The autumn school will have 4 courses and 5 invited speakers. Please refer to the planning for definitive hours.

Courses

C1) Rafaël Pinot -- The Marauders Map of adversarial examples: State of knowledge on evasion attacks in machine learning

C2) Adrien Taylor -- Convex Optimization and First-Order Algorithms for Data Science

    This short course introduces key algorithmic principles in first-order and convex optimization, with an emphasis on their relevance to data science and machine learning. It covers both classical foundations and recent developments, aiming to highlight core ideas behind algorithm design and analysis in modern optimization. The class assumes basic familiarity with linear algebra and calculus.

C3) Aymeric Dieuleveut -- Conformal prediction: from a general introduction towards conditional guarantees    

    In this introductory lecture, I will give an introduction to the setup of conformal prediction, in particular the setup, algorithmic solutions, and challenges. I will then focus on conditional guarantees: from impossibility theorems in the worst case, towards approximate results in asymptotic or non asymptotic setups. I will conclude by discussing how these techniques can be used in practice today.

C4) Marylou Gabrié -- Transport based generative modeling and applications to sampling   

    In this mini-course we will discuss the modeling and sampling of high-dimensional probability distributions in the current context of highly-effective generative models. We will focus in particular on generative models based on transport maps: normalizing flows, diffusion models and flow matchings.

Invited Speakers

Aurélien Bellet --TBA        

Laëtitia Chapel -- Approximating Optimal Transport plans with Sliced-Wasserstein   

Optimal Transport (OT) has become a key tool for comparing probability distributions, especially through the Wasserstein distance. Used as a loss function, it performs well across tasks such as classification, domain adaptation, and generative modeling. A major advantage of OT is that it produces an optimal coupling revealing explicit correspondences between samples, enabling applications like shape matching, color transfer, or aligning data distributions with priors in generative models.

However, computing transport plans remains computationally expensive. The Sliced-Wasserstein Distance (SWD) offers a faster way to approximate the Wasserstein distance by projecting distributions onto one-dimensional subspaces, where closed-form solutions exist. Importantly, SWD alone does not approximate the transport plan. Recent work introduces a slicing scheme that enables approximation of both the OT distance and the transport plan. After a quick review of OT and of the the vanilla Sliced-Wasserstein distance, I will introduce this new scheme and will demonstrate its practical value across applications, including a sliced OT-based conditional flow matching approach for image generation, where fast computation of transport plans is essential.

Thomas Moreau -- Optimization bilevel et unrolling   

Mathilde Mougeot -- TBA

Gabriel Cardoso -- Predictive posterior sampling from non-stationnary Gaussian process priors via Diffusion models with application to climate data.   

Bayesian models based on Gaussian processes (GPs) offer a flexible framework to predict spatially distributed variables with uncertainty. But the use of non-stationary priors, often necessary for capturing complex spatial patterns, makes sampling from the predictive posterior distribution (PPD) computationally intractable. In this talk, we propose using a two-step approach based on diffusion generative models (DGMs) to mimic PPDs associated with non-stationary GP priors: we replace the GP prior by a DGM surrogate, and leverage recent advances on training-free guidance algorithms for DGMs to sample from the desired posterior distribution. We apply our approach to a rich non-stationary GP prior from which exact posterior sampling is untractable and validate that the issuing distributions are close to their GP counterpart using several statistical metrics. We also demonstrate how one can fine-tune the trained DGMs to target specific parts of the GP prior. Finally we apply the proposed approach to solve inverse problems arising in environmental sciences.