Student Copula Markov Networks

Salha Mamane; Cheikh Tidiane Seck

stat.MLOct 13, 2026

Student Copula Markov Networks

Authors: Salha Mamane, Cheikh Tidiane Seck

Organizations: School of Statistics and Actuarial Science, University of the Witwatersrand · Department of Mathematics, Alioune Diop University of Bambey

Abstract

This paper extends the applicability of probabilistic graphical models to non Gaussian data. It establishes a characterization of the pairwise Markov property in undirected probabilistic graphical models in terms of copula densities. Building on this characterization, we derive a necessary condition for the pairwise Markov property in Student copula Markov networks. An Expectation-Conditional Maximization algorithm (ECM) is provided to facilitate the penalized maximum likelihood estimation and graph selection. The performance of the proposed algorithm is evaluated through simulation studies, which demonstrate its effectiveness in estimating model parameters and recovering the underlying graph structure.

Probabilistic Graphical Models

Probabilistic graphical models represent joint distributions with graphs to support structured inference, learning, and reasoning under uncertainty.

See all 52 papers

Network Learning with Semi-relaxed Gromov-Wasserstein
Jun 1, 2026Charles Dufour, Ulysse Naepels, Leonardo V. SantoroGraph Structure Learning Latent Variable Models
EPFL, Institute of Mathematics Lausanne, Switzerland
Mixing-Free and Signal-Optimal Learning of Gaussian Graphical Models from Glauber Dynamics
Jul 20, 2026Vignesh Tirukkonda, Gautam DasarathyGraph Structure Learning Probabilistic Graphical Models
Arizona State University
Learning Gaussian Graphical Models from a Glauber Trajectory Without Mixing
Jun 30, 2026Eric Shen, Tony Wu, Mahbod Majid +1Graph Structure Learning Probabilistic Graphical Models
MIT

Jun 1, 2026J/K move · Enter open · S save

Network Learning with Semi-relaxed Gromov-Wasserstein

Charles Dufour, Ulysse Naepels, Leonardo V. Santoro

EPFL, Institute of Mathematics Lausanne, Switzerland

Graph Structure Learning Latent Variable Models Stochastic Block Model Statistical Learning Theory Optimal Transport

Open paper AskPDF arXiv

Estimating the generative mechanism of large-scale networks is a fundamental challenge in statistical machine learning. It requires the identification of the latent connectivity structure, which is in general an NP-hard combinatorial problem due to the absence of canonical node labels. We address this challenge by allowing for probabilistic couplings, thereby relaxing the assignment problem. Our estimation framework can be formulated as a semi-relaxed Gromov-Wasserstein objective and provides a low-dimensional representation of the generative structure. We solve this via a block-coordinate conditional gradient algorithm. Despite the relaxation, the resulting solution is typically deterministic: in fact, we show that the optimality gap between the relaxed solution and the deterministic assignment vanishes at rate

O(1/n)

, where

n

is the number of nodes. This allows for tractable recovery of the underlying model and enables rigorous statistical analysis: we establish consistency and minimax-optimal convergence rates for both stochastic block models and Holder-smooth graphons. Our implementation scales efficiently with

n

, as demonstrated on both synthetic and real-world datasets.

Abstract

Probabilistic Graphical Models

Explore similar work

Network Learning with Semi-relaxed Gromov-Wasserstein

Mixing-Free and Signal-Optimal Learning of Gaussian Graphical Models from Glauber Dynamics

Learning Gaussian Graphical Models from a Glauber Trajectory Without Mixing