arXiv subjects

Xueqin Wang

Publications and source records attributed to Xueqin Wang.

At least 19 recordsLinked to original sources

arXiv2026

Elimination Geometry

This monograph develops elimination geometry (EG), a typed, native-loss, audit-oriented framework for studying when locally optimal objects can be realized by a shared deployment rule. Elimination and compression may erase distinctions required by prediction, inference, control, or representation. EG asks which distinctions are lost, whether the induced defect is visible to the declared task, and whether changing information, architecture, action space, or deployment domain can repair it. EG separates local solvability, global realizability, and finite-sample certifiability. It derives native defects from the original objective and distinguishes architecture obstruction from model approximation, generalization, and implementation error. The monograph synthesizes tools from geometry, optimization, information theory, statistics, and machine learning into interfaces for integrability, representation admissibility, resource constraints, observational overlap, and common deployment. Formal results address regular, coordination, singular, compositional, and resource-limited mechanisms with explicit antecedents and claim boundaries. Applications include sparse model selection, distribution-free prediction, observational treatment policies, routed expert and retrieval systems, and learned score fields. Obstruction-Aware Learning and Inference links structural diagnosis to finite-data authorization, mechanism-matched intervention, and independent validation. Reproducible synthetic and real-data studies illustrate how certificates can guide architecture repair while recording failed gates and unresolved cases. The framework requires the deployment contract, native endpoint, competing explanations, information and compute budgets, and validation rule to be fixed before a persistent performance floor is attributed to architecture.

cs.LG↗

arXiv2026

Identification of Genetic Factors Associated with Corpus Callosum Morphology: Conditional Strong Independence Screening for Non-Euclidean Responses

The corpus callosum, the largest white matter structure in the brain, plays a critical role in interhemispheric communication. Variations in its morphology are associated with various neurological and psychological conditions, making it a key focus in neurogenetics. Age is known to influence the structure and morphology of the corpus callosum significantly, complicating the identification of specific genetic factors that contribute to its shape and size. We propose a conditional strong independence screening method to address these challenges for ultrahigh-dimensional predictors and non-Euclidean responses. Our approach incorporates prior knowledge, such as age. It introduces a novel concept of conditional metric dependence, quantifying non-linear conditional dependencies among random objects in metric spaces without relying on predefined models. We apply this framework to identify genetic factors associated with the morphology of the corpus callosum. Simulation results demonstrate the efficacy of this method across various non-Euclidean data types, highlighting its potential to drive genetic discovery in neuroscience.

stat.AP↗

arXiv2026

Sparsity-Constraint Optimization via Splicing Iteration

Sparsity-constrained optimization underlies many problems in signal processing, statistics, and machine learning. State-of-the-art hard-thresholding (HT) algorithms rely on an appropriately selected continuous step-size parameter to ensure convergence. In this paper, we propose a naturally convergent iterative algorithm, SCOPE (Sparsity-Constrained Optimization via sPlicing itEration). The algorithm is capable of optimizing nonlinear differentiable objective functions that are strongly convex and smooth on low-dimensional subspaces. SCOPE replaces the gradient step with a splicing operation guided directly by the objective value, thereby eliminating the need to tune any continuous hyperparameter. Theoretically, it achieves a linear convergence rate and recovers the true support set when the sparsity level is correctly specified. We also establish parallel theoretical results without relying on restricted-isometry-property-type conditions. We apply SCOPE's versatility and power to solve sparse quadratic optimization, learn sparse classifiers, and recover sparse Markov networks for binary variables. With our C++ implementation of SCOPE, numerical experiments on these tasks show that it achieves superior support recovery performance, confirming both its algorithmic efficiency and theoretical guarantees.

stat.ML↗

arXiv2026

Nearly Optimal Subdata Selection

When, in terms of the number of data points, the size of a dataset exceeds available computing resources, or when labeling is expensive, an attractive solution consists of selecting only some of the data points (subdata) for further consideration. A central question for selecting subdata of size $n$ from $N$ available data points is which $n$ points to select. While an answer to this question depends on the objective, one approach for a parametric model and a focus on parameter estimation is to select subdata that retains maximal information. Identifying such subdata is a classical NP-hard problem due to its inherent discreteness. Based on optimal approximate design theory, we develop a new methodology for information-based subdata selection, resulting in subdata that approaches the optimal solution. To achieve this, we develop a novel algorithm that applies to a general model, accommodates arbitrary choices of $N$ and $n$, and supports multiple optimality criteria, and we prove its convergence. Moreover, the new methodology facilitates an assessment of the efficiency of subdata selected by any method by obtaining tight lower and upper bounds for the efficiency. We show that the subdata obtained through the new methodology is highly efficient and outperforms all existing methods.

stat.ME↗

arXiv2026

Communication-Efficient Decentralized Optimization via Double-Communication Symmetric ADMM

This paper focuses on decentralized composite optimization over networks without a central coordinator. We propose a novel decentralized symmetric ADMM algorithm that incorporates multiple communication rounds within each iteration, derived from a new constraint formulation that enables information exchange beyond immediate neighbors. While increasing per-iteration communication, our approach significantly reduces the total number of iterations and overall com- munication cost. We further design optimal communication rules that minimize the number of rounds and variables transmitted per iteration. The proposed algorithm is shown to achieve linear convergence under standard and relatively weak assumptions (e.g., metric subregularity). Extensive experiments on regression and classification tasks validate the theoretical results and demonstrate superior performance compared to existing decentralized optimization methods.

math.OC↗

arXiv2026

Sparse Equation Matching: A Derivative-Free Learning for General-Order Dynamical Systems

Equation discovery is a fundamental learning task for uncovering the underlying dynamics of complex systems, with wide-ranging applications in areas such as brain connectivity analysis, climate modeling, gene regulation, and physical simulation. However, many existing approaches rely on accurate derivative estimation and are limited to first-order dynamical systems, restricting their applicability in real-world scenarios. In this work, we propose Sparse Equation Matching (SEM), a unified framework that encompasses several existing equation discovery methods under a common formulation. SEM introduces an integral-based sparse regression approach using Green's functions, enabling derivative-free estimation of differential operators and their associated driving functions in general-order dynamical systems. The effectiveness of SEM is demonstrated through extensive simulations, benchmarking its performance against derivative-based approaches. We then apply SEM to electroencephalographic (EEG) data recorded during multiple oculomotor tasks, collected from 52 participants in a brain-computer interface experiment. Our method identifies active brain regions across participants and reveals task-specific connectivity patterns. These findings offer valuable insights into brain connectivity and the underlying neural mechanisms.

cs.LG↗

arXiv2026

Green's matching: an efficient approach to parameter estimation in complex dynamic systems

Parameters of differential equations are essential to characterize intrinsic behaviors of dynamic systems. Numerous methods for estimating parameters in dynamic systems are computationally and/or statistically inadequate, especially for complex systems with general-order differential operators, such as motion dynamics. This article presents Green's matching, a computationally tractable and statistically efficient two-step method, which only needs to approximate trajectories in dynamic systems but not their derivatives due to the inverse of differential operators by Green's function. This yields a statistically optimal guarantee for parameter estimation in general-order equations, a feature not shared by existing methods, and provides an efficient framework for broad statistical inferences in complex dynamic systems.

stat.ME↗

arXiv2025

Reconstruct Ising Model with Global Optimality via SLIDE

The reconstruction of interaction networks between random events is a critical problem arising from statistical physics and politics, sociology, biology, psychology, and beyond. The Ising model lays the foundation for this reconstruction process, but finding the underlying Ising model from the least amount of observed samples in a computationally efficient manner has been historically challenging for half a century. Using sparsity learning, we present an approach named SLIDE whose sample complexity is globally optimal. Furthermore, an algorithm is developed to give a statistically consistent solution of SLIDE in polynomial time with high probability. On extensive benchmarked cases, the SLIDE approach demonstrates dominant performance in reconstructing underlying Ising models, confirming its superior statistical properties. The application on the U.S. senators voting in the six congresses reveals that both the Republicans and Democrats noticeably assemble in each congress; interestingly, the assembling of Democrats is particularly pronounced in the latest congress.

stat.ME↗

arXiv2025

A Consistent and Scalable Algorithm for Best Subset Selection in Single Index Models

Analysis of high-dimensional data has led to increased interest in both single index models (SIMs) and the best-subset selection. SIMs provide an interpretable and flexible modeling framework for high-dimensional data, while the best-subset selection aims to find a sparse model from a large set of predictors. However, the best-subset selection in high-dimensional models is known to be computationally intractable. Existing proxy algorithms are appealing but do not yield the bestsubset solution. In this paper, we directly tackle the intractability by proposing a provably scalable algorithm for the best-subset selection in high-dimensional SIMs. We directly proved the subset selection consistency and oracle property for our algorithmic solution, distinguishing it from other state-of-the-art support recovery methods in SIMs. The algorithm comprises a generalized information criterion to determine the support size of the regression coefficients, eliminating the model selection tuning. Moreover, our method does not assume an error distribution or a specific link function and hence is flexible to apply. Extensive simulation results demonstrate that our method is not only computationally efficient but also able to exactly recover the best subset in various settings (e.g., linear regression, Poisson regression, heteroscedastic models).

stat.ML↗

arXiv2025

DeepSuM: Deep Sufficient Modality Learning Framework

Multimodal learning has become a pivotal approach in developing robust learning models with applications spanning multimedia, robotics, large language models, and healthcare. The efficiency of multimodal systems is a critical concern, given the varying costs and resource demands of different modalities. This underscores the necessity for effective modality selection to balance performance gains against resource expenditures. In this study, we propose a novel framework for modality selection that independently learns the representation of each modality. This approach allows for the assessment of each modality's significance within its unique representation space, enabling the development of tailored encoders and facilitating the joint analysis of modalities with distinct characteristics. Our framework aims to enhance the efficiency and effectiveness of multimodal learning by optimizing modality integration and selection.

cs.LG↗

arXiv2025

Rethinking Hard Thresholding Pursuit: Full Adaptation and Sharp Estimation

Hard Thresholding Pursuit (HTP) has aroused increasing attention for its robust theoretical guarantees and impressive numerical performance in non-convex optimization. In this paper, we introduce a novel tuning-free procedure, named Full-Adaptive HTP (FAHTP), that simultaneously adapts to both the unknown sparsity and signal strength of the underlying model. We provide an in-depth analysis of the iterative thresholding dynamics of FAHTP, offering refined theoretical insights. In specific, under the beta-min condition $\min_{i \in S^*}|{\boldsymbolβ}^*_i| \ge Cσ(\log p/n)^{1/2}$, we show that the FAHTP achieves oracle estimation rate $σ(s^*/n)^{1/2}$, highlighting its theoretical superiority over convex competitors such as LASSO and SLOPE, and recovers the true support set exactly. More importantly, even without the beta-min condition, our method achieves a tighter error bound than the classical minimax rate with high probability. The comprehensive numerical experiments substantiate our theoretical findings, underscoring the effectiveness and robustness of the proposed FAHTP.

math.ST↗

arXiv2024

Studentized Tests of Independence: Random-Lifter approach

The exploration of associations between random objects with complex geometric structures has catalyzed the development of various novel statistical tests encompassing distance-based and kernel-based statistics. These methods have various strengths and limitations. One problem is that their test statistics tend to converge to asymptotic null distributions involving second-order Wiener chaos, which are hard to compute and need approximation or permutation techniques that use much computing power to build rejection regions. In this work, we take an entirely different and novel strategy by using the so-called ``Random-Lifter''. This method is engineered to yield test statistics with the standard normal limit under null distributions without the need for sample splitting. In other words, we set our sights on having simple limiting distributions and finding the proper statistics through reverse engineering. We use the Central Limit Theorems (CLTs) for degenerate U-statistics derived from our novel association measures to do this. As a result, the asymptotic distributions of our proposed tests are straightforward to compute. Our test statistics also have the minimax property. We further substantiate that our method maintains competitive power against existing methods with minimal adjustments to constant factors. Both numerical simulations and real-data analysis corroborate the efficacy of the Random-Lifter method.

stat.ME↗

arXiv2024

skscope: Fast Sparsity-Constrained Optimization in Python

Applying iterative solvers on sparsity-constrained optimization (SCO) requires tedious mathematical deduction and careful programming/debugging that hinders these solvers' broad impact. In the paper, the library skscope is introduced to overcome such an obstacle. With skscope, users can solve the SCO by just programming the objective function. The convenience of skscope is demonstrated through two examples in the paper, where sparse linear regression and trend filtering are addressed with just four lines of code. More importantly, skscope's efficient implementation allows state-of-the-art solvers to quickly attain the sparse solution regardless of the high dimensionality of parameter space. Numerical experiments reveal the available solvers in skscope can achieve up to 80x speedup on the competing relaxation solutions obtained via the benchmarked convex solver. skscope is published on the Python Package Index (PyPI) and Conda, and its source code is available at: https://github.com/abess-team/skscope.

stat.ML↗

arXiv2024

Minimax and Communication-Efficient Distributed Best Subset Selection with Oracle Property

The explosion of large-scale data in fields such as finance, e-commerce, and social media has outstripped the processing capabilities of single-machine systems, driving the need for distributed statistical inference methods. Traditional approaches to distributed inference often struggle with achieving true sparsity in high-dimensional datasets and involve high computational costs. We propose a novel, two-stage, distributed best subset selection algorithm to address these issues. Our approach starts by efficiently estimating the active set while adhering to the $\ell_0$ norm-constrained surrogate likelihood function, effectively reducing dimensionality and isolating key variables. A refined estimation within the active set follows, ensuring sparse estimates and matching the minimax $\ell_2$ error bound. We introduce a new splicing technique for adaptive parameter selection to tackle subproblems under $\ell_0$ constraints and a Generalized Information Criterion (GIC). Our theoretical and numerical studies show that the proposed algorithm correctly finds the true sparsity pattern, has the oracle property, and greatly lowers communication costs. This is a big step forward in distributed sparse estimation.

stat.ML↗

arXiv2024

Reconstructing and Forecasting Marine Dynamic Variable Fields across Space and Time Globally and Gaplessly

Spatiotemporal projections in marine science are essential for understanding ocean systems and their impact on Earth's climate. However, existing AI-based and statistics-based inversion methods face challenges in leveraging ocean data, generating continuous outputs, and incorporating physical constraints. We propose the Marine Dynamic Reconstruction and Forecast Neural Networks (MDRF-Net), which integrates marine physical mechanisms and observed data to reconstruct and forecast continuous ocean temperature-salinity and dynamic fields. MDRF-Net leverages statistical theories and techniques, incorporating parallel neural network sharing initial layer, two-step training strategy, and ensemble methodology, facilitating in exploring challenging marine areas like the Arctic zone. We have theoretically justified the efficacy of our ensemble method and the rationality of it by providing an upper bound on its generalization error.The effectiveness of MDRF-Net's is validated through a comprehensive simulation study, which highlights its capability to reliably estimate unknown parameters. Comparison with other inversion methods and reanalysis data are also conducted, and the global test error is 0.455°C for temperature and 0.0714psu for salinity. Overall, MDRF-Net effectively learns the ocean dynamics system using physical mechanisms and statistical insights, contributing to a deeper understanding of marine systems and their impact on the environment and human use of the ocean.

stat.AP↗

arXiv2024

Quantiles, Ranks and Signs in Metric Spaces

Non-Euclidean data become more prevalent in practice, necessitating the development of a framework for statistical inference analogous to that for Euclidean data. Quantile is one of the most important concepts in traditional statistical inference; we introduce the counterpart, both locally and globally, for data objects in metric spaces. This is realized by expanding upon the metric distribution function proposed by Wang et al. (2021). Rank and sign are defined at local and global levels as a natural consequence of the center-outward ordering of metric spaces brought about by the local and global quantiles. The theoretical properties are established, such as the root-$n$ consistency and uniform consistency of the local and global empirical quantiles and the distribution-freeness of ranks and signs. The empirical metric median, which is defined here as the 0th empirical global metric quantile, is proven to be resistant to contamination by means of both theoretical and numerical approaches. Quantiles have been shown to be valuable through extensive simulations in a number of metric spaces. Moreover, we introduce a family of fast rank-based independence tests for a generic metric space. Monte Carlo experiments show good finite-sample performance of the test.

math.ST↗

arXiv2023

The impact of spatio-temporal travel distance on epidemics using an interpretable attention-based sequence-to-sequence model

Amidst the COVID-19 pandemic, travel restrictions have emerged as crucial interventions for mitigating the spread of the virus. In this study, we enhance the predictive capabilities of our model, Sequence-to-Sequence Epidemic Attention Network (S2SEA-Net), by incorporating an attention module, allowing us to assess the impact of distinct classes of travel distances on epidemic dynamics. Furthermore, our model provides forecasts for new confirmed cases and deaths. To achieve this, we leverage daily data on population movement across various travel distance categories, coupled with county-level epidemic data in the United States. Our findings illuminate a compelling relationship between the volume of travelers at different distance ranges and the trajectories of COVID-19. Notably, a discernible spatial pattern emerges with respect to these travel distance categories on a national scale. We unveil the geographical variations in the influence of population movement at different travel distances on the dynamics of epidemic spread. This will contribute to the formulation of strategies for future epidemic prevention and public health policies.

physics.soc-ph↗

arXiv2023

Regionalization of China's PM2.5 through Robust Spatio temporal Functional Clustering Method

The patterns of particulate matter with diameters that are generally 2.5 micrometers and smaller (PM2.5) are heterogeneous in China nationwide but can be homogeneous region-wide. To reduce the adverse effects from PM2.5, policymakers need to develop location-specific regulations based on nationwide clustering analysis of PM2.5 concentrations. However, such an analysis is challenging because the data have complex structures and are usually noisy. In this study, we propose a robust clustering framework using a novel concept of depth, which can handle both magnitude and shape outliers effectively and incorporate spatial information. We apply this framework to a PM2.5 dataset and reveal ten regions in China that have distinct PM2.5 patterns, and the homogeneity within each cluster is also confirmed. The clusters have clearly visible boundaries and enable policymakers to develop local emission control policies and establish regional collaborative systems to control air pollution in China.

stat.AP↗