arXiv subjects

Charles Dufour

Publications and source records attributed to Charles Dufour.

3 recordsLinked to original sources

arXiv2026

Decorated graphons for temporal network estimation

We propose a unified nonparametric framework for modeling time-evolving networks using decorated graphons (also known as probability-graphons): symmetric functions that assign to each node pair a probability distribution over binary edge time series. This generalizes the static decorated-graphon construction to dynamic graphs while preserving node exchangeability and allowing temporal dynamics such as memory and periodicity. Models in which edges evolve independently given the latent variables, such as autoregressive and Markov edge processes, arise as special cases. We develop a two-stage estimation procedure that separates temporal modeling from network structure. Because the network stage requires only mild regularity conditions on the edge-process estimator, a broad class of temporal edge models can be used in the first stage. We establish nonparametric convergence rates in both block-model and H\"older-smooth regimes, and make explicit how the rate depends on the number of observed time steps and on the quality of the edge-level estimation. We illustrate the method on simulated data and a hospital contact network, recovering latent community structure and time-varying interaction patterns. The framework gives a nonparametric baseline for dynamic network analysis with explicit convergence guarantees.

stat.ME↗

arXiv2026

Network Learning with Semi-relaxed Gromov-Wasserstein

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.

cs.LG↗

arXiv2024

Graphon estimation beyond binary edges: inference for decorated graphs with applications to multiplex and weighted networks

We introduce the first doubly non-parametric estimation method for decorated graphons, a generalisation of graphons that encodes edge weights, edge types, and other edge-level attributes in large networks. Graphons describe the limiting behaviour of large unlabelled networks through a symmetric measurable function governing the probability of edge formation, but the standard framework is restricted to binary edge information. Decorated graphons lift this restriction, yet no inference procedure has previously been available for them. The proposed estimator extends classical graphon estimation techniques to this enriched setting. We derive rates of convergence and show that, for compactly supported decorations, these rates agree with known non-parametric rates for estimating real-valued functions. Monte Carlo experiments confirm that the theoretical rates are attained in finite samples, and applications to synthetic and empirical networks show improved fit relative to binary-edge baselines. The method extends graphon-based inference to multiplex networks and attributed graphs simultaneously.

stat.ME↗