Probability and Statistics
Contact : François Portier
Probability and statistics are essential methodological foundations of data science. The societal needs for optimisation and security require an in-depth understanding of complex systems such as social networks, telecommunication networks or computer systems. The ever-increasing amount of data available favours a probabilistic treatment of the systems under study, including practical and theoretical guarantees regarding the behaviour of estimators, predictors, tests or any other statistical decision procedure.
This research theme is naturally linked to the « Machine Learning » theme and shares with it a large number of applications, with a particular interest in modelling and inference rather than prediction and optimisation.
The research activities of the Probability and Statistics theme include methodological and theoretical aspects in various fields, such as:
- Stochastic processes: Markov chains, time series, long-range dependencies, point processes, random graphs and hypergraphs.
- Large dimensions: semi-parametric models, parsimonious regression, infinite dimensional analysis.
- Rare events, Extreme values: Multivariate and spatial extremes, applications to anomaly detection and ranking, risk quantification of rare events.
- Quantification of uncertainty: bootstrapping, likelihood methods, empirical processes, clustering, reinforcement learning.
- Information theory: interactions with estimation problems, optimal transport and entropy inequalities.