Presentation

The SIMPAS team is part of the Centre de Mathématiques Appliquées within the École polytechnique.

The team brings together researchers from CMAP specializing in the broad area of randomness, in its widest sense. This includes data science, encompassing machine learning and artificial intelligence, as well as probabilistic modeling, such as simulation and numerical probability. Their work spans a wide spectrum within these fields, ranging from the theoretical foundations of algorithms to methodological developments and the efficient implementation of numerical schemes.

Research themes

• Machine Learning and Artificial Intelligence

  High-dimensional learning, neural networks, deep learning, adaptive control and model-free stochastic control, weakly supervised learning, stochastic optimization, reinforcement learning, generative models.

• Statistical Learning

  Empirical processes, random forests, kernel methods, missing data, principal and functional component analysis, sparse estimation, federated learning, transfer learning.

• Image and Signal Processing

  Multi-scale analysis, unsupervised classification, deep learning.

• Bayesian Methods

  Bayesian inference, Bayesian asymptotic statistics, Bayesian networks.

• Statistical Modeling for Life Sciences

  Model estimation, validation, and selection, mixed-effects models, pharmacokinetics.

• Markov Processes and Markov Chains

  Numerical approximation of non-linear dynamics (control, mean-field), dynamic programming equations, inference for continuous-time processes, hidden Markov models.

• Uncertainty Quantification

  Identification and propagation of uncertainties in numerical codes, intrusive and non-intrusive methods, chaos decomposition, Gaussian processes, metamodeling and response surface construction, design of numerical experiments, sensitivity analysis, robust optimization, risk analysis.

• Stochastic Simulation

  Particle methods, Markov Chain Monte Carlo (MCMC), rare events, stochastic algorithms, bandits, Monte Carlo regression, stochastic optimization, parallel computing.

• Generative Models in AI

  Diffusion models, variational autoencoders, normalizing flows, energy-based models, links with optimal transport.

• Mathematical Statistics

  Non-parametric estimation, model selection, classification, dimension reduction, robust statistics.