Vincent Lemaire

Stanislas Strasman, Gabriel Cardoso, Sylvain Le Corff et al.

Understanding the stability and long-time behavior of generative models is a fundamental problem in modern machine learning. This paper provides quantitative bounds on the sampling error of score-based generative models by leveraging stability and forgetting properties of the Markov chain associated with the reverse-time dynamics. Under weak assumptions, we provide the two structural properties to ensure the propagation of initialization and discretization errors of the backward process: a Lyapunov drift condition and a Doeblin-type minorization condition. A practical consequence is quantitative stability of the sampling procedure, as the reverse diffusion dynamics induces a contraction mechanism along the sampling trajectory. Our results clarify the role of stochastic dynamics in score-based models and provide a principled framework for analyzing propagation of errors in such approaches.

Vincent Lemaire, Nédra Meloulli, Pierre Jaquet

Sepsis remains one of the most complex and heterogeneous syndromes in intensive care, characterized by diverse physiological trajectories and variable responses to treatment. While deep learning models perform well in the early prediction of sepsis, they often lack interpretability and ignore latent patient sub-phenotypes. In this work, we propose a machine learning framework by opening up a new avenue for addressing this issue: a relational approach. Temporal data from electronic medical records (EMRs) are viewed as multivariate patient logs and represented in a relational data schema. Then, a propositionalisation technique (based on classic aggregation/selection functions from the field of relational data) is applied to construct interpretable features to "flatten" the data. Finally, the flattened data is classified using a selective naive Bayesian classifier. Experimental validation demonstrates the relevance of the suggested approach as well as its extreme interpretability. The interpretation is fourfold: univariate, global, local, and counterfactual.