arXiv subjects

Tianxi Li

Publications and source records attributed to Tianxi Li.

At least 19 recordsLinked to original sources

arXiv2026

Nonparametric estimation of time-varying network connections by multi-stage smoothing

We consider the problem of estimating the underlying edge probabilities of a time-varying network observed at multiple time points. The probability structure is represented by a time-varying graphon that satisfies temporal Hölder smoothness and piecewise Lipschitz conditions in the latent variables. We propose a multi-stage smoothing estimator that first applies temporal local smoothing to each edge and then performs node-domain smoothing using a data-driven neighborhood construction adapted from the method. An additional temporal smoothing step is introduced as an optional refinement when uniform accuracy over the entire time domain is required. Simulation studies demonstrate the benefits of combining temporal and node-domain smoothing under different generative models. We also apply the method to a real time-varying network dataset and show that it captures both smooth temporal evolution and structural patterns in the connectivity.

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arXiv2026

Multivariate Inference of Network Moments by Subsampling

Network moments--rescaled counts of motifs such as stars and triangles--are fundamental summaries of network structure, widely used in goodness-of-fit testing, model selection, and network comparison. While the univariate distribution of a single network moment can be approximated by subsampling, the consistency of subsampling for their {\it joint} distribution has remained unestablished. In this paper, we prove that node subsampling provides an asymptotically accurate approximation of the joint distribution of multiple network moments under a general sparse graphon model. The theoretical analysis requires a careful characterization of the dependence structure among network moments and the corresponding multivariate asymptotic convergence, going substantially beyond existing univariate results. Building on this foundation, we address a practically important open problem: two-sample testing between unmatchable networks with unequal edge densities. We propose a novel subsampling-based procedure that combines {\it sparsification} with a {\it sample-splitting} strategy. This yields the first subsampling-based inferential procedure valid for this setting, to our knowledge. We demonstrate the utility of multivariate subsampling inference through simulation studies and a real data application comparing coexpression networks of core and non-core genes in a study of parallel adaptation in Trinidadian guppies, where joint and conditional moment distributions reveal a structural difference that no marginal test can detect.

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arXiv2026

AgentDS Technical Report: Benchmarking the Future of Human-AI Collaboration in Domain-Specific Data Science

Data science plays a critical role in transforming complex data into actionable insights across numerous domains. Recent developments in large language models (LLMs) and artificial intelligence (AI) agents have significantly automated data science workflow. However, it remains unclear to what extent AI agents can match the performance of human experts on domain-specific data science tasks, and in which aspects human expertise continues to provide advantages. We introduce AgentDS, a benchmark and competition designed to evaluate both AI agents and human-AI collaboration performance in domain-specific data science. AgentDS consists of 17 challenges across six industries: commerce, food production, healthcare, insurance, manufacturing, and retail banking. We conducted an open competition involving 29 teams and 80 participants, enabling systematic comparison between human-AI collaborative approaches and AI-only baselines. Our results show that current AI agents struggle with domain-specific reasoning. AI-only baselines perform below the top quartile of competition participants, while the strongest solutions arise from human-AI collaboration. These findings challenge the narrative of complete automation by AI and underscore the enduring importance of human expertise in data science, while illuminating directions for the next generation of AI. Visit the AgentDS website here: https://agentds.org/ and open source datasets here: https://huggingface.co/datasets/lainmn/AgentDS .

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arXiv2026

GRAND: Graph Release with Assured Node Differential Privacy

Differential privacy is a well-established framework for safeguarding sensitive information in data. While extensively applied across various domains, its application to network data -- particularly at the node level -- remains underexplored. Existing methods for node-level privacy either focus exclusively on query-based approaches, which restrict output to pre-specified network statistics, or fail to preserve key structural properties of the network. In this work, we propose GRAND (Graph Release with Assured Node Differential privacy), which is, to the best of our knowledge, the first network release mechanism that releases networks while ensuring node-level differential privacy and preserving structural properties. Under a broad class of latent space models, we show that the released network asymptotically follows the same distribution as the original network. The effectiveness of the approach is evaluated through extensive experiments on both synthetic and real-world datasets.

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arXiv2025

Perturbation-Robust Predictive Modeling of Social Effects by Network Subspace Generalized Linear Models

Network-linked data, where multivariate observations are interconnected by a network, are becoming increasingly prevalent in fields such as sociology and biology. These data often exhibit inherent noise and complex relational structures, complicating conventional modeling and statistical inference. Motivated by empirical challenges in analyzing such data sets, this paper introduces a family of network subspace generalized linear models designed for analyzing noisy, network-linked data. We propose a model inference method based on subspace-constrained maximum likelihood, which emphasizes flexibility in capturing network effects and provides a robust inference framework against network perturbations. We establish the asymptotic distributions of the estimators under network perturbations, demonstrating the method's accuracy through extensive simulations involving random network models and deep-learning-based embedding algorithms. The proposed methodology is applied to a comprehensive analysis of a large-scale study on school conflicts, where it identifies significant social effects, offering meaningful and interpretable insights into student behaviors.

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arXiv2024

Bayesian thresholded modeling for integrating brain node and network predictors

Progress in neuroscience has provided unprecedented opportunities to advance our understanding of brain alterations and their correspondence to phenotypic profiles. With data collected from various imaging techniques, studies have integrated different types of information ranging from brain structure, function, or metabolism. More recently, an emerging way to categorize imaging traits is through a metric hierarchy, including localized node-level measurements and interactive network-level metrics. However, limited research has been conducted to integrate these different hierarchies and achieve a better understanding of the neurobiological mechanisms and communications. In this work, we address this literature gap by proposing a Bayesian regression model under both vector-variate and matrix-variate predictors. To characterize the interplay between different predicting components, we propose a set of biologically plausible prior models centered on an innovative joint thresholded prior. This captures the coupling and grouping effect of signal patterns, as well as their spatial contiguity across brain anatomy. By developing a posterior inference, we can identify and quantify the uncertainty of signaling node- and network-level neuromarkers, as well as their predictive mechanism for phenotypic outcomes. Through extensive simulations, we demonstrate that our proposed method outperforms the alternative approaches substantially in both out-of-sample prediction and feature selection. By implementing the model to study children's general mental abilities, we establish a powerful predictive mechanism based on the identified task contrast traits and resting-state sub-networks.

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arXiv2024

Supervised brain node and network construction under voxel-level functional imaging

Recent advancements in understanding the brain's functional organization related to behavior have been pivotal, particularly in the development of predictive models based on brain connectivity. Traditional methods in this domain often involve a two-step process by first constructing a connectivity matrix from predefined brain regions, and then linking these connections to behaviors or clinical outcomes. However, these approaches with unsupervised node partitions predict outcomes inefficiently with independently established connectivity. In this paper, we introduce the Supervised Brain Parcellation (SBP), a brain node parcellation scheme informed by the downstream predictive task. With voxel-level functional time courses generated under resting-state or cognitive tasks as input, our approach clusters voxels into nodes in a manner that maximizes the correlation between inter-node connections and the behavioral outcome, while also accommodating intra-node homogeneity. We rigorously evaluate the SBP approach using resting-state and task-based fMRI data from both the Adolescent Brain Cognitive Development (ABCD) study and the Human Connectome Project (HCP). Our analyses show that SBP significantly improves out-of-sample connectome-based predictive performance compared to conventional step-wise methods under various brain atlases. This advancement holds promise for enhancing our understanding of brain functional architectures with behavior and establishing more informative network neuromarkers for clinical applications.

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arXiv2024

The non-overlapping statistical approximation to overlapping group lasso

Group lasso is a commonly used regularization method in statistical learning in which parameters are eliminated from the model according to predefined groups. However, when the groups overlap, optimizing the group lasso penalized objective can be time-consuming on large-scale problems because of the non-separability induced by the overlapping groups. This bottleneck has seriously limited the application of overlapping group lasso regularization in many modern problems, such as gene pathway selection and graphical model estimation. In this paper, we propose a separable penalty as an approximation of the overlapping group lasso penalty. Thanks to the separability, the computation of regularization based on our penalty is substantially faster than that of the overlapping group lasso, especially for large-scale and high-dimensional problems. We show that the penalty is the tightest separable relaxation of the overlapping group lasso norm within the family of $\ell_{q_1}/\ell_{q_2}$ norms. Moreover, we show that the estimator based on the proposed separable penalty is statistically equivalent to the one based on the overlapping group lasso penalty with respect to their error bounds and the rate-optimal performance under the squared loss. We demonstrate the faster computational time and statistical equivalence of our method compared with the overlapping group lasso in simulation examples and a classification problem of cancer tumors based on gene expression and multiple gene pathways.

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arXiv2023

Fitting Low-rank Models on Egocentrically Sampled Partial Networks

The statistical modeling of random networks has been widely used to uncover interaction mechanisms in complex systems and to predict unobserved links in real-world networks. In many applications, network connections are collected via egocentric sampling: a subset of nodes is sampled first, after which all links involving this subset are recorded; all other information is missing. Compared with the assumption of ``uniformly missing at random", egocentrically sampled partial networks require specially designed modeling strategies. Current statistical methods are either computationally infeasible or based on intuitive designs without theoretical justification. Here, we propose an approach to fit general low-rank models for egocentrically sampled networks, which include several popular network models. This method is based on graph spectral properties and is computationally efficient for large-scale networks. It results in consistent recovery of missing subnetworks due to egocentric sampling for sparse networks. To our knowledge, this method offers the first theoretical guarantee for egocentric partial network estimation in the scope of low-rank models. We evaluate the technique on several synthetic and real-world networks and show that it delivers competitive performance in link prediction tasks.

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arXiv2023

Incrementality Bidding via Reinforcement Learning under Mixed and Delayed Rewards

Incrementality, which is used to measure the causal effect of showing an ad to a potential customer (e.g. a user in an internet platform) versus not, is a central object for advertisers in online advertising platforms. This paper investigates the problem of how an advertiser can learn to optimize the bidding sequence in an online manner \emph{without} knowing the incrementality parameters in advance. We formulate the offline version of this problem as a specially structured episodic Markov Decision Process (MDP) and then, for its online learning counterpart, propose a novel reinforcement learning (RL) algorithm with regret at most $\widetilde{O}(H^2\sqrt{T})$, which depends on the number of rounds $H$ and number of episodes $T$, but does not depend on the number of actions (i.e., possible bids). A fundamental difference between our learning problem from standard RL problems is that the realized reward feedback from conversion incrementality is \emph{mixed} and \emph{delayed}. To handle this difficulty we propose and analyze a novel pairwise moment-matching algorithm to learn the conversion incrementality, which we believe is of independent of interest.

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arXiv2022

Linear regression and its inference on noisy network-linked data

Linear regression on network-linked observations has been an essential tool in modeling the relationship between response and covariates with additional network structures. Previous methods either lack inference tools or rely on restrictive assumptions on social effects and usually assume that networks are observed without errors. This paper proposes a regression model with nonparametric network effects. The model does not assume that the relational data or network structure is exactly observed and can be provably robust to network perturbations. Asymptotic inference framework is established under a general requirement of the network observational errors, and the robustness of this method is studied in the specific setting when the errors come from random network models. We discover a phase-transition phenomenon of the inference validity concerning the network density when no prior knowledge of the network model is available while also showing a significant improvement achieved by knowing the network model. Simulation studies are conducted to verify these theoretical results and demonstrate the advantage of the proposed method over existing work in terms of accuracy and computational efficiency under different data-generating models. The method is then applied to middle school students' network data to study the effectiveness of educational workshops in reducing school conflicts.

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arXiv2022

Compressed spectral screening for large-scale differential correlation analysis with application in selecting Glioblastoma gene modules

Differential co-expression analysis has been widely applied by scientists in understanding the biological mechanisms of diseases. However, the unknown differential patterns are often complicated; thus, models based on simplified parametric assumptions can be ineffective in identifying the differences. Meanwhile, the gene expression data involved in such analysis are in extremely high dimensions by nature, whose correlation matrices may not even be computable. Such a large scale seriously limits the application of most well-studied statistical methods. This paper introduces a simple yet powerful approach to the differential correlation analysis problem called compressed spectral screening. By leveraging spectral structures and random sampling techniques, our approach could achieve a highly accurate screening of features with complicated differential patterns while maintaining the scalability to analyze correlation matrices of $10^4$--$10^5$ variables within a few minutes on a standard personal computer. We have applied this screening approach in comparing a TCGA data set about Glioblastoma with normal subjects. Our analysis successfully identifies multiple functional modules of genes that exhibit different co-expression patterns. The findings reveal new insights about Glioblastoma's evolving mechanism. The validity of our approach is also justified by a theoretical analysis, showing that the compressed spectral analysis can achieve variable screening consistency.

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arXiv2021

Diffusion Source Identification on Networks with Statistical Confidence

Diffusion source identification on networks is a problem of fundamental importance in a broad class of applications, including rumor controlling and virus identification. Though this problem has received significant recent attention, most studies have focused only on very restrictive settings and lack theoretical guarantees for more realistic networks. We introduce a statistical framework for the study of diffusion source identification and develop a confidence set inference approach inspired by hypothesis testing. Our method efficiently produces a small subset of nodes, which provably covers the source node with any pre-specified confidence level without restrictive assumptions on network structures. Moreover, we propose multiple Monte Carlo strategies for the inference procedure based on network topology and the probabilistic properties that significantly improve the scalability. To our knowledge, this is the first diffusion source identification method with a practically useful theoretical guarantee on general networks. We demonstrate our approach via extensive synthetic experiments on well-known random network models and a mobility network between cities concerning the COVID-19 spreading.

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arXiv2021

Network Estimation by Mixing: Adaptivity and More

Networks analysis has been commonly used to study the interactions between units of complex systems. One problem of particular interest is learning the network's underlying connection pattern given a single and noisy instantiation. While many methods have been proposed to address this problem in recent years, they usually assume that the true model belongs to a known class, which is not verifiable in most real-world applications. Consequently, network modeling based on these methods either suffers from model misspecification or relies on additional model selection procedures that are not well understood in theory and can potentially be unstable in practice. To address this difficulty, we propose a mixing strategy that leverages available arbitrary models to improve their individual performances. The proposed method is computationally efficient and almost tuning-free; thus, it can be used as an off-the-shelf method for network modeling. We show that the proposed method performs equally well as the oracle estimate when the true model is included as individual candidates. More importantly, the method remains robust and outperforms all current estimates even when the models are misspecified. Extensive simulation examples are used to verify the advantage of the proposed mixing method. Evaluation of link prediction performance on 385 real-world networks from six domains also demonstrates the universal competitiveness of the mixing method across multiple domains.

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arXiv2021

Community models for networks observed through edge nominations

Communities are a common and widely studied structure in networks, typically under the assumption that the network is fully and correctly observed. In practice, network data are often collected by querying nodes about their connections. In some settings, all edges of a sampled node will be recorded, and in others, a node may be asked to name its connections. These sampling mechanisms introduce noise and bias which can obscure the community structure and invalidate assumptions underlying standard community detection methods. We propose a general model for a class of network sampling mechanisms based on recording edges via querying nodes, designed to improve community detection for network data collected in this fashion. We model edge sampling probabilities as a function of both individual preferences and community parameters, and show community detection can be performed by spectral clustering under this general class of models. We also propose, as a special case of the general framework, a parametric model for directed networks we call the nomination stochastic block model, which allows for meaningful parameter interpretations and can be fitted by the method of moments. Both spectral clustering and the method of moments in this case are computationally efficient and come with theoretical guarantees of consistency. We evaluate the proposed model in simulation studies on both unweighted and weighted networks and apply it to a faculty hiring dataset, discovering a meaningful hierarchy of communities among US business schools.

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arXiv2021

Informative core identification in complex networks

In network analysis, the core structure of modeling interest is usually hidden in a larger network in which most structures are not informative. The noise and bias introduced by the non-informative component in networks can obscure the salient structure and limit many network modeling procedures' effectiveness. This paper introduces a novel core-periphery model for the non-informative periphery structure of networks without imposing a specific form for the informative core structure. We propose spectral algorithms for core identification as a data preprocessing step for general downstream network analysis tasks based on the model. The algorithm enjoys a strong theoretical guarantee of accuracy and is scalable for large networks. We evaluate the proposed method by extensive simulation studies demonstrating various advantages over many traditional core-periphery methods. The method is applied to extract the informative core structure from a citation network and give more informative results in the downstream hierarchical community detection.

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arXiv2020

Hierarchical community detection by recursive partitioning

The problem of community detection in networks is usually formulated as finding a single partition of the network into some "correct" number of communities. We argue that it is more interpretable and in some regimes more accurate to construct a hierarchical tree of communities instead. This can be done with a simple top-down recursive partitioning algorithm, starting with a single community and separating the nodes into two communities by spectral clustering repeatedly, until a stopping rule suggests there are no further communities. This class of algorithms is model-free, computationally efficient, and requires no tuning other than selecting a stopping rule. We show that there are regimes where this approach outperforms K-way spectral clustering, and propose a natural framework for analyzing the algorithm's theoretical performance, the binary tree stochastic block model. Under this model, we prove that the algorithm correctly recovers the entire community tree under relatively mild assumptions. We apply the algorithm to a gene network based on gene co-occurrence in 1580 research papers on anemia, and identify six clusters of genes in a meaningful hierarchy. We also illustrate the algorithm on a dataset of statistics papers.

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arXiv2020

Network cross-validation by edge sampling

While many statistical models and methods are now available for network analysis, resampling network data remains a challenging problem. Cross-validation is a useful general tool for model selection and parameter tuning, but is not directly applicable to networks since splitting network nodes into groups requires deleting edges and destroys some of the network structure. Here we propose a new network resampling strategy based on splitting node pairs rather than nodes applicable to cross-validation for a wide range of network model selection tasks. We provide a theoretical justification for our method in a general setting and examples of how our method can be used in specific network model selection and parameter tuning tasks. Numerical results on simulated networks and on a citation network of statisticians show that this cross-validation approach works well for model selection.

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