arXiv subjects

Jiajin Sun

Publications and source records attributed to Jiajin Sun.

5 recordsLinked to original sources

arXiv2026

Bridging Theory and Practice: Statistical Inference for Latent Space Models of Networks

Latent space models have been widely adopted in modeling network data. Developing statistical inference for estimated model parameters enables quantifying associated uncertainty and is pivotal for downstream tasks. Despite recent progress on statistical inference of maximum likelihood estimation, crucial gaps remain between asymptotic theoretical guarantees and practical use. Specifically, how are the oracle maximum likelihood estimators related to the solutions produced by algorithms in practice? Can rigorous guarantees be established for existing algorithms without unnecessary restrictions? To address these fundamental questions, we develop a unified analytical framework that bridges theory and practice of statistical inference for latent space models. First, for the maximum likelihood estimation, we relax the spectral-multiplicity constraint in the existing asymptotic theory to broaden the applicability. Second, we overcome the dependence on unknown true parameters in prior algorithmic analyses by developing novel adaptive criteria and theoretical tools. For the widely used algorithm based on the projected gradient descent and the singular value thresholding, we explicitly connect their outputs to the maximum likelihood estimator without relying on unknown information. Our results provide a solid foundation for practically useful and statistically principled statistical inference in network analysis.

math.ST↗

arXiv2025

Efficient Analysis of Latent Spaces in Heterogeneous Networks

This work proposes a unified framework for efficient estimation under latent space modeling of heterogeneous networks. We consider a class of latent space models that decompose latent vectors into shared and network-specific components across networks. We develop a novel procedure that first identifies the shared latent vectors and further refines estimates through efficient score equations to achieve statistical efficiency. Oracle error rates for estimating the shared and heterogeneous latent vectors are established simultaneously. The analysis framework offers remarkable flexibility, accommodating various types of edge weights under general distributions.

stat.ME↗

arXiv2025

Calibrating Geophysical Predictions under Constrained Probabilistic Distributions

Machine learning (ML) has shown significant promise in studying complex geophysical dynamical systems, including turbulence and climate processes. Such systems often display sensitive dependence on initial conditions, reflected in positive Lyapunov exponents, where even small perturbations in short-term forecasts can lead to large deviations in long-term outcomes. Thus, meaningful inference requires not only accurate short-term predictions, but also consistency with the system's long-term attractor that is captured by the marginal distribution of state variables. Existing approaches attempt to address this challenge by incorporating spatial and temporal dependence, but these strategies become impractical when data are extremely sparse. In this work, we show that prior knowledge of marginal distributions offers valuable complementary information to short-term observations, motivating a distribution-informed learning framework. We introduce a calibration algorithm based on normalization and the Kernelized Stein Discrepancy (KSD) to enhance ML predictions. The method here employs KSD within a reproducing kernel Hilbert space to calibrate model outputs, improving their fidelity to known physical distributions. This not only sharpens pointwise predictions but also enforces consistency with non-local statistical structures rooted in physical principles. Through synthetic experiments-spanning offline climatological CO2 fluxes and online quasi-geostrophic flow simulations-we demonstrate the robustness and broad utility of the proposed framework.

physics.ao-ph↗

arXiv2025

Semiparametric Modeling and Analysis for Longitudinal Network Data

We introduce a semiparametric latent space model for analyzing longitudinal network data. The model consists of a static latent space component and a time-varying node-specific baseline component. We develop a semiparametric efficient score equation for the latent space parameter by adjusting for the baseline nuisance component. Estimation is accomplished through a one-step update estimator and an appropriately penalized maximum likelihood estimator. We derive oracle error bounds for the two estimators and address identifiability concerns from a quotient manifold perspective. Our approach is demonstrated using the New York Citi Bike Dataset.

math.ST↗

arXiv2023

Pairwise Covariates-adjusted Block Model for Community Detection

One of the most fundamental problems in network study is community detection. The stochastic block model (SBM) is a widely used model, for which various estimation methods have been developed with their community detection consistency results unveiled. However, the SBM is restricted by the strong assumption that all nodes in the same community are stochastically equivalent, which may not be suitable for practical applications. We introduce a pairwise covariates-adjusted stochastic block model (PCABM), a generalization of SBM that incorporates pairwise covariate information. We study the maximum likelihood estimates of the coefficients for the covariates as well as the community assignments. It is shown that both the coefficient estimates of the covariates and the community assignments are consistent under suitable sparsity conditions. Spectral clustering with adjustment (SCWA) is introduced to efficiently solve PCABM. Under certain conditions, we derive the error bound of community detection under SCWA and show that it is community detection consistent. In addition, we investigate model selection in terms of the number of communities and feature selection for the pairwise covariates, and propose two corresponding algorithms. PCABM compares favorably with the SBM or degree-corrected stochastic block model (DCBM) under a wide range of simulated and real networks when covariate information is accessible.

stat.ME↗