Junhui Wang

Haoran Zhang, Junhui Wang

Longitudinal network consists of a sequence of temporal edges among multiple nodes, where the temporal edges are observed in real time. It has become ubiquitous with the rise of online social platform and e-commerce, but largely under-investigated in literature. In this paper, we propose an efficient estimation framework for longitudinal network, leveraging strengths of adaptive network merging, tensor decomposition and point process. It merges neighboring sparse networks so as to enlarge the number of observed edges and reduce estimation variance, whereas the estimation bias introduced by network merging is controlled by exploiting local temporal structures for adaptive network neighborhood. A projected gradient descent algorithm is proposed to facilitate estimation, where the upper bound of the estimation error in each iteration is established. A thorough analysis is conducted to quantify the asymptotic behavior of the proposed method, which shows that it can significantly reduce the estimation error and also provides guideline for network merging under various scenarios. We further demonstrate the advantage of the proposed method through extensive numerical experiments on synthetic datasets and a militarized interstate dispute dataset.

Haoran Zhang, Junhui Wang

Signed networks are frequently observed in real life with additional sign information associated with each edge, yet such information has been largely ignored in existing network models. This paper develops a unified embedding model for signed networks to disentangle the intertwined balance structure and anomaly effect, which can greatly facilitate the downstream analysis, including community detection, anomaly detection, and network inference. The proposed model captures both balance structure and anomaly effect through a low rank plus sparse matrix decomposition, which are jointly estimated via a regularized formulation. Its theoretical guarantees are established in terms of asymptotic consistency and finite-sample probability bounds for network embedding, community detection and anomaly detection. The advantage of the proposed embedding model is also demonstrated through extensive numerical experiments on both synthetic networks and an international relation network.

Mingyang Ren, Yaoming Zhen, Junhui Wang

Tensor Gaussian graphical models (GGMs), interpreting conditional independence structures within tensor data, have important applications in numerous areas. Yet, the available tensor data in one single study is often limited due to high acquisition costs. Although relevant studies can provide additional data, it remains an open question how to pool such heterogeneous data. In this paper, we propose a transfer learning framework for tensor GGMs, which takes full advantage of informative auxiliary domains even when non-informative auxiliary domains are present, benefiting from the carefully designed data-adaptive weights. Our theoretical analysis shows substantial improvement of estimation errors and variable selection consistency on the target domain under much relaxed conditions, by leveraging information from auxiliary domains. Extensive numerical experiments are conducted on both synthetic tensor graphs and a brain functional connectivity network data, which demonstrates the satisfactory performance of the proposed method.

Dongjie Huo, Junhui Wang, Chao Gao et al.

Mobile robots operating in human-centered environments must generate not only collision-free paths but also trajectories that follow local behavioral conventions. Conventional costmap-based navigation emphasizes geometric feasibility and often overlooks such requirements, which can result in socially inappropriate behaviors. This paper presents NORM-Nav, a zero-shot framework that integrates natural language behavioral constraints into costmap-based planning. An LLM parses each instruction into structured constraints and grounds them using real-time vision--LiDAR perception. These constraints are encoded as multi-layer costmaps that represent geometric, semantic, directional, and velocity cues and are directly compatible with standard grid-based planners. Simulation and real-world experiments indicate that NORM-Nav improves task success rates and produces trajectories closer to human references than representative baselines. The project website is available at https://ei-nav.github.io/NORM-Nav.

Yang Liu, Xichou Zhu, Zhou Shen et al.

Large Language Models (LLMs) have recently displayed their extraordinary capabilities in language understanding. However, how to comprehensively assess the sentiment capabilities of LLMs continues to be a challenge. This paper investigates the ability of LLMs to detect and react to sentiment in text modal. As the integration of LLMs into diverse applications is on the rise, it becomes highly critical to comprehend their sensitivity to emotional tone, as it can influence the user experience and the efficacy of sentiment-driven tasks. We conduct a series of experiments to evaluate the performance of several prominent LLMs in identifying and responding appropriately to sentiments like positive, negative, and neutral emotions. The models' outputs are analyzed across various sentiment benchmarks, and their responses are compared with human evaluations. Our discoveries indicate that although LLMs show a basic sensitivity to sentiment, there are substantial variations in their accuracy and consistency, emphasizing the requirement for further enhancements in their training processes to better capture subtle emotional cues. Take an example in our findings, in some cases, the models might wrongly classify a strongly positive sentiment as neutral, or fail to recognize sarcasm or irony in the text. Such misclassifications highlight the complexity of sentiment analysis and the areas where the models need to be refined. Another aspect is that different LLMs might perform differently on the same set of data, depending on their architecture and training datasets. This variance calls for a more in-depth study of the factors that contribute to the performance differences and how they can be optimized.

Yang Liu, Xichou Zhu, Zhou Shen et al.

The recent advances in large language models (LLMs) have significantly expanded their applications across various fields such as language generation, summarization, and complex question answering. However, their application to privacy compliance and technical privacy reviews remains under-explored, raising critical concerns about their ability to adhere to global privacy standards and protect sensitive user data. This paper seeks to address this gap by providing a comprehensive case study evaluating LLMs' performance in privacy-related tasks such as privacy information extraction (PIE), legal and regulatory key point detection (KPD), and question answering (QA) with respect to privacy policies and data protection regulations. We introduce a Privacy Technical Review (PTR) framework, highlighting its role in mitigating privacy risks during the software development life-cycle. Through an empirical assessment, we investigate the capacity of several prominent LLMs, including BERT, GPT-3.5, GPT-4, and custom models, in executing privacy compliance checks and technical privacy reviews. Our experiments benchmark the models across multiple dimensions, focusing on their precision, recall, and F1-scores in extracting privacy-sensitive information and detecting key regulatory compliance points. While LLMs show promise in automating privacy reviews and identifying regulatory discrepancies, significant gaps persist in their ability to fully comply with evolving legal standards. We provide actionable recommendations for enhancing LLMs' capabilities in privacy compliance, emphasizing the need for robust model improvements and better integration with legal and regulatory requirements. This study underscores the growing importance of developing privacy-aware LLMs that can both support businesses in compliance efforts and safeguard user privacy rights.

Mingyang Ren, Xin He, Junhui Wang

Directed acyclic graph (DAG) has been widely employed to represent directional relationships among a set of collected nodes. Yet, the available data in one single study is often limited for accurate DAG reconstruction, whereas heterogeneous data may be collected from multiple relevant studies. It remains an open question how to pool the heterogeneous data together for better DAG structure reconstruction in the target study. In this paper, we first introduce a novel set of structural similarity measures for DAG and then present a transfer DAG learning framework by effectively leveraging information from auxiliary DAGs of different levels of similarities. Our theoretical analysis shows substantial improvement in terms of DAG reconstruction in the target study, even when no auxiliary DAG is overall similar to the target DAG, which is in sharp contrast to most existing transfer learning methods. The advantage of the proposed transfer DAG learning is also supported by extensive numerical experiments on both synthetic data and multi-site brain functional connectivity network data.

Changyu Liu, Yuling Jiao, Junhui Wang et al.

Wasserstein distributionally robust optimization (WDRO) strengthens statistical learning under model uncertainty by minimizing the local worst-case risk within a prescribed ambiguity set. Although WDRO has been extensively studied in parametric settings, its theoretical properties in nonparametric frameworks remain underexplored. This paper investigates WDRO for nonparametric regression. We first establish a structural distinction based on the order $k$ of the Wasserstein distance, showing that $k=1$ induces Lipschitz-type regularization, whereas $k > 1$ corresponds to gradient-norm regularization. To address model misspecification, we analyze the excess local worst-case risk, deriving non-asymptotic error bounds for estimators constructed using norm-constrained feedforward neural networks. This analysis is supported by new covering number and approximation bounds that simultaneously control both the function and its gradient. The proposed estimator achieves a convergence rate of $n^{-2β/(d+2β)}$ up to logarithmic factors, where $β$ depends on the target's smoothness and network parameters. This rate is shown to be minimax optimal under conditions commonly satisfied in high-dimensional settings. Moreover, these bounds on the excess local worst-case risk imply guarantees on the excess natural risk, ensuring robustness against any distribution within the ambiguity set. We show the framework's generality across regression and classification problems. Simulation studies and an application to the MNIST dataset further illustrate the estimator's robustness.

Jun Zhang, Jie Feng, Long Chen et al.

Multimodal large language models (MLLMs) have demonstrated powerful capabilities in general spatial understanding and reasoning. However, their fine-grained spatial understanding and reasoning capabilities in complex urban scenarios have not received significant attention in the fields of both research and industry. To fill this gap, we focus primarily on road markings as a typical example of fine-grained spatial elements under urban scenarios, given the essential role of the integrated road traffic network they form within cities. Around road markings and urban traffic systems, we propose RoadBench, a systematic benchmark that comprehensively evaluates MLLMs' fine-grained spatial understanding and reasoning capabilities using BEV and FPV image inputs. This benchmark comprises six tasks consisting of 9,121 strictly manually verified test cases. These tasks form a systematic evaluation framework that bridges understanding at local spatial scopes to global reasoning. They not only test MLLMs' capabilities in recognition, joint understanding, and reasoning but also assess their ability to integrate image information with domain knowledge. After evaluating 14 mainstream MLLMs, we confirm that RoadBench is a challenging benchmark for MLLMs while revealing significant shortcomings in existing MLLMs' fine-grained spatial understanding and reasoning capabilities within urban scenarios. In certain tasks, their performance even falls short of simple rule-based or random selection baselines. These findings, along with RoadBench itself, will contribute to the comprehensive advancement of spatial understanding capabilities for MLLMs. The benchmark code, example datasets, and raw evaluation results are available in the supplementary material.

Shirong Xu, Jingnan Zhang, Junhui Wang

Paired comparison data, where users evaluate items in pairs, play a central role in ranking and preference learning tasks. While ordinal comparison data intuitively offer richer information than binary comparisons, this paper challenges that conventional wisdom. We propose a general parametric framework for modeling ordinal paired comparisons without ties. The model adopts a generalized additive structure, featuring a link function that quantifies the preference difference between two items and a pattern function that governs the distribution over ordinal response levels. This framework encompasses classical binary comparison models as special cases, by treating binary responses as binarized versions of ordinal data. Within this framework, we show that binarizing ordinal data can significantly improve the accuracy of ranking recovery. Specifically, we prove that under the counting algorithm, the ranking error associated with binary comparisons exhibits a faster exponential convergence rate than that of ordinal data. Furthermore, we characterize a substantial performance gap between binary and ordinal data in terms of a signal-to-noise ratio (SNR) determined by the pattern function. We identify the pattern function that minimizes the SNR and maximizes the benefit of binarization. Extensive simulations and a real application on the MovieLens dataset further corroborate our theoretical findings.

Changyu Liu, Yuling Jiao, Junhui Wang et al.

We propose a general approach to evaluating the performance of robust estimators based on adversarial losses under misspecified models. We first show that adversarial risk is equivalent to the risk induced by a distributional adversarial attack under certain smoothness conditions. This ensures that the adversarial training procedure is well-defined. To evaluate the generalization performance of the adversarial estimator, we study the adversarial excess risk. Our proposed analysis method includes investigations on both generalization error and approximation error. We then establish non-asymptotic upper bounds for the adversarial excess risk associated with Lipschitz loss functions. In addition, we apply our general results to adversarial training for classification and regression problems. For the quadratic loss in nonparametric regression, we show that the adversarial excess risk bound can be improved over those for a general loss.

Wei Zhou, Xin He, Wei Zhong et al.

Directed acyclic graph (DAG) models are widely used to represent causal relationships among random variables in many application domains. This paper studies a special class of non-Gaussian DAG models, where the conditional variance of each node given its parents is a quadratic function of its conditional mean. Such a class of non-Gaussian DAG models are fairly flexible and admit many popular distributions as special cases, including Poisson, Binomial, Geometric, Exponential, and Gamma. To facilitate learning, we introduce a novel concept of topological layers, and develop an efficient DAG learning algorithm. It first reconstructs the topological layers in a hierarchical fashion and then recoveries the directed edges between nodes in different layers, which requires much less computational cost than most existing algorithms in literature. Its advantage is also demonstrated in a number of simulated examples, as well as its applications to two real-life datasets, including an NBA player statistics data and a cosmetic sales data collected by Alibaba.

Ruixuan Zhao, Xin He, Junhui Wang

Acyclic model, often depicted as a directed acyclic graph (DAG), has been widely employed to represent directional causal relations among collected nodes. In this article, we propose an efficient method to learn linear non-Gaussian DAG in high dimensional cases, where the noises can be of any continuous non-Gaussian distribution. This is in sharp contrast to most existing DAG learning methods assuming Gaussian noise with additional variance assumptions to attain exact DAG recovery. The proposed method leverages a novel concept of topological layer to facilitate the DAG learning. Particularly, we show that the topological layers can be exactly reconstructed in a bottom-up fashion, and the parent-child relations among nodes in each layer can also be consistently established. More importantly, the proposed method does not require the faithfulness or parental faithfulness assumption which has been widely assumed in the literature of DAG learning. Its advantage is also supported by the numerical comparison against some popular competitors in various simulated examples as well as a real application on the global spread of COVID-19.

Shaogao Lv, Xin He, Junhui Wang

This paper considers the partially functional linear model (PFLM) where all predictive features consist of a functional covariate and a high dimensional scalar vector. Over an infinite dimensional reproducing kernel Hilbert space, the proposed estimation for PFLM is a least square approach with two mixed regularizations of a function-norm and an $\ell_1$-norm. Our main task in this paper is to establish the minimax rates for PFLM under high dimensional setting, and the optimal minimax rates of estimation is established by using various techniques in empirical process theory for analyzing kernel classes. In addition, we propose an efficient numerical algorithm based on randomized sketches of the kernel matrix. Several numerical experiments are implemented to support our method and optimization strategy.

Yaoming Zhen, Junhui Wang

Conventional network data has largely focused on pairwise interactions between two entities, yet multi-way interactions among multiple entities have been frequently observed in real-life hypergraph networks. In this article, we propose a novel method for detecting community structure in general hypergraph networks, uniform or non-uniform. The proposed method introduces a null vertex to augment a non-uniform hypergraph into a uniform multi-hypergraph, and then embeds the multi-hypergraph in a low-dimensional vector space such that vertices within the same community are close to each other. The resultant optimization task can be efficiently tackled by an alternative updating scheme. The asymptotic consistencies of the proposed method are established in terms of both community detection and hypergraph estimation, which are also supported by numerical experiments on some synthetic and real-life hypergraph networks.

Long Feng, Junhui Wang

Most high-dimensional matrix recovery problems are studied under the assumption that the target matrix has certain intrinsic structures. For image data related matrix recovery problems, approximate low-rankness and smoothness are the two most commonly imposed structures. For approximately low-rank matrix recovery, the robust principal component analysis (PCA) is well-studied and proved to be effective. For smooth matrix problem, 2d fused Lasso and other total variation based approaches have played a fundamental role. Although both low-rankness and smoothness are key assumptions for image data analysis, the two lines of research, however, have very limited interaction. Motivated by taking advantage of both features, we in this paper develop a framework named projected robust PCA (PRPCA), under which the low-rank matrices are projected onto a space of smooth matrices. Consequently, a large class of image matrices can be decomposed as a low-rank and smooth component plus a sparse component. A key advantage of this decomposition is that the dimension of the core low-rank component can be significantly reduced. Consequently, our framework is able to address a problematic bottleneck of many low-rank matrix problems: singular value decomposition (SVD) on large matrices. Theoretically, we provide explicit statistical recovery guarantees of PRPCA and include classical robust PCA as a special case.

Xin He, Junhui Wang, Shaogao Lv

Variable selection is central to high-dimensional data analysis, and various algorithms have been developed. Ideally, a variable selection algorithm shall be flexible, scalable, and with theoretical guarantee, yet most existing algorithms cannot attain these properties at the same time. In this article, a three-step variable selection algorithm is developed, involving kernel-based estimation of the regression function and its gradient functions as well as a hard thresholding. Its key advantage is that it assumes no explicit model assumption, admits general predictor effects, allows for scalable computation, and attains desirable asymptotic sparsistency. The proposed algorithm can be adapted to any reproducing kernel Hilbert space (RKHS) with different kernel functions, and can be extended to interaction selection with slight modification. Its computational cost is only linear in the data dimension, and can be further improved through parallel computing. The sparsistency of the proposed algorithm is established for general RKHS under mild conditions, including linear and Gaussian kernels as special cases. Its effectiveness is also supported by a variety of simulated and real examples.

Junhui Wang

Multivariate regression model is a natural generalization of the classical univari- ate regression model for fitting multiple responses. In this paper, we propose a high- dimensional multivariate conditional regression model for constructing sparse estimates of the multivariate regression coefficient matrix that accounts for the dependency struc- ture among the multiple responses. The proposed method decomposes the multivariate regression problem into a series of penalized conditional log-likelihood of each response conditioned on the covariates and other responses. It allows simultaneous estimation of the sparse regression coefficient matrix and the sparse inverse covariance matrix. The asymptotic selection consistency and normality are established for the diverging dimension of the covariates and number of responses. The effectiveness of the pro- posed method is also demonstrated in a variety of simulated examples as well as an application to the Glioblastoma multiforme cancer data.

Yixin Fang, Junhui Wang, Wei Sun

Recently, many regularized procedures have been proposed for variable selection in linear regression, but their performance depends on the tuning parameter selection. Here a criterion for the tuning parameter selection is proposed, which combines the strength of both stability selection and cross-validation and therefore is referred as the prediction and stability selection (PASS). The selection consistency is established assuming the data generating model is a subset of the full model, and the small sample performance is demonstrated through some simulation studies where the assumption is either held or violated.

Tu Xu, Junhui Wang

Conventional multiclass conditional probability estimation methods, such as Fisher's discriminate analysis and logistic regression, often require restrictive distributional model assumption. In this paper, a model-free estimation method is proposed to estimate multiclass conditional probability through a series of conditional quantile regression functions. Specifically, the conditional class probability is formulated as difference of corresponding cumulative distribution functions, where the cumulative distribution functions can be converted from the estimated conditional quantile regression functions. The proposed estimation method is also efficient as its computation cost does not increase exponentially with the number of classes. The theoretical and numerical studies demonstrate that the proposed estimation method is highly competitive against the existing competitors, especially when the number of classes is relatively large.

Wei Sun, Junhui Wang, Yixin Fang

Penalized regression models are popularly used in high-dimensional data analysis to conduct variable selection and model fitting simultaneously. Whereas success has been widely reported in literature, their performances largely depend on the tuning parameters that balance the trade-off between model fitting and model sparsity. Existing tuning criteria mainly follow the route of minimizing the estimated prediction error or maximizing the posterior model probability, such as cross-validation, AIC and BIC. This article introduces a general tuning parameter selection criterion based on a novel concept of variable selection stability. The key idea is to select the tuning parameters so that the resultant penalized regression model is stable in variable selection. The asymptotic selection consistency is established for both fixed and diverging dimensions. The effectiveness of the proposed criterion is also demonstrated in a variety of simulated examples as well as an application to the prostate cancer data.