectors is a fundamental problem in statistics. It is observed from empirical studies that many existing omnibus consistent tests may not work well for some strongly nonmonotonic and nonlinear relationships. To explore the reasons behind this issue, we novelly transform the multivariate independence testing problem equivalently into checking the equality of two bivariate means. An important observation we made is that the power loss is mainly due to cancellation of positive and negative terms in dependence metrics, making them very close to zero. Motivated by this observation, we propose a class of consistent metrics with a positive integer $γ$ that exactly characterize independence. Theoretically, we show that the metrics with even and infinity $γ$ can effectively avoid the cancellation, and have high powers under the alternatives that two mean differences offset each other. Since we target at a wide range of dependence scenarios in practice, we further suggest to combine the p-values of test statistics with different $γ$'s through the Fisher's method. We illustrate the advantages of our proposed tests through extensive numerical studies.

stat.ME↗

arXiv2023

RKHS-based Latent Position Random Graph Correlation

In this article, we consider the problem of testing whether two latent position random graphs are correlated. We propose a test statistic based on the kernel method and introduce the estimation procedure based on the spectral decomposition of adjacency matrices. Even if no kernel function is specified, the sample graph covariance based on our proposed estimation method will converge to the population version. The asymptotic distribution of the sample covariance can also be obtained. We design a procedure for testing independence under permutation tests and demonstrate that our proposed test statistic is consistent and valid. Our estimation method can be extended to the spectral decomposition of normalized Laplacian matrices and inhomogeneous random graphs. Our method achieves promising results on both simulated and real data.

stat.ME↗

arXiv2022

Enhancing and Dissecting Crowd Counting By Synthetic Data

In this article, we propose a simulated crowd counting dataset CrowdX, which has a large scale, accurate labeling, parameterized realization, and high fidelity. The experimental results of using this dataset as data enhancement show that the performance of the proposed streamlined and efficient benchmark network ESA-Net can be improved by 8.4\%. The other two classic heterogeneous architectures MCNN and CSRNet pre-trained on CrowdX also show significant performance improvements. Considering many influencing factors determine performance, such as background, camera angle, human density, and resolution. Although these factors are important, there is still a lack of research on how they affect crowd counting. Thanks to the CrowdX dataset with rich annotation information, we conduct a large number of data-driven comparative experiments to analyze these factors. Our research provides a reference for a deeper understanding of the crowd counting problem and puts forward some useful suggestions in the actual deployment of the algorithm.

cs.CV↗

arXiv2022

BBA-net: A bi-branch attention network for crowd counting

In the field of crowd counting, the current mainstream CNN-based regression methods simply extract the density information of pedestrians without finding the position of each person. This makes the output of the network often found to contain incorrect responses, which may erroneously estimate the total number and not conducive to the interpretation of the algorithm. To this end, we propose a Bi-Branch Attention Network (BBA-NET) for crowd counting, which has three innovation points. i) A two-branch architecture is used to estimate the density information and location information separately. ii) Attention mechanism is used to facilitate feature extraction, which can reduce false responses. iii) A new density map generation method combining geometric adaptation and Voronoi split is introduced. Our method can integrate the pedestrian's head and body information to enhance the feature expression ability of the density map. Extensive experiments performed on two public datasets show that our method achieves a lower crowd counting error compared to other state-of-the-art methods.

cs.CV↗

arXiv2019

Penalized Interaction Estimation for Ultrahigh Dimensional Quadratic Regression

Quadratic regression goes beyond the linear model by simultaneously including main effects and interactions between the covariates. The problem of interaction estimation in high dimensional quadratic regression has received extensive attention in the past decade. In this article we introduce a novel method which allows us to estimate the main effects and interactions separately. Unlike existing methods for ultrahigh dimensional quadratic regressions, our proposal does not require the widely used heredity assumption. In addition, our proposed estimates have explicit formulas and obey the invariance principle at the population level. We estimate the interactions of matrix form under penalized convex loss function. The resulting estimates are shown to be consistent even when the covariate dimension is an exponential order of the sample size. We develop an efficient ADMM algorithm to implement the penalized estimation. This ADMM algorithm fully explores the cheap computational cost of matrix multiplication and is much more efficient than existing penalized methods such as all pairs LASSO. We demonstrate the promising performance of our proposal through extensive numerical studies.

stat.ME↗

arXiv2018

Model-Free Conditional Feature Screening with Exposure Variables

In high dimensional analysis, effects of explanatory variables on responses sometimes rely on certain exposure variables, such as time or environmental factors. In this paper, to characterize the importance of each predictor, we utilize its conditional correlation given exposure variables with the empirical distribution function of response. A model-free conditional screening method is subsequently advocated based on this idea, aiming to identify significant predictors whose effects may vary with the exposure variables. The proposed screening procedure is applicable to any model form, including that with heteroscedasticity where the variance component may also vary with exposure variables. It is also robust to extreme values or outlier. Under some mild conditions, we establish the desirable sure screening and the ranking consistency properties of the screening method. The finite sample performances are illustrated by simulation studies and an application to the breast cancer dataset.

stat.ME↗

arXiv2017

Robust Decoding from 1-Bit Compressive Sampling with Least Squares

In 1-bit compressive sensing (1-bit CS) where target signal is coded into a binary measurement, one goal is to recover the signal from noisy and quantized samples. Mathematically, the 1-bit CS model reads: $y = \eta \odot\textrm{sign} (\Psi x^* + \epsilon)$, where $x^{*}\in \mathcal{R}^{n}, y\in \mathcal{R}^{m}$, $\Psi \in \mathcal{R}^{m\times n}$, and $\epsilon$ is the random error before quantization and $\eta\in \mathcal{R}^{n}$ is a random vector modeling the sign flips. Due to the presence of nonlinearity, noise and sign flips, it is quite challenging to decode from the 1-bit CS. In this paper, we consider least squares approach under the over-determined and under-determined settings. For $m>n$, we show that, up to a constant $c$, with high probability, the least squares solution $x_{\textrm{ls}}$ approximates $ x^*$ with precision $\delta$ as long as $m \geq\widetilde{\mathcal{O}}(\frac{n}{\delta^2})$. For $m< n$, we prove that, up to a constant $c$, with high probability, the $\ell_1$-regularized least-squares solution $x_{\ell_1}$ lies in the ball with center $x^*$ and radius $\delta$ provided that $m \geq \mathcal{O}( \frac{s\log n}{\delta^2})$ and $\|x^*\|_0 := s < m$. We introduce a Newton type method, the so-called primal and dual active set (PDAS) algorithm, to solve the nonsmooth optimization problem. The PDAS possesses the property of one-step convergence. It only requires to solve a small least squares problem on the active set. Therefore, the PDAS is extremely efficient for recovering sparse signals through continuation. We propose a novel regularization parameter selection rule which does not introduce any extra computational overhead. Extensive numerical experiments are presented to illustrate the robustness of our proposed model and the efficiency of our algorithm.

math.NA↗