Dauphine Digital - Our Research
High-Dimensional Probabilities and Statistics
Learn how to harness large amounts of data
Developing mathematics and algorithmics to analyze and process large amounts of data is a crucial challenge, with the need to account for phenomena that commonly occur with high-dimensional data by utilizing emerging methods and concepts in probabilities and statistics.
Studies conducted at Dauphine-PSL on these topics are both methodological and digital.
Inverse problems
High-dimensional statistics
High-dimensional probability
Random graphs and matrices
Markov chain Monte Carlo
Stochastic algorithms
Approximate Bayesian computation
Applications
The scope of application is massive, potentially covering the full spectrum of data science: social networks, astrophysics, genetics, neuroscience, and more.
The choice and validation of models are also of interest to researchers at Dauphine-PSL.
In this area, creating toolboxes for practitioners and introducing algorithms based on massively parallel architecture has proven useful.
Our Research in the University's Labs
This topic of high-dimensional phenomena is explored at Dauphine-PSL, especially at CEREMADE, in relation to high-dimensional statistics, stochastic inverse problems, random graph and random matrix models, approximate Bayesian statistics (ABC methods), and stochastic algorithms.
These research initiatives draw upon connections with mathematical analysis and statistical physics.
Our Researchers
Emmanuel Bacry, Djalil Chafaï, Laëtitia Comminges, Laure Dumaz, Marc Hoffmann, Joseph Lehec, Vincent Rivoirard, Christian Robert, Angelina Roche, Fabrice Rossi, Robin Ryder, Justin Salez, Julien Stoehr, Irène Waldspurger
Sample Publications
- Clarté, G., Robert, C. P., Ryder, R and Stoehr, J. (2019) Component-wise approximate Bayesian computation via Gibbs-like steps. arXiv:1905.13599
- Collier, Olivier; Comminges, Laëtitia; Tsybakov, Alexandre B.; Verzelen, Nicolas. Optimal adaptive estimation of linear functionals under sparsity. Ann. Statist. 46 (2018), no. 6A, 3130–3150.
- Bernton, Espen; Jacob, Pierre E.; Gerber, Mathieu; Robert, Christian P. Approximate Bayesian computation with the Wasserstein distance. J. R. Stat. Soc. Ser. B. Stat. Methodol. 81 (2019), no. 2, 235–269.
- Waldspurger, Irène Phase retrieval with random Gaussian sensing vectors by alternating projections. IEEE Trans. Inform. Theory 64 (2018), no. 5, 3301–3312.
- Donnet, Sophie; Rivoirard, Vincent; Rousseau, Judith; Scricciolo, Catia. Posterior concentration rates for empirical Bayes procedures with applications to Dirichlet process mixtures. Bernoulli 24 (2018), no. 1, 231–256.
- Roche, Angelina. Local optimization of black-box functions with high or infinite-dimensional inputs: application to nuclear safety. Comput. Statist. 33 (2018), no. 1, 467–485.
- Chafaï, Djalil; Guédon, Olivier; Lecué, Guillaume; Pajor, Alain. Interactions between compressed sensing random matrices and high dimensional geometry.
Panoramas et Synthèses 37. Société Mathématique de France, Paris, 2012. 181 pp. ISBN: 978-2-85629-370-6 - A Endert, W Ribarsky, C Turkay, BL Wong, I Nabney, ID Blanco, F Rossi, The State of the Art in Integrating Machine Learning into Visual Analytics, Computer Graphics Forum (2017)
- K Françoisse, I Kivimäki, A Mantrach, F Rossi, M Saerens, A bag-of-paths framework for network data analysis, Neural Networks (2017)