Arnak Dalalyan is a Professor of Statistics at ENSAE Paris. He obtained his PhD (2001) from Le Mans University on Statistics for Random Processes. He was a postdoctoral fellow (2002–03) at the Humboldt University of Berlin, an assistant professor (2003–08) at Paris 6 University, and a research professor at ENPC (2008–2011). He is also a Hi! PARIS Fellow for the 2021-2024 period.

His Hi! PARIS Fellowship project focuses on SAGMOS: Statistical Analysis of Generative Models: Sampling Guarantees and Robustness.

Statistical methods are omnipresent in the most powerful artificial intelligence technologies. The algorithms that are currently used rely on high-dimensional and highly-overparameterized models (such as deep neural networks) for which classical theoretical results do not lead to a good understanding of the empirically observed phenomena. The goal of this project is to develop mathematical tools that are tailored to the high-dimensional and highly-parameterized models by focusing on model averaging, approximate sampling, generative modeling, and robustness. While most recent approaches to theoretically justify the success of deep learning try to quantify the performance of the trained model as a solution to an optimization problem, we intend to study this question through the lens of model averaging and sampling from a given distribution.

The project also intends to investigate optimality properties in generative models such as conditional generative models and cycle-generative models. More precisely, we will focus on getting finite-sample statistical guarantees which will clearly highlight the impact of a suitably defined notion of intrinsic dimension (as opposed to the ambient dimension) on the risk. These kinds of guarantees are paramount in machine learning to ensure the reliability of the obtained algorithms. Furthermore, we will pay special attention to the stability and robustness properties: robustness to the model mis-specification and robustness to the presence of outliers in data.