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Statistical Estimation of Time-varying Networks with Node Heterogeneity by Mengxue Li -
Vendredi 23 octobre 2026 à 16h00 - Auditoire MORE53 - Place Montesquieu, 2 - 1348 Louvain-la-Neuve -
Network data provide a natural representation of complex interactions among individuals, with nodes denoting the individuals and edges encoding their pairwise relationships, and arise widely in the social sciences, neuroscience, biology, economics, and finance. In many applications, network sparsity, node heterogeneity, temporal evolution, and repeated observations occur simultaneously, posing substantial challenges for statistical modeling and estimation. This dissertation develops a statistical framework for heterogeneous time-varying networks by using the degree-corrected stochastic block model as a unifying foundation, with particular emphasis on likelihood-based parameter estimation and community detection from the (replicated) time-varying networks.
The first project focuses on building a time-varying degree-corrected stochastic block model, which allows the degree parameters, community connectivity parameters, and community memberships to evolve over time. A time-localised profile likelihood procedure is then developed to estimate the time-varying parameters and latent community structure. Under mild smoothness and sparsity conditions, we establish consistency of the resulting estimators and show how temporal smoothing offsets the limited information available from sparse network observations. The methodology is evaluated through extensive simulations and applications to two social networks.
The second part studies replicated time-varying networks observed across multiple subjects or data sources. We propose a mixed-effects degree-corrected stochastic block model that separates the shared connectivity from source-specific variation while recovering the trajectories of time-varying degree parameters. Estimation is carried out using a time-localised likelihood approach conditional on the given community memberships. Statistical properties, including consistency and asymptotic normality, are established for the resulting estimators. The methodology is evaluated through extensive simulations and an application to dynamic functional brain connectivity networks from the Human Connectome Project.
Finally, as an extension to the previous project to the situation of unknown memberships, we develop a residualised joint spectral embedding method for the detection of community structure shared across heterogeneous replicated dynamic networks. The method first fits a community-free auxiliary model to remove the heterogeneity from nodes and sources, then aggregates standardized residual matrices through their inner products, and estimates the common community structure from the leading eigenspace of the aggregation. The framework accommodates multiple edge distributions within a one-parameter exponential-family formulation and is evaluated through extensive simulations and an application to the dynamic brain functional connectivity networks under the resting-state condition.
Jury members :
Prof. Rainer von Sachs (UCLouvain) (Supervisor)
Prof. Eugen Pircalabelu (UCLouvain) (Supervisor)
Prof. Christian Hafner (UCLouvain) (Chairperson)
Prof. Laura Symul (UCLouvain) (Secretary)
Prof. Hernando Ombao (KAUST, Saudi Arabia)
Dr. Swati Chandna (Birkbeck, University of London, U.K.)
Pay attention : the public defense of Mengxue Li will also take place in the form of a videoconference (Meeting ID: 373 225 138 527 736 - Passcode: qx2Tc7Nn)
