From
Timetable to
Place ENS Paris-Saclay
Samuel GRUFFAZ
From Motor Style Quantification In Time Series To Markov Chain Monte Carlo Within Stochastic Approximation
Summary
Peux tu faire la version française de ce résumé de thèse ? This thesis addresses the problem of identifying and quantifying individual style in physiological time series, with applications in neurophysiology and personalized medicine. In the first part, we model inter- and intra-individual variability as transformations of common patterns. Two unsupervised and interpretable methods are developed. For regularly sampled signals, we use a variant of Convolutional Dictionary Learning (PerCDL), which captures temporal variability through time warping for gait analysis. For irregularly sampled signals, we adapt the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework from shape analysis to time series, supported by a novel kernel-based RKHS representation. Both methods yield meaningful features for classification and visualization in clinical and experimental datasets.
The style identification problem echoes mixed-effects modeling, which incorporates both individual latent variables and population parameters. That's why the second part focuses on parameter estimation within Bayesian mixed-effects models using the MCMC-SAEM algorithm. We address the computational challenges of Markov Chain Monte Carlo (MCMC) methods within stochastic approximation. First, we provide the first convergence proof of the No-U-Turn Sampler (NUTS), establishing geometric ergodicity. We also introduce Geodesic Slice Sampling, the first practical slice sampler on Riemannian manifolds, and demonstrate its utility in models with latent manifold-valued variables. Finally, we explore the impact of using asymptotically biased MCMC samplers. We show that the Unadjusted Langevin Algorithm (ULA), despite its bias, performs well in practice and is easier to tune than its Metropolis-adjusted counterpart.
Overall, this thesis bridges interpretable time series modeling with advanced Bayesian computation, providing both theoretical insights and practical tools for analyzing individual variability in physiological data.
Key-words
Bayesian statistics, Monte-Carlo Markov chain, time series analysis, biomedical applications, dictionary learning, Riemannian geometry
Supervision
- Nicolas VAYATIS
- Alain DURMUS
Comitee
- Julien Mairal
- Anthony Lee,
- Alain Trouvé
- Estelle Kuhn
- Stéphanie Allasonnière,
- Thomas Moreau