arXiv subjects

Ji Zhu

Publications and source records attributed to Ji Zhu.

At least 19 recordsLinked to original sources

arXiv2026

Conditional-Independence-Regularized Distributional Autoencoders for Mixed-Type Data

Mixed-type data containing both numerical and categorical variables arise in many scientific and real-world applications. Existing representation learning and generative modeling approaches typically focus either on reconstruction accuracy or unconditional data generation, but often fail to recover the full conditional distribution of the data while preserving interpretable structural relationships between heterogeneous variable types. In this work, we introduce Conditional-Independence-Regularized Distributional Autoencoders, a framework for learning low-dimensional representations of mixed-type data through conditional distribution matching and structural regularization. Our method combines an energy-score-based objective for numerical variables, a likelihood-based objective for categorical variables, and an auxiliary conditional independence regularization term encouraging the learned representation to capture the dependence between numerical and categorical components. We provide theoretical analysis showing that the optimal representation balances unexplained numerical variability, conditional entropy of categorical variables, and residual conditional dependence. Empirically, the proposed method achieves strong performance on both synthetic and real-world datasets, substantially improving categorical distribution recovery, achieving competitive overall conditional distribution recovery, and preserving mixed-type dependence structure. The code has been made available at GitHub.

stat.ME↗

arXiv2026

Conformal Prediction for Dyadic Regression Under Complex Missingness

We develop a framework for conformal prediction in dyadic regression problems under complex missingness mechanisms. At the theoretical level, we develop general technical tools for establishing finite-sample validity of conformal prediction under distributional invariance conditions weaker than exchangeability. A key result handles the case where the sample itself is a random subset of the index set, a setting not covered by existing theory, via a novel bijection argument that constructs an explicit measure-preserving correspondence between events. In addition, we propose conformal prediction procedures for jointly exchangeable arrays, including full conformal, split conformal, a row-column approach exploiting similarities within rows and columns, and a selective conformal procedure achieving mask-conditional validity. For missing elements, we establish asymptotic validity of a weighted conformal procedure under a nonparametric graphon model for the missingness mechanism. We further establish conditional validity results for both continuous and discrete responses; to the best of our knowledge, this is the first formal proof of asymptotic conditional validity for weighted conformal prediction under a missing-not-at-random assumption. The proposed methods are illustrated on synthetic and real network data.

math.ST↗

arXiv2026

Efficient Synthetic Network Generation via Latent Embedding Reconstruction

Network data are ubiquitous across the social sciences, biology, and information systems. Generating realistic synthetic network data has broad applications from network simulation to scientific discovery. However, many existing black-box approaches for network generation tend to overfit observed data while overlooking characteristic network structure, and incur substantial computational overhead at scale. These practical challenges call for synthetic network generation methods that are both efficient and capable of capturing structural properties of networks. In this paper, we introduce Synthetic Network Generation via Latent Embedding Reconstruction (SyNGLER), a general and efficient framework for synthetic network generation that builds on latent space network models. Given an observed network, SyNGLER first learns low-dimensional latent node embeddings via a latent space network model and then reconstructs the latent space by building a distribution-free generator over these embeddings. For generation, SyNGLER first samples (or resamples) node embeddings from the generator in the latent space and then produces synthetic networks using the latent space network model. Through the latent space framework, SyNGLER preserves unique characteristics in networks such as sparsity and node degree heterogeneity, while allowing for efficient training with lower computational cost than many existing deep architectures. We provide theoretical guarantees by developing consistency results on the distance between the true and synthetic edge distributions. Empirical studies further demonstrate the effectiveness of SyNGLER, which efficiently produces networks that better preserve key network characteristics such as network moments and degree distributions compared with existing approaches. Code is available at https://github.com/FeifanJiang/syngler.

stat.ML↗

arXiv2026

Theoretical Analysis of Engression and Reverse Markov Engression

Engression is a recently proposed and effective framework for conditional distribution learning. Its multi-step Reverse Markov extension further improves generative flexibility by decomposing complex conditional sampling into sequential reverse transitions. Despite their strong empirical performance, rigorous finite-sample statistical guarantees for these methods remain unavailable. In this paper, under deep neural network parameterizations, we establish nonasymptotic convergence bounds for Engression by directly controlling the Energy Distance between the learned and target conditional distributions. For the Reverse Markov framework, we further develop an Energy-Distance-based chain rule that enables a rigorous analysis of error propagation across reverse steps. Our analysis yields corresponding excess-risk bounds that are near-optimal up to logarithmic factors relative to the classical minimax rate over a general H\"older class.

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arXiv2026

From Simple to Composite Perturbations: A Unified Decomposition Framework for Stochastic Block Models

Statistical inference for stochastic block models typically relies on the spectrum of the normalized adjacency matrix $\A^*$. In practice, the true probability matrix $\mathbf{B}$ is unknown and must be replaced by a plug-in estimator $\hat{\mathbf{B}}$. This substitution introduces two distinct types of estimation error: a simple perturbation $\boldsymbol{\Delta}$, arising when $\hat{\mathbf{B}}$ replaces $\mathbf{B}$ only in the numerator, and a composite perturbation $\tilde{\boldsymbol{\Delta}}$, arising when the replacement occurs in both the numerator and the denominator. Under both perturbation regimes, we decompose the total sum of squares into three components and conduct a detailed analysis of their asymptotic properties. This reveals a key, and perhaps surprising, distinction between simple and composite perturbations: the cross term $\tr({\A^*}\bDelta)$ is asymptotically negligible, whereas its composite counterpart $\tr({\A^*}\tilde{\bDelta})$ is not. Motivated by this, we develop a unified decomposition framework, expressing the composite perturbation matrix as $\tilde{\bDelta}=\check{\A}+\bDelta+\check{\bDelta}$, where $\check{\A}$ is a bias matrix of the normalized adjacency matrix, $\bDelta$ is the simple perturbation, and $\check{\bDelta}$ is a bias matrix of $\bDelta$. This structured decomposition allows us to precisely isolate and control each source of error, leading to a refined limiting theory for two key classes of test statistics. Concretely, for the largest eigenvalue statistic, we improve the existing condition from $K=O(n^{1/6-\tau})$ to the optimal rate $K=o(n^{1/6})$ under both simple and composite perturbations. For the linear spectral statistic, our unified decomposition framework provides the necessary structure to systematically control these errors term by term, leading to a complete and rigorous proof of asymptotic normality.

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arXiv2026

Balanced Stochastic Block Model for Community Detection in Signed Networks

Community detection, discovering the underlying communities within a network from observed connections, is a fundamental problem in network analysis, yet it remains underexplored for signed networks. In signed networks, both edge connection patterns and edge signs are informative, and structural balance theory (e.g., triangles aligned with ``the enemy of my enemy is my friend'' and ``the friend of my friend is my friend'' are more prevalent) provides a global higher-order principle that guides community formation. We propose a Balanced Stochastic Block Model (BSBM), which incorporates balance theory into the network generating process such that balanced triangles are more likely to occur. We develop a fast profile pseudo-likelihood estimation algorithm with provable convergence and establish that our estimator achieves strong consistency under weaker signal conditions than methods for the binary SBM that rely solely on edge connectivity. Extensive simulation studies and two real-world signed networks demonstrate strong empirical performance.

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arXiv2026

Locally sparse varying coefficient mixed model with application to longitudinal microbiome differential abundance

Differential abundance (DA) analysis in microbiome studies has recently been used to uncover a plethora of associations between microbial composition and various health conditions. While current approaches to DA typically apply only to cross-sectional data, many studies feature a longitudinal design to better understand the underlying microbial dynamics. To study DA in longitudinal microbial studies, we introduce a novel varying coefficient mixed-effects model with local sparsity. The proposed method can identify time intervals of significant group differences while accounting for temporal dependence. Specifically, we exploit a penalized kernel smoothing approach for parameter estimation and include a random effect to account for serial correlation. In particular, our method operates effectively regardless of whether sampling times are shared across subjects, accommodating irregular sampling and missing observations. Simulation studies demonstrate the necessity of modeling dependence for precise estimation and support recovery. The application of our method to a longitudinal study of mice oral microbiome during cancer development revealed significant scientific insights that were otherwise not discernible through cross-sectional analyses. An R implementation is available at https://github.com/fontaine618/LSVCMM.

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arXiv2025

Latent space models for grouped multiplex networks

Complex multilayer network datasets have become ubiquitous in various applications, including neuroscience, social sciences, economics, and genetics. Notable examples include brain connectivity networks collected across multiple patients or trade networks between countries collected across multiple goods. Existing statistical approaches to such data typically focus on modeling the structure shared by all networks; some go further by accounting for individual, layer-specific variation. However, real-world multilayer networks often exhibit additional patterns shared only within certain subsets of layers, which can represent treatment and control groups, or patients grouped by a specific trait. Identifying these group-level structures can uncover systematic differences between groups of networks and influence many downstream tasks, such as testing and low-dimensional visualization. To address this gap, we introduce the GroupMultiNeSS model, which enables the simultaneous extraction of shared, group-specific, and individual latent structures from a sample of networks on a shared node set. For this model, we establish identifiability, develop a fitting procedure using convex optimization in combination with a nuclear norm penalty, and prove a guarantee of recovery for the latent positions as long as there is sufficient separation between the shared, group-specific, and individual latent subspaces. We compare the model with MultiNeSS and other models for multiplex networks in various synthetic scenarios and observe an apparent improvement in the modeling accuracy when the group component is accounted for. Experiment with the Parkinson's disease brain connectivity dataset demonstrates the superiority of GroupMultiNeSS in highlighting node-level insights on biological differences between the treatment and control patient groups.

cs.SI↗

arXiv2025

Interpretable Network-assisted Random Forest+

Machine learning algorithms often assume that training samples are independent. When data points are connected by a network, the induced dependency between samples is both a challenge, reducing effective sample size, and an opportunity to improve prediction by leveraging information from network neighbors. Multiple methods taking advantage of this opportunity are available, but many, including graph neural networks, are not easily interpretable, limiting their usefulness for understanding how models make predictions. Others, such as network-assisted linear regression, are interpretable but often yield worse prediction performance. We bridge this gap by proposing a family of flexible network-assisted models built upon a generalization of random forests (RF+), which achieves highly-competitive prediction accuracy and can be understood through intrinsic interpretability measures, derived directly from the model parameters and structure. In particular, we develop a suite of interpretation tools that enable researchers to both identify important features that drive model predictions and quantify the importance of the network contribution to prediction. Importantly, we provide global and local feature importances as well as sample influence measures to assess the impact of individual observations. This suite of tools broadens the scope and applicability of network-assisted machine learning for high-impact problems where interpretability and transparency are essential.

stat.ML↗

arXiv2025

FAIR: Framing AIs Role in Programming Competitions -- Understanding How LLMs Are Changing the Game in Competitive Programming

This paper investigates how large language models (LLMs) are reshaping competitive programming. The field functions as an intellectual contest within computer science education and is marked by rapid iteration, real-time feedback, transparent solutions, and strict integrity norms. Prior work has evaluated LLMs performance on contest problems, but little is known about how human stakeholders -- contestants, problem setters, coaches, and platform stewards -- are adapting their workflows and contest norms under LLMs-induced shifts. At the same time, rising AI-assisted misuse and inconsistent governance expose urgent gaps in sustaining fairness and credibility. Drawing on 37 interviews spanning all four roles and a global survey of 207 contestants, as well as an API-based crawl of Codeforces contest logs (2022-2025) for quantitative analysis, we contribute: (i) an empirical account of evolving workflows, (ii) an analysis of contested fairness norms, and (iii) a chess-inspired governance approach with actionable measures -- real-time LLMs checks in online contests, peer co-monitoring and reporting, and cross-validation against offline performance -- to curb LLMs-assisted misuse while preserving fairness, transparency, and credibility.

cs.HC↗

arXiv2025

Modeling Non-Uniform Hypergraphs Using Determinantal Point Processes

Most statistical models for networks focus on pairwise interactions between nodes. However, many real-world networks involve higher-order interactions among multiple nodes, such as co-authors collaborating on a paper. Hypergraphs provide a natural representation for these networks, with each hyperedge representing a set of nodes. The majority of existing hypergraph models assume uniform hyperedges (i.e., edges of the same size) or rely on diversity among nodes. In this work, we propose a new hypergraph model based on non-symmetric determinantal point processes. The proposed model naturally accommodates non-uniform hyperedges, has tractable probability mass functions, and accounts for both node similarity and diversity in hyperedges. For model estimation, we maximize the likelihood function under constraints using a computationally efficient projected adaptive gradient descent algorithm. We establish the consistency and asymptotic normality of the estimator. Simulation studies confirm the efficacy of the proposed model, and its utility is further demonstrated through edge predictions on several real-world datasets.

stat.ME↗

arXiv2025

Recurrent Event Analysis with Ordinary Differential Equations

This paper introduces a general framework for analyzing recurrent event data by modeling the conditional mean function of the recurrent event process as the solution to an Ordinary Differential Equation (ODE). This approach not only accommodates a wide range of semi-parametric recurrent event models, including both non-homogeneous Poisson processes (NHPPs) and non-Poisson processes, but also is scalable and easy-to-implement. Based on this framework, we propose a Sieve Maximum Pseudo-Likelihood Estimation (SMPLE) method, employing the NHPP as a working model. We establish the consistency and asymptotic normality of the proposed estimator, demonstrating that it achieves semi-parametric efficiency when the NHPP working model is valid. Furthermore, we develop an efficient resampling procedure to estimate the asymptotic covariance matrix. To assess the statistical efficiency and computational scalability of the proposed method, we conduct extensive numerical studies, including simulations under various settings and an application to a real-world dataset analyzing risk factors associated with Intensive Care Unit (ICU) readmission frequency.

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arXiv2025

Modeling Hypergraphs with Diversity and Heterogeneous Popularity

While relations among individuals make an important part of data with scientific and business interests, existing statistical modeling of relational data has mainly been focusing on dyadic relations, i.e., those between two individuals. This article addresses the less studied, though commonly encountered, polyadic relations that can involve more than two individuals. In particular, we propose a new latent space model for hypergraphs using determinantal point processes, which is driven by the diversity within hyperedges and each node's popularity. This model mechanism is in contrast to existing hypergraph models, which are predominantly driven by similarity rather than diversity. Additionally, the proposed model accommodates broad types of hypergraphs, with no restriction on the cardinality and multiplicity of hyperedges, which previous models often have. Consistency and asymptotic normality of the maximum likelihood estimates of the model parameters have been established. The proof is challenging, owing to the special configuration of the parameter space. Further, we apply the projected accelerated gradient descent algorithm to obtain the parameter estimates, and we show its effectiveness in simulation studies. We also demonstrate an application of the proposed model on the What's Cooking data and present the embedding of food ingredients learned from cooking recipes using the model.

stat.ME↗

arXiv2025

Denoising Diffused Embeddings: a Generative Approach for Hypergraphs

Hypergraph data, which capture multi-way interactions among entities, are increasingly prevalent in the big data era. Generating new hyperlinks from an observed, usually high-dimensional hypergraph is an important yet challenging task with diverse applications in areas such as electronic health record analysis and biological research. This task is fraught with several challenges. The discrete nature of hyperlinks renders many existing generative models inapplicable. Additionally, powerful machine learning-based generative models often operate as black boxes, providing limited interpretability. Key structural characteristics of hypergraphs, including node degree heterogeneity and hyperlink sparsity, further complicate the modeling process and must be carefully addressed. To tackle these challenges, we propose Denoising Diffused Embeddings (DDE), a general and efficient generative modeling architecture for hypergraphs. DDE exploits low-rank structure in high-dimensional hypergraphs via a conditional hyperlink likelihood model that links discrete hyperlinks to a continuous latent embedding space and leverages a score-based diffusion model to reconstruct that space. Theoretically, we show that when true latent embeddings are accessible, DDE exactly reduces the task of generating new high-dimensional hyperlinks to generating new low-dimensional embeddings. Moreover, we analyze the implications of using estimated embeddings in DDE, revealing how hypergraph characteristics such as dimensionality, node degree heterogeneity, and hyperlink sparsity impact its generative performance. Simulation studies demonstrate the superiority of DDE over existing methods, in terms of both computational efficiency and generative performance. Furthermore, an application to a symptom co-occurrence hypergraph derived from electronic medical records uncovers interesting findings and highlights the advantages of DDE.

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arXiv2024

Flexible Modeling of Information Diffusion on Networks with Statistical Guarantees

Modeling information spread through a network is one of the key problems of network analysis, with applications in a wide array of areas such as marketing and public health. Most approaches assume that the spread is governed by some probabilistic diffusion model, often parameterized by the strength of connections between network members (edge weights), highlighting the need for methods that can accurately estimate them. Multiple prior works suggest such estimators for particular diffusion models; however, most of them lack a rigorous statistical analysis that would establish the asymptotic properties of the estimator and allow for uncertainty quantification. In this paper, we develop a likelihood-based approach to estimate edge weights from the observed information diffusion paths under the proposed General Linear Threshold (GLT) model, a broad class of discrete-time information diffusion models that includes both the well-known linear threshold (LT) and independent cascade (IC) models. We first derive necessary and sufficient conditions that make the edge weights identifiable under this model. Then, we derive a finite sample error bound for the estimator and demonstrate that it is asymptotically normal under mild conditions. We conclude by studying the GLT model in the context of the Influence Maximization (IM) problem, that is, the task of selecting a subset of $k$ nodes to start the diffusion, so that the average information spread is maximized. Extensive experiments on synthetic and real-world networks demonstrate that the flexibility of the proposed class of GLT models, coupled with the proposed estimation and inference framework for its parameters, can significantly improve estimation of spread from a given subset of nodes, prediction of node activation, and the quality of the IM problem solutions.

cs.SI↗

arXiv2024

Mesoscale two-sample testing for networks

Networks arise naturally in many scientific fields as a representation of pairwise connections. Statistical network analysis has most often considered a single large network, but it is common in a number of applications to observe multiple networks on a shared node set. When these networks are grouped by case-control status or another categorical covariate, the classical statistical question of two-sample comparison arises. In this work, we address the problem of testing for statistically significant differences in a given arbitrary subset of connections. This general framework allows an analyst to focus on a single node, a specific region of interest, or compare whole networks. Our ability to conduct ``mesoscale'' testing on a meaningful group of edges is particularly relevant for applications such as neuroimaging and distinguishes our approach from prior work, which tends to focus either on a single node or the whole network. In this mesoscale setting, we develop statistically sound projection-based tests for two-sample comparison in both weighted and binary edge networks. The key to our approach is to leverage network information from outside the set of interest to learn informative low-rank projections which leads to more powerful tests.

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arXiv2024

Heterogeneous Treatment Effects under Network Interference: A Nonparametric Approach Based on Node Connectivity

In network settings, interference between units makes causal inference more challenging as outcomes may depend on the treatments received by others in the network. Typical estimands in network settings focus on treatment effects aggregated across individuals in the population. We propose a framework for estimating node-wise counterfactual means, allowing for more granular insights into the impact of network structure on treatment effect heterogeneity. We develop a doubly robust and non-parametric estimation procedure, KECENI (Kernel Estimator of Causal Effect under Network Interference), which offers consistency and asymptotic normality under network dependence. The utility of this method is demonstrated through an application to microfinance data, revealing the impact of network characteristics on treatment effects.

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arXiv2024

A General Latent Embedding Approach for Modeling Non-uniform High-dimensional Sparse Hypergraphs with Multiplicity

Recent research has shown growing interest in modeling hypergraphs, which capture polyadic interactions among entities beyond traditional dyadic relations. However, most existing methodologies for hypergraphs face significant limitations, including their heavy reliance on uniformity restrictions for hyperlink orders and their inability to account for repeated observations of identical hyperlinks. In this work, we introduce a novel and general latent embedding approach that addresses these challenges through the integration of latent embeddings, vertex degree heterogeneity parameters, and an order-adjusting parameter. Theoretically, we investigate the identifiability conditions for the latent embeddings and associated parameters, and we establish the convergence rates of their estimators along with asymptotic distributions. Computationally, we employ a projected gradient ascent algorithm for parameter estimation. Comprehensive simulation studies demonstrate the effectiveness of the algorithm and validate the theoretical findings. Moreover, an application to a co-citation hypergraph illustrates the advantages of the proposed method.

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