Optimal Transport for Machine Learning
Optimal Transport (OT) is a foundational mathematical theory that connects optimization, partial differential equations, and probability. It offers a powerful framework for comparing probability distributions and has recently become an important tool in machine learning, especially for designing and evaluating
Introduction to Probabilistic Graphical Models and Deep Generative Models
This course provides a unifying introduction to probabilistic modelling through the framework of graphical models, together with their associated learning and inference algorithms. It is one of the few historical courses at the core of the MVA program. Recent developments
Convex optimization and applications in machine learning
L’objectif de ce cours est d’apprendre à reconnaître, manipuler et résoudre une classe relativement large de problèmes convexes émergents dans des domaines comme, par exemple, l’apprentissage, la finance ou le traitement du signal.
Computational Statistics
This course will detail statistical computational methods and bayesian inference. The course will start with the stochastic gradient algorithm, its theoretical properties and numerical bottlenecks. After a brief introduction to Bayesian inference we will discuss the numerical challenges when computing
Méthodes mathématiques pour les neurosciences
Nous présentons dans ce cours quelques outils mathématiques qui interviennent de manière systématique dans de nombreux problèmes de modélisation en neurosciences.
Image denoising : the human machine competition
1-Explore the structure of images at « patch » level. (Patches are small image extracts that are processed in computational neural networks and in recent image processing. The current dimension that start being well understood is about 8×8=64 to 60×60=3600) 2-Apply it
3D computer vision
Explore the theoretical foundations of 3D computer vision from multiple views, with emphasis on binocular stereo, and show the practical limitations in the algorithmic state of the art. Présentation : here
Sub-pixel image processing
Explore ways (and applications) of linking continuous and discrete image models: How to translate a continuous image processing model into a discrete numerical algorithm? Conversely, how to extract geometric informations from a discrete array of pixels? Presentation : here
Introduction à l’imagerie numérique
Le premier objectif de ce cours est de familiariser les étudiants avec les images numériques. En particulier, le cours présentera les grands principes de la formation et de l’acquisition des images numériques (capteurs, échantillonnage, quantification, dynamique, bruit) et les éléments
Medical image analysis based on generative, geometric and biophysical models
The course is an introduction to medical image anlaysis, in particular registration and segmentation. It is complemented by a course at the second semester detailing some advanced techniques in statistical and mechnaical modeling for computational anatomy and physiology.