M2 Mathématiques, Vision, Apprentissage

Pascal Monasse, Renaud Marlet, Mathieu Aubry.

6 in-class lectures of 3 hours (electronic slides made available to students). 5 home assignments with C++ source code to complete and written report. Written examination (2.5h).

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.

Basic graduate level notions of linear algebra and optimization. Basic programming in C, C++ or java.

Hartley, Richard, and Andrew Zisserman. Multiple view geometry in computer vision. Cambridge university press, 2003. Szeliski, Richard. Computer vision: algorithms and applications. Springer Science & Business Media, 2010.

Octobre - Novembre.

PARIS

Michalis Vazirgiannis.

Grading for the course will be based on a final data challenge plus lab based evaluation.

The ALTEGRAD course ( 28 hours) aims at providing an overview of state-of-the-art ML and AI methods for text and graph data with a significant focus on applications. Each session will comprise two hours of lecture followed by two hours of programming sessions.

Octobre - Novembre - Décembre - Janvier.

PALAISEAU - GIF-SUR-YVETTE

Emmanuel Dupoux, Benoit Sagot.

During the courses, we will use on-line quizzes (on the smartphone/computer) to probe comprehension and trigger discussion. The validation is continuous: there is no final exam, but a combination of quizzes during the lessons (20%) and two practical assignments (TDs), (40% each).

Peech and natural language processing is a subfield of artificial intelligence used in an increasing number of applications; yet, while some aspects are on par with human performances, others are lagging behind. This course will present the full stack of speech and language technology, from automatic speech recognition to parsing and semantic processing. The course will present, at each level, the key principles, algorithms and mathematical principles behind the state of the art, and confront them with what is know about human speech and language processing. Students will acquire detailed knowledge of the scientific issues and computational techniques in automatic speech and language processing and will have hands on experience in implementing and evaluating the important algorithms.

Basic linear algebra, calculus, probability theory.

Janvier - Février - Mars.

PARIS

Andrés Almansa, Said Ladjal, Alasdair Newson.

Structure of the course:

7 sessions of 3 hours each (course + practical session)

2 review and project preparation sessions

1 project presentation session

A detailed description of the course is provided in the course website https://delires.wp.imt.fr

Evaluation is based on the students’ individual reports on practical sessions and on a longer project, and on the final project presentation session.

The miniaturisation of sensors and the evolution of computational capabilities has led to the ubiquitous presence of images. However, the increasing demand for image-based content also requires sophisticated post-processing (filtering, restoration etc.), in order to ensure good quality results. At the heart of these post-processings are image models, which allow us to establish powerful and efficient algorithms. Deep learning is the latest addition to a long list of such image models. The aim of this course is to present recent techniques based on deep learning for the quality of images, and to compare them to pre-existing methods. We will explore many applications such as denoising, super-resolution, deblurring, texture synthesis and natural image generation. In each case we will present the strengths and limitations of the different techniques studied. In particular, we will present a critical analysis of the methods and show some of the pitfalls in which they sometimes fall.

Applied Mathematics (Linear Algebra, Numerical Analysis, Differential Calculus, Fourier Analysis) Programming (Python, Matlab) The basic concepts of image processing, optimization and deep learning are useful but will be introduced in the course.

- Zhang et al (2018). FFDNet. doi:10.1109/TIP.2018.2839891 - Kim et al (2016). Deeply-Recursive Convolutional Network for Image Super-Resolution. doi:10.1109/CVPR.2016.181 - Carvalho et al (2018). Deep Depth from Defocus. arXiv:1809.01567 - Ryu et al (201.

Janvier - Février - Mars.

PALAISEAU

Stanley Durrleman.

Organisation du cours: Le cours se décomposera en 7 séances de 3h. Validation: La validation se fera sur projet.

L'observation d'un phénomène de manière répétée dans le temps (données longitudinales) soulève le problème de la définition de distribution statistique de trajectoires. Il se trouve que la géométrie différentielle se révèle un outil particulièrement adapté pour définir de telles distributions. Elle permet également de traiter de manière adéquate les données structurées dans des modèles génératifs, où la métrique Riemanienne sert à pénaliser des variations ne respectant pas la structure des données.
Ce cours donnera aux étudiants les fondements des approches géométriques en apprentissage statistique. Nous utiliserons les données morphométriques et longitudinales comme des exemples particulièrement parlant de l'intérêt de ces techniques. Nous montrerons de nombreuses applications issues principalement de l'étude du vieillissement cérébral et de la progression de maladies neurodégénératives à partir de données d'imagerie anatomique et fonctionnelle. D'autres exemples seront donnés sur des problèmes de vision par ordinateur.

Le cours ne nécessite pas de prérequis. Les notions de géométrie différentielle et d'inférence statistique seront rappelées au fur et à mesure. Certaines notions abordées dans ce cours : modèles à effets mixtes, modèles de formes, statistiques sur des variétés, et algorithmes stochastiques.

Janvier - Février - Mars.

GIF-SUR-YVETTE

RICHARD Gaël, BADEAU Roland.

The course contains 13,5 h theoretical lectures 10,5 h practical sessions (TP) in Matlab (or Python if preferred) Lectures are planned to be in French but slides will be in English

UE validation is done through papers reading/analysis with written report and oral presentation.

The aim of this course is to span several domains of audio signal analysis including audio indexing (or machine listening), high-resolution audio spectral analysis, audio source separation, and audio transformations (3D sound rendering, sound effects and sound modifications).

Basics of signal processing.

Y. Grenier, R. Badeau, G. Richard « Polycopiés de cours sur le traitement du signal audio (in French) », Télécom ParisTech. M. Mueller, D. Ellis, A. Klapuri, G. Richard, Signal Processing for Music Analysis", IEEE Journ. on Selected Topics in Sig. Proc., October 2011.

Janvier - Février - Mars.

PALAISEAU

Emmanuel Bacry.

Organization of courses :

Only Courses

Validation : Oral and written report on an academic paper.

Initiation to several signal processing techniques specific to audio processing

Topics :

Time-Frequency Analysis
Denoising (old/bad recordings)
Audio signal modification (pitch shifting, slowing down,...)
Audio Synthesis
Speech or Music recognition
Estimation of intsantaneous frequencyfréquence fondamentale
Psycho-acoustic
Audio Filtering
LPC : Linear Prediction Coding.

Basics of linear algebra, calculus and Fourier transform.

Janvier - Février - Mars.

GIF-SUR-YVETTE

Rémi Bardenet (CNRS, Univ. Lille), https://rbardenet.github.io Julyan Arbel (Inria, Univ. Grenoble-Alpes), https://www.julyanarbel.com.

The course consists in lectures and practicals. Evaluation is project-based, each project revolving around a research paper. Students form groups (the number of students by project will depend on the number of students in the class). Each group reads and reports on a research paper from a list. We strongly encourage a dash of creativity: students should identify a weak point, shortcoming or limitation of the paper, and try to push in that direction. This can mean extending a proof, implementing another feature, investigating different experiments, etc. Deliverables are a small report and a short oral presentation in front of the class, in the form of a student seminar, which will take place during the last lecture.

By the end of the course, the students should
* have a high-level view of the main approaches to making decisions under uncertainty.
* be able to detect when being Bayesian helps and why.
* be able to design and run a Bayesian ML pipeline for standard supervised or unsupervised learning.
* have a global view of the current limitations of Bayesian approaches and the research landscape.
* be able to understand the abstract of most Bayesian ML papers.

Detailed content:
# Decision theory
* Describe frameworks for modelling uncertainty and making decisions.
* Introduce minimax and Bayes rules.

# Bayesian principles
* Formalize expected utility, discuss interpretations
* Show how most tasks of the MLer fit into the framework: supervised and unsupervised learning, active learning, model choice, etc.
* Practical session 1

# Bayesian computation for ML
* ML-specific Monte Carlo approaches: variational principles, advanced MCMC.
* Practical session 2

# Bayesian nonparametrics
* Popular BNP models: Gaussian, Dirichlet, Pitman-Yor, Gibbs-type, Stick-breaking, Indian Buffet processes, etc.
* Practical session 3

# Bayesian methods for deep learning
* Bayesian deep neural networks (BNN).
* Dropout as a Bayesian approximation.
* Bayesian Generative Adversarial Networks.
* Practical session 4.

* An undergraduate course in probability. * It is recommended to have followed either the course of P. Latouche and N. Chopin on "Probabilistic graphical models" or the course of S. Allassonière on "Computational statistics" during the first semester. * Practicals will be in Python and R. A basic knowledge of both languages is required, students should be able to read and write simple programs and load libraries.

* Parmigiani, G. and Inoue, L. 2009. Decision theory: principles and approaches. Wiley. * Robert, C. 2007. The Bayesian choice. Springer. * Murphy, K. 2012. Machine learning: a probabilistic perspective. MIT Press. * Ghosal, S., & Van der Vaart, A. W. 2017. Fundamentals of nonparametric Bayesian inference. Cambridge University Press.

Janvier - Février - Mars.

GIF-SUR-YVETTE

- 7 lectures (3 hours), each comprising formal lectures and practical illustrations - Final group home project presentation (3 hours).

Objective of the course:
The course aims at introducing both concepts and methods used in clinical (or medical) research. It is integrated to the health science theme of the master program.
The course will both emphasize the principles and concepts underlying the different goals of clinical research (prediction and causation) and develop on specific statistical methods that can be used to plan studies and analyze data in this context.
It will focus on notions and methods that are not covered by other courses of the master (e.g. design, survival analysis, causal inference), that will be tackled both from the theoretical and applied point-of-view.
Methods will be illustrated on several practical examples.

There are no formal prerequisites to this course, but undergraduate courses in probability or statistics will help.

- Harrell FE. Regression Modeling Strategies. Springer-Verlag, 2014. - Herna?n M, Brumback B, Robins J. Marginal structural models to estimate the joint causal effect of nonrandomized treatments. Journal of the American Statistical Association 2001; 96:44.

Janvier - Février - Mars.

GIF-SUR-YVETTE

- 6 courses of 3h each + final presentation of the project - Evaluation on a mini-project (written report, slides, oral presentation) - Homework : 3 numerical tours (python notebooks).

Optimal transport (OT) is a fundamental mathematical theory at the interface between optimization, partial differential equations and probability. It has recently emerged as an important tool to tackle a surprisingly large range of problems in data sciences, such as shape registration in medical imaging, structured prediction problems in supervised learning and training deep generative networks. This course will interleave the description of the mathematical theory with the recent developments of scalable numerical solvers. This will highlight the importance of recent advances in regularized approaches for OT which allow one to tackle high dimensional learning problems. The course will feature numerical sessions using Python.

- Python programming - Basics of convex analysis (convex function, convex set) - Basics of differential calculus (computation of gradient) - Basics of optimization (gradient descent, linear programming).

- Gabriel Peyré and Marco Cuturi, Computational Optimal Transport, https://optimaltransport.github.io (course notes, slides, codes). - Gabriel Peyré, The Numerical Tours of Data Sciences, www.numerical-tours.com (for the homework and the projects). - Fili.

Octobre - Novembre - Décembre.

PARIS

Cours magistraux : Stéphanie Allassonnière TP (cette année) Thomas Lartigue.

20h of tutorials 10h of training classes with theory developments and implementations.

This course propose to introduce several stochastic optimisation algorithms and sampling methods.The goal is to understand the theory and the numerical implementations issues related to these algorithms.
The course is structures as follows.
Introduction to Bayesian inference and decision theory
The stochastic gradient descent
The EM algorithms and its extensions
MCMC simulation methods and adaptives MCMC samplers
Simulated annealing and ABC optimisation method.
Theory of convergence of stochastic approximations to understand the theoretical guaranties of the previous algorithms.
Examples will be shown in relation to application in the medical field.

We assume that the students are familiar with the notions introduced in a "Introduction to Probability theory" course. We also assume that they know the conditional expectation and Markov Chains in finite time and finite space.

For references on probabilities, you can look at Jean-François Legall's course which is available online. You will find the basics of measurement theory, probabilities and Markov chains. Non-uniform random variate generation, Luc Devroye (available online) The bayesian Choice, Christian Robert Méthodes de Monte Carlo par Chaines de Markov, Christian Robert Stochastic approximations with decreasing gain: Convergence and Asymptotic theory, Bernard Delyon.

Octobre - Novembre - Décembre.

GIF-SUR-YVETTE

The objective of this course is to learn to recognize, transform and solve a broad class of convex optimization problems arising in various fields such as machine learning, finance or signal processing. The course starts with a basic primer on convex analysis followed by a quick overview of convex duality theory. The second half of the course is focused on algorithms, including first-order and interior point methods, together with bounds on their complexity. The course ends with illustrations of these techniques in various applications.

Good knowledge and practice of Linear algebra.

- Convex Optimization, S. Boyd and L. Vandenberghe, Cambridge University Press. - Introductory Lectures on Convex Optimization, Y. Nesterov, Springer. - Lectures on Modern Convex Optimization, A. Nemirovski and A. Ben-Tal, SIAM.

Octobre - Novembre.

PARIS

Louis Martin (Facebook); Edouard Grave (Facebook) Diane Larlus (Naver Labs) David Picard (ENPC) Mathieu Aubry (ENPC).

3h sessions, some only lecture, some only practical work, some mixed.

Get you started in the theory and practice of Deep Learning: With the increase of computational power and amounts of available data, but also with the development of novel training algorithms and new whole approaches, many breakthroughs occurred over the few last years in Deep Learning for object and spoken language recognition, text generation, and robotics. This class will cover the fundamental aspects and the recent developments in deep learning in different domains: Computer Vision, Natural Language Processing, and Deep Reinforcement Learning. The course aims to introduce students to Deep Learning through the development of practical projects. We expect that by the end of the course, the students will be able to implement and develop new methods in different domains.

- history of deep learning and its relation to cognitive science;

- feedforward networks, regularisation and optimization;

- representation learning & siamese networks;

- GAN & transfer learning;

- recurrent networks and LSTM for Natural Language Processing;

- object detection;

- self-supervised methods;

- deep reinforcement learning.

There is no official prerequisite for this course. However, the students are expected to have basic knowledge of Python.

Deep Learning. Ian Goodfellow, Yoshua Bengio, and Aaron Courville, MIT Press, 2016. A Selective Overview of Deep Learning. Jianqing Fan, Cong Ma, Yiqiao Zhong. arXiv 2019.

Octobre - Novembre - Décembre - Janvier.

GIF-SUR-YVETTE

Guillaume Charpiat, Victor Berger + T.B.A.

The course will comprise lectures as well as practical and theoretical exercises (mini-projects, in PyTorch), which will be evaluated. The practical sessions will be run on personal laptops (no GPU needed). Announcements will be made through a dedicated mailing-list; questions and discussions will take place on a Piazza forum. Course webpage: https://www.lri.fr/~gcharpia/deeppractice/.

Despite impressive mediatized results, deep learning methods are still poorly understood, neural networks are often difficult to train, and the results are black-boxes missing explanations, which is problematic given the societal impact of machine learning today (used as assistance in medicine, hiring process, bank loans...). Besides, real world problems usually do not fit the standard assumptions or frameworks of the most famous academic work (e.g., data quantity and quality). This course aims at providing insights and tools to address these practical aspects, based on mathematical concepts.

We will first emphasize the gap between practice and classical theory (e.g., number of parameters), and reconcile them thanks to recent theoretical advances.

After a review of recent architectures, we will study visualization techniques, and check that undesired biases present in the dataset (e.g., sensitivity to gender when matching CVs to job offers) are not reproduced.

We will then investigate practical issues when training neural networks, in particular data quantity (small or big data), application to reinforcement learning and physical problems, and automatic hyper-parameter tuning.

- The "Introduction to Deep Learning" course by Vincent Lepetit (taking place during the 1st semester) - Notions in machine learning, Bayesian statistics, analysis, differential calculus - Basic knowledge of Python and PyTorch.

Related books: - "Deep Learning" by I. Goodfellow, Y. Bengio and A. Courville

Examples of references: - "Do Deep Nets Really Need to be Deep?"; L. J. Ba, R. Caruana; NIPS 2014 - "Graph Attention Networks"; P. Velickovic, G. Cucurull, A. Casanova, A. Romero, P. Lio, Y. Bengio; ICLR 2018 - "Women also Snowboard: Overcoming Bias in Captioning Models"; L. A. Hendricks, K. Burns, K. Saenko, T Darrell, A Rohrbach; FAT-ML 2018 - "Scaling description of generalization with number of parameters in deep learning"; M. Geiger, A. Jacot, S. Spigler, F. Gabriel, L. Sagun, S. d'Ascoli, G. Biroli, C. Hongler

Janvier - Février - Mars.

GIF-SUR-YVETTE

Laurent Cohen.

About half on deformable models and half on geodesic methods. 10 sessions of 3 hours, including 3 or 4 with 2 hours on laptop Validation by Project.

Deformable models are elastic models of curves or surfaces that deform in the image domain in order to extract shapes of objects.
This consists in minimizing an energy combining internal smoothing terms and dat based terms.
A main drawaback of these methods lies in the curve or surface being trapped in a local minima.
Therefore many approaches were introduced in order to avoid local minima,
like the balloon model, region based terms, shape prior.
The geodesic formulation allows to ensure finding the global minimum of the energy
among all paths that link given end points.
These minimal paths correspond to minimal geodesics according to some adapted metric.
Finding a geodesic distance can be solved by the Eikonal equation using the fast and efficient Fast Marching method.
Introduced first as a way to find the global minimum of a simplified active contour energy, these methods have been extended to cover all kinds of active contour energy terms. Also, various methods have been introduced that improve either the interactive aspects or their efficiency in order to make completely automatic or minimally interactive tools for image segmentation.
Also, a way to penalize the curvature in the framework of geodesic minimal paths was introduced, leading to more natural results in vessel extraction for example.
In this course we will present different mathematical methods, numerical and algorithmic aspects to solve the problem, as well as concrete applications, mainly in the medical domain.

Admission to MVA sufficient.

- Minimal Paths and Fast Marching Methods for Image Analysis. , Laurent D. Cohen, In Mathematical Models in Computer Vision: The Handbook, Springer 2005.

- Geodesic Methods in Computer Vision and Graphics, Gabriel Peyré, Mickaël Péchaud, Rena.

Janvier - Février - Mars.

PARIS

Nikos Paragios, Yuliya Tarabalka, and Karteek Alahari.

8 lectures of 3 hours. Quizzes and projet during the course.

Probabilistic graphical models provide a powerful paradigm to jointly exploit probability theory and graph theory for solving complex real-world problems. They form an indispensable component in several research areas, such as statistics, machine learning, computer vision, where a graph expresses the conditional (probabilistic) dependence among random variables. This course will focus on discrete models, that is, cases where the random variables of the graphical models are discrete. After an introduction to the basics of graphical models, the course will then focus on problems in representation, inference, and learning of graphical models. We will cover classical as well as state of the art algorithms used for these problems. Several applications in machine learning and computer vision will be studied.

Solid understanding of mathematical methods, including linear algebra, probability, integral transforms and differential equations.

Probabilistic graphical models: principles and techniques, Daphne Koller and Nir Friedman, MIT Press

Convex Optimization, Stephen Boyd and Lieven Vanderbeghe

Numerical Optimization, Jorge Nocedal and Stephen J. Wright

Introduction to Operations Research, Frederick S. Hillier and Gerald J. Lieberman

An Analysis of Convex Relaxations for MAP Estimation of Discrete MRFs, M. Pawan Kumar, Vladimir Kolmogorov and Phil Torr

Convergent Tree-reweighted Message Passing for Energy Minimization, Vladimir Kolmogorov.

Janvier - Février - Mars.

GIF-SUR-YVETTE

Sébastien Gerchinovitz (MCF à l'Institut de Mathématiques de Toulouse), François Malgouyres, (Pr à l'Institut de Mathématiques de Toulouse), Edouard Pauwels (MCF à l'Institut de Recherche en Informatique de Toulouse), Nicolas Thome (Pr au Conservatoire National des arts et métiers, laboratoire CEDRIC).

Le cours sur 10 séances dont les thèmes sont: Introduction à l'apprentissage avec des réseaux; Optimisation non-convexe; Paysage de a fonction objectif; Stabilité de l'optimum; Expressivité des réseaux feed-forward; Erreur de généralisation des réseaux de neurones; Quelques propriétés mathématiques des GANs; Deep Learning moderne; Deep Learning robuste Cours; Deep Learning robuste TP;.

L'objectif principal de ce cours est de présenter des résultats représentatifs de la recherche actuelle sur les justifications mathématiques des algorithmes d'apprentissage profond; puis de faire le lien avec la mise en pratique de ces algorithmes. Nous commencerons par formaliser différents modèles de réseaux et par décrire des algorithmes de back-propagation utilisés pour leur minimisation. Le c{\oe}ur du contenu mathématique du cours consistera ensuite en la présentation de résultats récents sur :
- l'optimisation non-convexe ;
- les propriétés du paysage de la fonction objectif ;
- la stabilité des minimiseurs (notamment dans le cas de réseaux linéaires structurés); l'interprétabilité des réseaux;
- l'expressivité des réseaux, leur complexité de Rademacher et la régularisation avec le dropout ;
- des propriétés des Generative Adversarial Networks (GANs).
- des propriétés de robustesse décisionnelle des réseaux profonds (incertitude, stabilité)

Ces résultats mathématiques seront complétés par la présentation moins mathématisée de différentes architectures et propriétés de réseaux utilisés en pratique.

Master 1 de Mathématiques, les bases en optimisation et apprentissage statistique.

- Bolte, Sabach, Teboulle, "Proximal alternating linearized minimization for nonconvex and nonsmooth problems", Math. Prog. Vol 146, no 1-2, pp 59-594, 2014. - Baldi, Hornik, "Neural networks and principal component analysis: Learning from examples witho.

Janvier - Février - Mars.

GIF-SUR-YVETTE

Each section of the course is divided into 1h30' lecture and 1h30' lab. The labs will include Python programming of optimization algorithms and will provide the students the opportunity to apply the methods seen in lecture to applicative examples in the context of datascience.

In a wide range of application fields (inverse problems, machine learning, computer vision, data analysis, networking,...), large scale optimization problems need to be solved.
The objective of this course is to introduce the theoretical background which makes it possible to develop efficient algorithms to successfully address these problems by taking advantage of modern multicore or distributed computing architectures. This course will be mainly focused on nonlinear optimization tools for dealing with convex problems. Proximal tools, splitting techniques and Majorization-Minimization strategies which are now very popular for processing massive datasets will be presented. Illustrations of these methods on various applicative examples will be provided.

There is no official prerequisite for this course. However, the students are expected to : Have basic knowledge of linear algebra and functionnal analysis. Be familiar with Python programming.

- D. Bertsekas, Nonlinear programming, Athena Scientic, Belmont, Massachussets, 1995. - Y. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course, Springer, 2004. - S. Boyd and L. Vandenberghe, Convex optimization, Cambridge University Pre.

Octobre - Novembre - Décembre.

GIF-SUR-YVETTE

TP: Joan Glaunes (Université Paris-Descartes) Cours: Alain Trouvé (ENS Paris-Saclay).

Le cours alternera 9 seances de cours et 3 seances de TP.

Inspiré par les recherches développées depuis les années 2000 dans le cadre de l'anatomie numérique (Computational Anatomie) pour l'analyse de la variabilité des formes biologiques, ce cours propose plus largement une exposition d'une théorie mathématique des espaces de formes qui consiste à construire des métriques riemanniennes sur des espaces d'objets (n-uplets de points, courbes, régions binaires, surfaces, champ de tenseurs, images en niveau de gris, mesures etc) considérés comme des variétés de dimension finie ou infinie à partir de l'étude des déformations infinitésimales naturelles agissant sur ces objets.

Nous montrerons que la construction et l'étude de ces métriques, le calcul effectif des géodésiques en lien avec le controle optimal dans ces espaces de formes et la compréhension des cartes exponentielles locales sont des questions d'une grande importance théorique et pratique.

Le cours abordera afin les outils algorithmiques puissants qui ont été développé récemment qui permettent de déployer les techniques du cours sur des jeux massifs de données.

Une bonne connaissance du calcul différentiel en dimension finie et dans les espaces de Banach. Une certaine familiarité avec les variétés différentielles pourra être utile.

L. Younes, Shapes and Diffeomorphisms, Springer 2010.

Janvier - Février - Mars - Avril.

GIF-SUR-YVETTE

Michal Valko, Omar Darwiche Domingues, Pierre Perrault, Daniele Calandriello.

The course will feature 11 sessions, 8 lectures and 3 recitations (TD), each of them 2 hours long. There may be a special session with guest lectures. There may be also an extra homework with extra credit. The evaluation is be based on reports from TD and from the projects. Several project topics will be proposed but the students will be able to come up with their own and they will be able to work in groups of 2-3 people. The slides and the scribes from the lectures are the best reference and are made to be comprehensive There is no recommended textbook. The material we cover is mostly based on research papers, some of which very recent.

The graphs come handy whenever we deal with relations between the objects. This course, focused on learning, will present methods involving two main sources of graphs in ML: 1) graphs coming from networks, e.g., social, biological, technology, etc. and 2) graphs coming from flat (often vision) data, where a graph serves as a useful nonparametric basis and is an effective data representation for such tasks such as spectral clustering, manifold or semi-supervised learning. We will also discuss online decision-making on graphs, suitable for recommender systems or online advertising. Finally, we will always discuss the scalability of all approaches and learn how to address huge graphs in practice. The lectures will show not only how but mostly why things work. The students will learn relevant topics from spectral graph theory, learning theory, bandit theory, graph neural networks, necessary mathematical concepts and the concrete graph-based approaches for typical machine learning problems. The practical sessions will provide hands-on experience on interesting applications (e.g., online face recognizer) and state-of-the-art graphs processing tools.

Octobre - Novembre - Décembre.

PARIS

The course consist of theoretical lectures and practical workshops. Two types of practical workshops •IPOL workshops: testing image denoising methods on the IPOL platform (Image Processing On Line, www.ipol.im). No programming is required. •Deep-learning workshops: guided workshops were we will experiment training and using CNNs for denoising. These require some basic Python programming.

Material provided: - Lecture notes in English with exercises - online workshops at IPOL (image processing on line, www.ipol.im) - online directed Python workshops.

This course addresses one of the fundamental problems of signal and image processing, the separation of noise and signal. It was already the key problem of Shannon's foundational Mathematical Theory of Communication. This problem has uncountable applications for image formation, image and video post-production, and feature detection. Since the 70s, several denoising approaches have been identified and can be grouped in a handful of useful 'denoising principles' with notable progress, from Fourier analysis, wavelet theory to sparse decompositions and non-local methods. In 2016, neural denoisers have started outperforming (slightly) human made denoising algorithms. Their principles are quite different. Human algorithms adopt mathematical assumptions about the image structure to denoise them. Neural algorithms learn image structure from vast collections of images. We will explain the classical theories, the neural devices and demonstrate what perspectives and cross-fertilization this comparison yields. Both theories process image patches.

Prerequisites : Elementary probability theory (discrete and continuous) Fourier analysis, differential calculus.

• A. Buades, B. Coll, and J. M. Morel. A review of image denoising algorithms, with a new one. Multiscale Modeling Simulation 2005. • K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian. Image denoising by sparse 3D transform-domain collaborative filtering. IEEE Transactions on image processing , 2007. • D.Zoran and Y.Weiss. Scale invariance and noise in natural images. In Computer,Vision, 2009 IEEE 12th International Conference, 2009. • G. Facciolo, N. Pierazzo, and J.-M. Morel. Conservative Scale Recomposition for Multiscale Denoising SIAM Journal on Imaging Sciences

Octobre - Novembre - Décembre.

GIF-SUR-YVETTE

Théo Papadopoulo (INRIA Sophia Antipolis) et Bertrand Thirion (INRIA Saclay).

Validation : Written exam (problem, exercises and questions on a previously given article) + project.

This lecture deals with brain functional imaging and its application to create brain computer interfaces using two non-invasive techniques used to estimate brain activity: 1) M/EEG which measures the electro-magnetic field created by cortical currents, 2) functional MRI which measures a signal (BOLD) linked to energy consumption in the brain.
Some basic notions of electromagnetics :
Maxwell equations : quasistatic regime,Biot and Savart law.
Source modelling.
Forward and Inverse problems in M/EEG
Forward problem  solution using finite elements.
Denoising M/EEG signals.
Inverse problem (MUSIC, Beamforming, Imaging).
Validation.
Statistical analysis for brain imaging
statistical analysis of images.
Probabilistic error control non-parametric testing
Statistical analysis of covariance models to capture brain connectivity
The brain decoding inverse problem.
Towards Brain Computer Interfaces
Communication through brain activity.
Extraction and classification of salient features.
Feedback role.

Integral calculus, elements of statistics, numerical computation, linear algebra, optimisation, Python.

We provide some lecture notes covering most of the course content. * Handbook of Functional MRI Data Analysis, R.Poldrack, J.Mumford.

Janvier - Février - Mars.

GIF-SUR-YVETTE

Julie Delon (Université de Paris) et Yann Gousseau (Télécom Paris).

7 séances de cours (3h) 2 séances de TP (3h).

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), les ingrédients principaux de la structure des images (radiométrie, couleur, texture, artefacts d'acquisition), tout en s'attachant à donner une connaissance des outils les plus classiques du traitement des images et de la photographie computationnelle.

Le deuxième objectif est de confronter dans une approche thématique divers outils mathématiques approfondis par ailleurs dans le master (Ondelettes, EDP, approches variationnelles, approches stochastiques, réseaux de neurones convolutionnels). Le cours sera aussi souvent que possible illustré par des exemples d'applications issus des domaines de la photographie numérique grand public, de l'imagerie médicale ou de l'imagerie aérienne.

Bases de probabilité, de statistique et d'analyse de Fourier (Cours de L3 suffisant) ; bases de traitement du signal.

Octobre - Novembre - Décembre.

PARIS - PALAISEAU

Herve Delingette et Xavier Pennec.

Organization of courses : 7 courses

Validation : Projects + article presentation + quizz (mini exam).

The course is an introduction to medical image analysis, ranging from generic image analysis such as image registration and image segmentation to more advanced techniques in statistical and mechanical modeling for computational anatomy and physiology.

Handbook of Medical Imaging, Volume 2. Medical Image Processing and Analysis (SPIE Press Monograph Vol. PM80/SC), J. Michael Fitzpatrick (Author), Milan Sonka, 2009. Medical Image Registration, Joseph V. Hajnal (Editor), Derek L.G. Hill, D. J. Hawkes, 2001. Handbook of Medical Imaging: Processing and Analysis, 2nd edition. I. Bankman Editor. Academic Press, 2008. Medical Image Computing and Computer Assisted Intervention (Annual Conference) MICCAI, http://www.miccai.org/conferences.

Octobre - Novembre - Décembre.

GIF-SUR-YVETTE

Nicolas Vayatis.

Organization :

8 theoretical sessions

3 practical sessions

Validation :

Part 1 : partial exam (mandatory)

Part 2 : final exam or paper review project (report+oral presentation)

Re-take : written exam or project (proposed only for students who attended Part 1 and Part 2).

Courses objetctives:
The course presents the mathematical foundations for supervised learning.

Topics :
Typology of learning problems
Statistical models and main algorithms for classification, scoring, ...
Performance criteria and inference principles
Convex risk minimization
Complexity measures
Aggregation and ensemble methods
Main theorems.

Undergraduate courses in Analysis and Probability.

S. Boucheron, O. Bousquet, and G. Lugosi. Theory of Classification: a Survey of Recent Advances. ESAIM: Probability and Statistics, 9:323375, 2005.

L. Devroye, L. Györfi, G. Lugosi, A Probabilistic Theory of Pattern Recognition, Springer, New York, 1996.

Octobre - Novembre - Décembre.

GIF-SUR-YVETTE

Jean-Philippe Vert et Julien Mairal.

The final note will be an average of a homework (20%), a data challenge (40%), and a final written exam (40%). You can work on the project alone or with up to two friends. Data challenge is now online. Instructions will be given in class to access it.

Many problems in machine learning applications can be formalized as classical statistical problems, e.g., pattern recognition, or regression, with the caveat that the data are often not vectors of numbers. For example, protein sequences and structures in computational biology, or time series in finance.
Kernel methods are a class of algorithms well suited for such problems. Indeed they extend the applicability of many statistical methods initially designed for vectors to any type of data, without the need for explicit vectorization. The price to pay is the need to define a so-called positive definite kernel function between the objects.
The goal of this course is to present the mathematical foundations of kernel methods. We will start with a presentation of the theory of positive definite kernels and reproducing kernel Hilbert spaces, which will allow us to introduce several kernel methods including kernel principal component analysis and support vector machines. Then we will come back to the problem of defining the kernel. We will present a few examples of kernel for strings and graphs. Finally we will touch upon topics of active research, such as large-scale kernel methods and deep kernel machines.

- basic knowledge of linear algebra, probability, statistics, and a good knowledge of linear models in machine learning are required. - basic knowledge of Hilbertian and Fourier analysis is useful. - having followed a course on optimization is also useful.

N. Aronszajn, "Theory of reproducing kernels", Transactions of the American Mathematical Society, 68:337-404, 1950. C. Berg, J.P.R. Christensen et P. Ressel, "Harmonic analysis on semi-groups", Springer, 1994. N. Cristianini and J. Shawe-Taylor, "Kernel Methods for Pattern Analysis", Cambridge University Press, 2004. B. Schölkopf et A. Smola, "Learning with kernels", MIT Press, 2002. B. Schölkopf, K. Tsuda et J.-P. Vert, "Kernel methods in computational biology", MIT Press, 2004. V. Vapnik, "Statistical Learning Theory", Wiley, 1998.

Janvier - Février - Mars - Avril.

PARIS

Stéphane Mallat.

Le cours sera évalué par un projet à partir de l'un des challenges sur le site web: challengedata.ens.fr.

Le cours présente les liens entre les réseaux de neurones convolutifs et
les décompositions multiéchelles et la transformée en ondelettes. Le
cours commencera par un rappel sur algorithmes d'apprentissage par
réseaux de neurones profonds. On montrera le lien avec les
représentations multiéchelles en générales avec des applications plus
particulières pour l'image et le son. Les transformées en ondelettes et
représentations temps-fréquences seront introduites. On verra ce
qu'apporte les réseaux de neurones profonds par rapport à ces
représentations prédéfinis et le cours se terminera sur des questions
ouvertes.

Janvier - Février - Mars.

PARIS

Etienne Tanré et Romain Veltz.

We present mathematical tools that are central to modeling in neuroscience. The prerequisites to the course are a good knowledge of differential calculus and probability theory from the viewpoint of measure theory. The thrust of the lectures is to show the applicability to neuroscience of the mathematical concepts without giving up mathematical rigor. The concepts presented in the lectures will be illustrated by exercise sessions.

-Introduction to dynamical systems: orbits and phase portraits, invariant manifolds, center manifold in finite dimension.
-Introduction to bifurcation theory: dimension 1 (saddle-node, transcritical, pitchfork), dimension 2 (Hopf), center manifold, normal form, equivariant bifurcations.
-Applications: single spiking neuron dynamics, Turing mechanism for cortical pattern formation, geometric visual hallucinations.
-Mesoscopic models of visual cortical areas: anatomical structure of the visual cortex (V1), functional architecture of V1, neural fields models.
-Neuronal models: aspatial Hodgkin-Huxley model, simplified models, synaptic models, spatial models.
-Importance of noise: Brownian motion, stochastic differential equations, application to neurons.

The prerequisites to the course are a good knowledge of differential calculus and probability theory.

Kandel, Eric R., Principles of neural science, 2013. Byrne, John H., Ruth Heidelberger, et Melvin Neal Waxham, From molecules to networks: an introduction to cellular and molecular neuroscience, 2014. Gerstner, Wulfram, Werner M. Kistler, Richard Naud, et Liam Paninski. Neuronal dynamics: from single neurons to networks and models of cognition, 2014. Koch, Christof. Biophysics of Computation: Information Processing in Single Neurons. 2004. Bressloff, Paul C. Waves in Neural Media, 2014. Eugène Izhikevich, Dynamical systems in neuroscience: the geometry of excitability and bursting, 2006. G

Octobre - Novembre - Décembre.

PARIS

Lectures with slides (in English) and at the blackboard. Course validation: Regular attendance is mandatory to get credits from this Course. Modalities: personal work (numerical simulations, mathematical analysis...) based on an article on a topic related to the Course. The choice of the paper must be validated by the teacher (a list of papers will be posted on the course website, but the students can also submit their own suggestions). The student must return a report (about 10 pages) and give an oral presentation (20mn + questions), both presenting a critical reading of the paper and his/her personal contribution. The question session may also include questions on the Course.

Practical information, course material (bibliography, slides and related papers), and updates, are provided on the Course website: http://www.lps.ens.fr/~nadal/Cours/MVA/ Access to the course material, whenever copyright-protected, is restricted to registered students.

This Course is an introduction to the mathematical modelling of the neural basis of learning, adaptation, and decision making. The Course emphasizes the historical and conceptual links between the fields of computational neuroscience and machine learning. Models and analysis make use of concepts and tools from statistical physics, dynamical systems, Bayesian statistics, and, for an important part, information theory. Although the Course is essentially about neuroscience and cognitive science, it also provides openings to other domains and themes – physics of disordered systems, combinatorial optimization, evolutionary biology, complex systems in the social sciences. In this Course, the conceptual and qualitative aspects (What we want to study and Why, Why the results matter) are as important as the How (mathematical details).

Main topics:
Learning: neural networks and synaptic plasticity - the Hebb paradigm
Short term memory – models of attractor neural networks
Supervised learning – from the perceptron to the Cerebellum
Unsupervised learning – Hebbian learning and PCA
Neural coding: an information theoretic approach
Categorical perception – The Groundwork of Cognition
Decision making.

There is no prerequisite. The Course is intended for the MVA students, but also open (on request, within the limits of available places) to students of other masters, as well as PhD students, in mathematics, computer/data science or physics. The necessary concepts and tools are introduced during the lectures (notably for what concerns the basis of information theory). Some knowledge of neurobiology, information theory, dynamical systems or statistical physics will be helpful but not necessary.

Theoretical / computational neuroscience L. Abbott and P. Dayan, Theoretical Neuroscience, MIT Press, 2nd ed., 2005. Online: http://www.gatsby.ucl.ac.uk/~lmate/biblio/dayanabbott.pdf G. B. Ermentrout and D. H. Terman, Mathematical Foundations of Neuroscience, Springer, 2010. W. Gerstner, W. M. Kistler, R. Naud and L. Paninski, Neuronal Dynamics, Cambridge Univ. Press, 2014. Online: https://neuronaldynamics.epfl.ch/ Neurobiology and Cognition La cognition. Du neurone à la société, sous la direction de D. Andler, T. Collins et C. Tallon-Baudry, Folio essais (n. 636), Série XL, Gallimard, 2018

Janvier - Février - Mars.

GIF-SUR-YVETTE

François GOULETTE, Jean-Emmanuel DESCHAUD, Tamy BOUBEKEUR.

6 séances de 4h : 2h cours, 2h TP informatique. Les TP se font sur les ordinateurs des étudiants, avec des logiciels libres à installer. 1 séminaire de recherche de 3h 1 journée de présentation des projets d'élèves.

Ce cours donne un panorama des concepts et techniques d'acquisition, de traitement et de visualisation des nuages de points 3D, et de leurs fondements mathématiques et algorithmiques.

Systèmes de perception 3D
Traitements et opérateurs
Recalage
Segmentation de nuages de points
Reconstruction de courbes et surfaces
Modélisation par primitives
Rendu de nuages de points et maillages.

Pré-requis scientifiques : géométrie, algèbre linéaire, probabilités. Pré-requis techniques (utiles pour le projet) : programmation (C, C++, Python ou Matlab).

Images de profondeur, dir. J. Gallice, 2001, Hermès Science. Modélisation 3D automatique, F. Goulette, 1998, Presses de l'Ecole des Mines. Traitement de nuages de points denses et modélisation 3D d'environnements par système mobile LiDAR / Caméra, J.-E. Deschaud, 2010, thèse de doctorat MINES ParisTech. Rendu Par Points, Christophe Schlick, Patrick Reuter et Tamy Boubekeur, Informatique Graphique et Rendu, Hermès Publishing, 2007 Point-based graphics, M. Gross and H. Pfister editors, 2007, Morgan Kaufmann. Computer Graphics: Principle and Practice Physically-based

Janvier - Février - Mars.

PARIS

Ivan Laptev, Jean Ponce, Cordelia Schmid, Josef Sivic,.

Organization of courses :

10 lectures of 3 hours each. All materials and lectures will be in English. Reports from assignments and the final project can be done in French or English.

Validation : There will be three programming assignments representing 50% of the grade and a research-oriented final project (including report and presentation) representing 50% of the grade.

Automated object recognition - and more generally scene analysis - from photographs and videos is the great challenge of computer vision. The objective of this course is to provide a coherent introductory overview of the image, object and scene models, as well as the methods and algorithms, used today to address this challenge.

Topics :

Instance-level recognition: camera geometry, local-invariant features, correspondence, efficient visual search
Category-level recognition: bags of features, sparse coding and dictionary learning
Neural networks, optimization methods
Convolutional neural networks for visual recognition
Motion and human actions
3D object recognition
Weakly-supervised learning for visual recognition.

Basic linear algebra, analysis and probability.

D.A. Forsyth and J. Ponce, "Computer Vision: A Modern Approach'', Prentice-Hall, 2nd edition, 2011 J. Ponce, M. Hebert, C. Schmid, and A. Zisserman, "Toward Category-Level Object Recognition'', Lecture Notes in Computer Science 4170, Springer-Verlag, 2007. R. Szeliski, "Computer Vision: Algorithms and Applications", Springer, 2010, Available online: http://szeliski.org/Book/.

Octobre - Novembre - Décembre.

PARIS

Jérôme Bobin.

Le cours sera composé de 8 cours/TP de 3h. Il est donc fortement conseillé aux étudiants de se munir d’un laptop lors du cours pour mettre en oeuvre les concepts et outils développés pendant le cours. L’évaluation du cours se fera sur la base d’un rapport de projet à résoudre au terme des séances de cours. Ce projet mettre en oeuvre les outils présentés pendant les cours/TP.

Le cours a pour objectif de présenter des outils avancés pour l’analyse données et la résolution de problèmes inverses en imagerie, avec applications en astrophysique. Un accent important sera mis sur la mise en pratique de ces méthodes et leur utilisation sur des problèmes concrets. Le contenu du cours sera le suivant:

- Modélisation parcimonieuse de données, représentations analytiques et par apprentissage statistique
- Problèmes inverses et solutions par méthode parcimonieuse: débitage, déconvolution, inpainting et compressed sensing
- Algorithmie pour la résolution de problèmes inverses, algorithmes proximaux
- Outils dédié à l’analyse de données multivaluées (e.g. données multi/hyperspectrales) par factorisation non-supervisée de matrices: analyse en composantes indépantes, séparation non-supervisée de sources parcimonieuses, factorisation non-negative de matrices.
- Résolution de problèmes inverses et apprentissage statistique: apprentissage de régularisation et applications
- Applications en astrophysique?.

Les étudiants doivent avoir de bonnes connaissances en algèbre linéaire, statistiques, statistiques, programmation basique.

- J.-L. Starck, F. Murtagh, and J. M. Fadili, Sparse image and signal processing: wavelets, curvelets, morphological diversity, Cambridge University Press, 2010. - N. Parikh, S. Boyd, et al., Proximal algorithms, Foundations and Trends in Optimization 1 (.

Janvier - Février - Mars.

GIF-SUR-YVETTE

Gaillard, Pierre.

In sequential learning, data are acquired and treated on the fly; feedbacks are received and algorithms uploaded on the fly. This field has received a lot of attention recently because of the possible applications coming from internet. They include choosing which ads to display, repeated auctions, spam detection, experts/algorithm aggregation (and boosting), etc. The objectives of the course is to introduce and study the main concepts (regret, calibration, etc.) of sequential learning, construct algorithms and show connection with game theory. We will also cover the bandit setting (cf the course of Reinforcement learning) and its generalization, the partial monitoring.

Probability theory and convex optimisation notions.

Prediction, learning, and games. N. Cesa-Bianchi and G. Lugosi, 2006. Regret Analysis of Stochastic and Nonstochastic Multi-armed Bandit Problems. S. Bubeck and N. Cesa-Bianchi, 2012. Bandit algorithms. T. Lattimore and Csaba Szepesvári, 2018. Introduction to online convex optimization. E Hazan, 2016.

Janvier - Février - Mars.

GIF-SUR-YVETTE

Nicolas Chopin et Pierre Latouche.

The course will provide an overview of probabilistic machine learning
(that is, learning approaches derived some form of probabilistic modelling)
with particular emphasis on graphical models (probabilistic models where
dependences are represented by a graph). In particular, the following topics
will be covered (not necessarily in this order):
* maximum likelihood and Bayesian estimation
* linear and logistic regression
* clustering: k-means vs mixture models, the EM algorithm
* graphical models: definitions, exact and approximate inference algorithm (sum-product)
* Gaussian processes.

Pré-requis : Eléments de statistiques et probabilités, niveau L3/M1.

The course will survey a subset of the topics covered in the following book:

Pattern Recognition And Machine Learning, Chris Bishop, Springer.

Octobre - Novembre - Décembre.

GIF-SUR-YVETTE

L'UE se compose de 8 cours de 3 heures chacun (cours au tableau) de janvier à mars, plus un cours pour les exposés des étudiants. L'évaluation consiste en un projet réalisé seul ou en binôme, avec remise d'un rapport écrit et d'un code (ou d'un notebook jupyter) et présentation d'un exposé lors du 9ème cours. Le rattrapage éventuel consiste en un nouveau projet (éventuellement lié au projet original) avec remise d'un rapport écrit et d'un code (ou d'un notebook jupyter).

On introduit dans ce cours des techniques d'analyse stochastique et statistique utiles en particulier pour résoudre des problèmes inverses et d'imagerie.
Dans un problème d'imagerie typique (en échographie par exemple), on souhaite imager un milieu, qui peut être le corps humain en imagerie médicale ou la croûte terrestre en imagerie sismique.
On dispose d'un ensemble de sources qui émettent des ondes et d'un ensemble de récepteurs qui enregistrent les ondes réfléchies par le milieu.
Il s'agit de traiter les données enregistrées pour reconstruire le milieu, en construire une image.
Malheureusement, d'une part ces problèmes sont mal posés, dans le sens où les seules données expérimentales ne suffisent pas à déterminer le milieu.
Il est donc nécessaire d'ajouter des contraintes ou des a priori qui permettent de régulariser le problème et de réduire l'espace de recherche.
D'autre part, les données expérimentales sont entachées de bruit, qui peut être du bruit de source, du bruit de mesure, ou du bruit de milieu.
Il se trouve que des idées originales pour traiter ces problèmes sont apparues récemment.
Ces idées sont basées sur des outils probabilistes qu'on développera dans ce cours.

Un minimum de pré-requis en probabilité et statistique est nécessaire, typiquement vecteurs gaussiens et estimation paramétrique.

Des notes de cours (en anglais) sont distribuées : 1) Quelques résultats sur l'équation des ondes : fonction et identités de Green. - Expérience de retournement temporel des ondes. 2) Problèmes inverses mal posés : analyse bayésienne et régularisation. - Imagerie par moindres carrés. 3) Propriétés spectrales des processus aléatoires stationnaires. - Imagerie par corrélations croisées. 4) Propriétés des processus gaussiens. - Caractérisation du bruit de speckle. 5) Théorie des matrices aléatoires. - Détection, localisation et identification de réflecteurs. Voir aussi : [1] H. Ammari, J

Janvier - Février - Mars.

GIF-SUR-YVETTE

Alessandro Lazaric, Matteo Pirotta.

Reinforcement learning is a machine learning paradigm studying how autonomous agents can learn how to solve a given task through direct interaction with an unknown environment. In this course, we study how to formalize this decision-making problem in the framework of Markov decision processes (MDPs), we review a few dynamic programming algorithms to solve MDPs, and then we move towards reinforcement learning algorithms such as temporal difference learning and Q-learning and they approximate versions (e.g., policy gradient methods and DQN). A part of the course is devoted to studying the exploration-exploitation dilemma, which is fundamental to guarantee sample efficiency while learning online. Starting from the simple multi-armed bandit problem, we move towards the general reinforcement learning case passing through practically relevant settings such as linear and contextual bandit. In each part of the course, we cover the modeling part, a few theoretical results and performance guarantees of basic algorithms, and then we review more modern scalable algorithms based on deep learning techniques.

Basics of statistics and linear algebra for the formal part, basics of programming (in Python) for the practical sessions.

- "Reinforcement Learning: An Introduction" R. Sutton and A. Barto, http://incompleteideas.net/book/bookdraft2017nov5.pdf - "Markov Decision Processes", M. Puterman - "Dynamic Programming and Optimal Control", D. Bertsekas - "Algorithms for Reinforcement.

Octobre - Novembre - Décembre.

GIF-SUR-YVETTE

Florence Tupin, Gabriele Facciolo, Andrés Almansa, Carlo de Franchis, Enric Meinhardt, Emanuele Dalsasso.

The courses will be closely linked to practical work sessions (during the course or to do on your own) giving you a straightforward expertise to handle these data. Usage of a personal laptop is encouraged for practical sessions.

Evaluation is done through practical works and a project done all along the period. The projects are dedicated to current issues raised by the newly launched or upcoming sensors and rely on machine learning and/or image processing methods.

If there is one source of big data today, it is the continuous stream of high-resolution images from Earth observation satellites. A good understanding of these systems and instruments allows to fully take advantage of this source of information. This course is a well balanced mix of mathematical modeling of these systems and practical works handling remote sensing images retrieved either from space agencies or private providers to solve real-scale imaging problems.
The following subjects are covered during the course: (1) modeling of optical and SAR (Synthetic Aperture Radar) acquisition systems and radiometric and geometric corrections; (2) recovering 3D information from optical and SAR sensors (stereo-vision and multi-stereo, point matching, sub-pixel accuracy, interferometry), (3) time series creation and analysis (change detection, multi-temporal change analysis, either on single modality or combining heterogeneous sensors). The required mathematical tools are introduced along the way. Namely, variational calculus, discrete and continuous optimization, approximation theory and spectral analysis, mathematical morphology, statistical modeling and inference.

Linear algebra, multivariable calculus, Fourier analysis, image processing, programming in python.

- Tupin et al. (2014). Remote Sensing Imagery. John Wiley & Sons. - Nicolas (2017), Les Bases de l’Imagerie Satellitaire, Notes de cours Telecom ParisTech. - CNES, ONERA, IGN (2008), Imagerie Spatiale Des principes d’acquisition au traitement des images.

Janvier - Février - Mars.

PARIS

Lionel Moisan.

L'objectif du cours est de comprendre en détail, sous plusieurs angles différents,
le lien entre les images numériques, par nature discrètes, et la réalité continue
qu'elles représentent. Le plan du cours est le suivant:

1) Formation et représentation des images numériques.
Projection perspective, diffraction, numérisation, échantillonnage. Théorème de
Shannon, aliasing.

2) Interpolation et transformations géométriques.
Interpolation de Shannon et transformée de Fourier discrète, décomposition periodic+smooth.
Interpolations directes et indirectes, splines, interprétation spectrale.
Translations sous-pixelliques, zoom, rotation, extrapolation de spectre.
Aliasing et super-résolution.

3) Interprétation de la phase de la transformée de Fourier.
Images à phase aléatoire, champs gaussiens et synthèse de textures.
Cohérence de phase et mesure de netteté.
Application à la déconvolution aveugle.

4) Pixel infinitésimal et opérateurs différentiels.
Consistance des schémas aux différences finies.
Variation totale de Shannon.

Intégration et transformation de Fourier, espaces L^p et l^p. Probabilités (vecteur aléatoire, vecteur gaussien). Notions de base en calcul différentiel et géométrie différentielle plane.

Des notions sur les distributions ne sont pas indispensables mais sont un plus.

L. Moisan, Modeling and Image Processing (polycopié de cours, en anglais)

L. Moisan, ``Periodic plus smooth image decomposition'', Journal of Mathematical Imaging and Vision, vol 39:2, pp. 161-179, 2011.

R. Abergel, L. Moisan, ``The Shannon Total Variation'', Journal of Mathematical Imaging and Vision, 2017.

A. Leclaire, L. Moisan, ``No-reference image quality assessment and blind deblurring with sharpness metrics exploiting Fourier phase information'', Journal of Mathematical Imaging and Vision, 2015.

Octobre - Novembre - Décembre.

PARIS

COUILLET Romain et NAJIM Jamal.

Le cours est essentiellement magistral et dispensé au tableau (sauf dernier cours "séminaire" sur l'utilisation moderne de la théorie en apprentissage). Plusieurs DM (devoirs maison, assez simples) ponctuent la première partie pour se familiariser avec l'utilisation des outils. Deux TPs (travaux pratiques sur ordinateur, Matlab ou Python) concluent la première partie (TP Inférence statistique) ainsi qu'une application de la deuxième (TP Détection de communautés sur des graphes). L'évaluation finale s'effectue par DS (devoir sur table), la note finale étant une moyenne des notes du DS, des TPs et des DMs (ceux n'ayant pas rendu une partie des DMs, TPs n'étant alors évalués que sur le DS).

Le cours, divisé en deux parties, introduit les rudiments théoriques de la théorie des matrices aléatoires puis son application à l'apprentissage automatisé.
Dans la première partie, il est question de la compréhension des comportements spectraux de grandes matrices aléatoires (théorème de Marcenko-Pastur, loi du demi-cercle, modèles dits "spike"), de l'apprentissage et l'utilisation des outils théoriques (transformée de Stieltjes, méthodes gaussiennes) et de leur application à l'inférence statistiques de modèles matriciels (estimation de fonctionelles du spectre, de formes quadratiques, etc.).
La deuxième partie exploite alors ces outils pour démontrer une nette rupture à la fois intuitive, pratique et théorique de l'apprentissage statistique en grandes dimensions: il est notamment démontré que nombre de méthodes, apprises par ailleurs au cours du MVA (SVM, méthodes par noyaux et par graphes), voient leurs intuitions et leurs performances s'effondrer lorsque des données de (pas toujours si) grandes tailles sont prises en compte. Les applications concrètes visées concernent entre autres: le clustering spectral, les méthodes à noyaux, la détection de communautés sur des graphes et la classification supervisée (le spectre de la théorie ne s'arrêtant pas là).

* Bases de théorie des probabilités (notions de théorie de la mesure, de convergences de mesures de probas). * Bases d'algèbre linéaire (spectre de matrices, notamment symmétriques/hermitiennes). * Bases (rappelées en cours) d'analyse notamment complexe (notion d'analyticité, intégration complexe).

* Polycopié du cours: https://romaincouillet.hebfree.org/docs/courses/rmt/poly.pdf * Première partie de R. Couillet, M. Debbah, "Random Matrix Methods for Wireless Communications", Cambridge University Press, 2001. https://romaincouillet.hebfree.org/docs/book_outline.pdf * Autres références sur demande.

Janvier - Février - Mars.

GIF-SUR-YVETTE

Julien Tierny et Frédéric Chazal.

- 6 lectures of 2 hours - 6 practical sessions of 2 hours - 1 final research seminar (3 hours).

Topological Data Analysis (TDA) [1, 2, 3, 4, 5, 6] is a sound family of techniques that is gaining an increasing importance for the interactive analysis and visualization of data in imaging and machine learning applications. Given the increasing size and complexity of current data sets, these approaches aim at helping users understand the complexity of their data by providing insights about its topological and geometric structure.

The soundness, efficiency and robustness of TDA made it increasingly popular in the last few years in a variety of 2D and 3D imaging applications, for various feature extraction tasks. In higher dimensions, these techniques have recently found various applications in unsupervised (clustering) and supervised machine learning.

The purpose of this course is to introduce the main concepts of the recent field of Topological Data Analysis and illustrate their use in imaging and machine learning applications, both from a mathematical and practical point of view [7, 8].

Admission to MVA. Programming skills in Python (and/or C++) are recommended.

[1] H. Edelsbrunner, J. Harer, "Computational Topology: An Introduction", American Mathematical Society, 2010. [2] J. Milnor. "Morse Theory", Princeton University Press, 1963. [3] A. Fomenko and T. Kunii, "Topological modeling for visualization", Springer 1997. [4] J. Tierny, "Topological Data Analysis for Scientific Visualization", Springer, 2018. [5] S. Oudot, "Persistence Theory: From Quiver Representations to Data Analysis". AMS Mathematical Surveys and Monographs, volume 209, 2015. [6] F. Chazal, B. Michel, "An introduction to Topological Data Analysis: fundamental and practical aspects

Octobre - Novembre - Décembre.

GIF-SUR-YVETTE