Publications

Main Papers

I.Kaddouri, Z.Naulet, E.Gassiat, “On the impossibility of detecting a late change-point in the preferential attachment random graph model”, Bernoulli 32 (1) 96-126, 2026. [journal] [arXiv] [HAL]

E.Gassiat, I.Kaddouri, Z.Naulet, “Clustering risk in Non-parametric Hidden Markov and I.I.D. Models”, The Annals of Statistics Vol. 53, No. 6, 2409–2429, 2025. [journal] [arXiv] [HAL]

My Thesis

Title: Inference on dependent data : Contributions to hidden Markov and preferential attachment graph models. [slides] [manuscript]

Abstract: This thesis is devoted to the study of statistical inference in settings where data are dependent. Such dependence can arise through temporal dynamics, as in Hidden Markov models, or through structural evolution, as in preferential attachment graph models. The first part focuses on clustering in both i.i.d. and Hidden Markov model (HMM) settings. We analyze the Bayes risk of clustering and compare it to the Bayes risk of classification. Our results show that the minimizers of these risks do not always coincide, but this distinction is largely theoretical: in practice, the Bayes classifier performs nearly optimally for clustering tasks. Simulations complement our theoretical findings and illustrate the near-optimality of classifier-based clustering strategies. The second part develops a refined analysis of clustering under Gaussian Hidden Markov models in the regime where the hidden chain mixes slowly. We provide a precise characterization of the Bayes risk in terms of the signal-to-noise ratio and the mixing properties of the chain. Based on this characterization, we propose some Bayes-optimal clustering procedures. Interestingly, our study uncovers surprising behaviors of the Bayes risk in certain parameter regimes, showing that temporal dependence can lead to non-standard phenomena that are absent in the i.i.d. case. The third part studies change-point detection in growing networks modeled by preferential attachment with time-dependent rules. We focus on a late-change scenario, where the modification occurs near the end of the network’s growth, and formulate the problem as a hypothesis test. We show that for unlabeled graphs, detecting such changes becomes impossible when they occur too late, supporting a broader conjecture on detectability limits. In contrast, when node labels are observed, we identify a sharp threshold: detection is possible only if the delay between the change and observation is sufficiently large.