Descriptif des cours
Cours obligatoires
- Optimization for Machine Learning
Optimization for Machine Learning
Ects : 4
Enseignant responsable :
Volume horaire : 24
Description du contenu de l'enseignement :
This course delves into the mathematical underpinnings and algorithmic strategies essential for understanding and applying Machine Learning techniques. Central to the course is the exploration of optimization, a pivotal element in contemporary advancements in machine learning. This exploration encompasses fundamental approaches such as linear regression, SVMs, and kernel methods, and extends to the dynamic realm of deep learning. Deep learning has become a leading methodology for addressing a variety of challenges in areas like imaging, vision, and natural language processing. The course content is structured to provide a comprehensive overview of the mathematical foundations, algorithmic methods, and a variety of modern applications utilizing diverse optimization techniques. Participants will engage in both traditional lectures and practical numerical sessions using Python. The curriculum is divided into three parts: The first focuses on smooth and convex optimization techniques, including gradient descent and duality. The second part delves into advanced methods like non-smooth optimization and proximal methods. Lastly, the third part addresses large-scale methods such as stochastic gradient descent and automatic differentiation, with a special focus on their applications in neural networks, including both shallow and deep architectures.
Detailed Syllabus:
1. Foundational Concepts in Differential Calculus and Gradient Descent: - Introduction to differential calculus - Principles of gradient descent - Application of gradient descent in optimization
2. Automatic Differentiation and Its Applications: - Understanding the mechanics of automatic differentiation - Implementing automatic differentiation using modern Python frameworks
3. Advanced Gradient Descent Techniques: - In-depth study of gradient descent theory - Accelerated gradient methods - Stochastic gradient algorithms and their applications
4. Exploring Convex and Non-Convex Optimization: - Fundamentals of convex analysis - Strategies and challenges in non-convex optimization
5. Special Topics in Optimization: - Introduction to non-smooth optimization methods - Study of semidefinite programming (SDP) - Exploring interior points and proximal methods
6. Large-Scale Optimization Methods and Neural Networks: - Techniques in large-scale methods, focusing on stochastic gradient descent - Applications of automatic differentiation in neural networks - Overview of neural network architectures: shallow and deep networks
Bibliographie-lectures recommandées
- Theory and algorithms: Convex Optimization, Boyd and Vandenberghe
- Introduction to matrix numerical analysis and optimization, Philippe Ciarlet
- Proximal algorithms, N. Parikh and S. Boyd
- Introduction to Nonlinear Optimization - Theory, Algorithms and Applications, Amir Beck
- Numerics: Python and Jupyter installation: use only Python 3 with Anaconda distribution.
- The Numerical Tours of Signal Processing, Gabriel Peyré
- Scikitlearn tutorial, Fabian Pedregosa, Jake VanderPlas
- Foundations of Machine Learning
Foundations of Machine Learning
Ects : 4
Enseignant responsable :
- FRANCIS BACH
Volume horaire : 24
Description du contenu de l'enseignement :
The course will introduce the theoretical foundations of machine learning, review the most successful algorithms with their theoretical guarantees, and discuss their application in real world problems. The covered topics are:
-
Part 1: Supervised Learning Theory: the batch setting
- Intro
- Surrogate Losses
- Uniform Convergence and PAC Learning
- Empirical Risk Minimization and ill-posed problems
- Concentration Inequalities
- Universal consistency, PAC Learnability
- VC dimension
- Rademacher complexity
- Non Uniform Learning and Model Selection
- biais-variance tradeoff
- Structural Minimization Principle and Minimum Description Length Principle
- Regularization
-
Part 2: Supervised Learning Theory and Algorithms in the Online Setting
- Foundations of Online Learning
- Beyond the Perceptron algorithm
-
Partie 3: Ensemble Methods and Kernels Methods
- SVMs, Kernels
- Kernel approximation algorithms in the primal
- Ensemble methods: bagging, boosting, gradient boosting, random forests
-
Partie 4: Algorithms for Unsupervised Learning
- Dimensionality reduction: PCA, ICA, Kernel PCA, ISOMAP, LLE
- Representation Learning
- Expectation Maximization, Latent models and Variational methods
Pré-requis recommandés :
- Linear models
Pré-requis obligatoire :
- Linear Algebra - Statistics and Probability
Compétences à acquérir :
The aim of this course is to provide the students with the fundamental concepts and tools for developing and analyzing machine learning algorithms.
Mode de contrôle des connaissances :
- Each student will have to have the role of scribe during one lecture, taking notes during the class and sending the notes to the teacher in pdf. - Final exam
Bibliographie-lectures recommandées
The most important book: - Shalev-Shwartz, S., & Ben-David, S. (2014). Understanding machine learning: From theory to algorithms. Cambridge university press. Also: - Mohri, M., Rostamizadeh, A., & Talwalkar, A. (2012). Foundations of machine learning. MIT press. - Vapnik, V. (2013). The nature of statistical learning theory. Springer science & business media. - Bishop Ch. (2006). Pattern recognition and machine learning. Springer - Friedman, J., Hastie, T., & Tibshirani, R. (2001). The elements of statistical learning (Vol. 1, No. 10). New York, NY, USA:: Springer series in statistics. - James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112). New York: springer.
- Reinforcement learning
Reinforcement learning
Ects : 4
Enseignant responsable :
- OLIVIER CAPPE
Volume horaire : 24
Description du contenu de l'enseignement :
- Models: Markov decision processes (MDP), multiarmed bandits and other models
- Planning: finite and infinite horizon problems, the value function, Bellman equations, dynamic programming, value and policy iteration
- Basic learning tools: Monte Carlo methods, temporal-difference learning, policy gradient
- Probabilistic and statistical tools for RL: Bayesian approach, relative entropy and hypothesis testing, concentration inequalities
- Optimal exploration in multiarmed bandits: the explore vs exploit tradeoff, lower bounds, the UCB algorithm, Thompson sampling
- Extensions: Contextual bandits, optimal exploration for MDP
Compétences à acquérir :
Reinforcement Learning (RL) refers to scenarios where the learning algorithm operates in closed-loop, simultaneously using past data to adjust its decisions and taking actions that will influence future observations. Algorithms based on RL concepts are now commonly used in programmatic marketing on the web, robotics or in computer game playing. All models for RL share a common concern that in order to attain one's long-term optimality goals, it is necessary to reach a proper balance between exploration (discovery of yet uncertain behaviors) and exploitation (focusing on the actions that have produced the most relevant results so far).
The methods used in RL draw ideas from control, statistics and machine learning. This introductory course will provide the main methodological building blocks of RL, focussing on probabilistic methods in the case where both the set of possible actions and the state space of the system are finite. Some basic notions in probability theory are required to follow the course. The course will imply some work on simple implementations of the algorithms, assuming familiarity with Python.
Mode de contrôle des connaissances :
- Individual homework (in Python)
- Final exam
Bibliographie-lectures recommandées
Bibliographie, lectures recommandées
- M. Puterman. Markov Decision Processes: Discrete Stochastic Dynamic Programming. John Wiley & Sons, 1994.
- R. Sutton and A. Barto. Introduction to Reinforcement Learning. MIT Press, 1998.
- C. Szepesvari. Algorithms for Reinforcement Learning. Morgan & Claypool Publishers, 2010.
- T. Lattimore and C. Szepesvari. Bandit Algorithms. Cambridge University Press. 2019.
- Data Science Lab
Data Science Lab
Ects : 4
Enseignant responsable :
Volume horaire : 24
Description du contenu de l'enseignement :
Students enrolled in this class will form groups and choose one topic among a list of proposed topics in the core areas of the master such as supervised or unsupervised learning, recommendation, game AI, distributed or parallel data-science, etc. The topics will generally consist in applying a well-established technique on a novel data-science challenge or in applying recent research results on a classical data-science challenge. Either way, each topic will come with its own novel scientific challenge to address. At the end of the module, the students will give an oral presentation to demonstrate their methodology and their findings. Strong scientific rigor as well as very good engineering and communication skills will be necessary to complete this module successfully.
Compétences à acquérir :
The goal of this module is to provide students with a hands-on experience on a novel data-science/AI challenge using state-of-the-art tools and techniques discussed during other classes of this master.
- Large dimensional statistics
Large dimensional statistics
- Optimal transport (ENS)
Optimal transport (ENS)
Ects : 4
Volume horaire : 24
Description du contenu de l'enseignement :
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.
- Motivations, basics of probabilistic modeling and matching problems.
- Monge problem, 1D case, Gaussian distributions.
- Kantorovitch formulation, linear programming, metric properties.
- Shrödinger problem, Sinkhorn algorithm.
- Duality and c-transforms, Brenier’s theory, W1, generative modeling.
- Semi-discrete OT, quantization, Sinkhorn dual and divergences
- Bayesian inference
Bayesian inference
Cours optionnels - 5 cours à choisir parmi :
- Computational statistics methods and MCMC
Computational statistics methods and MCMC
- Bayesian machine learning
Bayesian machine learning
- Graphical models
Graphical models
Compétences à acquérir :
Modélisation probabiliste, apprentissage et inférence sur les modèles graphiques. Les principaux thèmes abordés sont :Maximum de vraisemblance.Régression linéaire.Régression logistique.Modèle de mélange, partitionnement.Modèles graphiques.Familles exponentielles.Algorithme produit-somme.Hidden Markov models.Inférence approximéeMéthodes bayésiennes.
- Dimension reduction and manifold learning
Dimension reduction and manifold learning
Ects : 4
Volume horaire : 24
Description du contenu de l'enseignement :
Modern machine learning typically deals with high-dimensional data. The fields concerned are very varied and include genomics, image, text, time series, or even socioeconomic data where more and more unstructured features are routinely collected. As a counterpart of this tendency towards exhaustiveness, understanding these data raises challenges in terms of computational resources and human understandability. Manifold Learning refers to a family of methods aiming at reducing the dimension of data while preserving certain of its geometric and structural characteristics. It is widely used in machine learning and experimental science to compress, visualize and interpret high-dimensional data. This course will provide a global overview of the methodology of the field, while focusing on the mathematical aspects underlying the techniques used in practice.
Pré-requis obligatoire :
Linear algebra, basic probability theory, statistics, Python coding
Compétences à acquérir :
- Curse of dimensionality, manifold hypothesis and intrinsic dimension(s) - Multidimensional scaling - Linear dimension reduction (random projections, principal component analysis) - Non-linear spectral methods (kernel PCA, ISOMAP, MVU, Laplacian eigenmaps) - Ad-hoc distance-preserving methods (diffusion maps, LLE) - Probabilistic dimension reduction and clustering (SNE, UMAP) - Neural network-based dimensionality reduction
Bibliographie-lectures recommandées
- Ghojogh, B., M. Crowley, F. Karray, and A. Ghodsi (2023). Elements of dimensionality reduction and manifold learning - Lee, J. A., M. Verleysen, et al. (2007). Nonlinear dimensionality reduction
- Non-convex inverse problems
Non-convex inverse problems
Ects : 4
Enseignant responsable :
Volume horaire : 24
Description du contenu de l'enseignement :
An inverse problem is a problem where the goal is to recover an unknown object (typically a vector with real coordinates, or a matrix), given a few ``measurements'' of this object, and possibly some information on its structure. In this course, we will discuss examples of such problems, motivated by applications as diverse as medical imaging, optics and machine learning. We will especially focus on the questions: which algorithms can we use to numerically solve these problems? When and how can we prove that the solutions returned by the algorithms are correct? These questions are relatively well understood for convex inverse problems, but the course will be on non-convex inverse problems, whose study is much more recent, and a very active research topic.
The course will be at the interface between real analysis, statistics and optimization. It will include theoretical and programming exercises.
Compétences à acquérir :
Understand what is a non-convex inverse problems; get some familiarity with the most classical algorithms to solve them.
- Mixing times of Markov chains
Mixing times of Markov chains
Ects : 4
Enseignant responsable :
Volume horaire : 24
Description du contenu de l'enseignement :
How many times must one shuffle a deck of 52 cards? This course is a self-contained introduction to the modern theory of mixing times of Markov chains. It consists of a guided tour through the various methods for estimating mixing times, including couplings, spectral analysis, discrete geometry, and functional inequalities. Each of those tools is illustrated on a variety of examples from different contexts: interacting particle systems, card shuffling, random walks on groups, graphs and networks, etc. Finally, a particular attention is devoted to the celebrated cutoff phenomenon, a remarkable but still mysterious phase transition in the convergence to equilibrium of certain Markov chains.
Compétences à acquérir :
See the webpage of the course.
Mode de contrôle des connaissances :
Final written exam, in class.
En savoir plus sur le cours :
www.ceremade.dauphine.fr/~salez/mix.html
Bibliographie-lectures recommandées
See the webpage of the course.
- Kernel methods
Kernel methods
Ects : 4
Volume horaire : 24
Description du contenu de l'enseignement :
Reproducing kernel Hilbert spaces et le “ kernel trick ” Théorème de représentation Kernel PCA Kernel ridge regression Support vector machines Noyaux sur les semigroupes Noyaux pour le texte, les graphes, etc.
Compétences à acquérir :
Présenter les bases théoriques et des applications des méthodes à noyaux en apprentissage.
- Large language models
Large language models
Ects : 4
Enseignant responsable :
Volume horaire : 24
Description du contenu de l'enseignement :
The course focuses on modern and statistical approaches to NLP.
Natural language processing (NLP) is today present in some many applications because people communicate most everything in language : post on social media, web search, advertisement, emails and SMS, customer service exchange, language translation, etc. While NLP heavily relies on machine learning approaches and the use of large corpora, the peculiarities and diversity of language data imply dedicated models to efficiently process linguistic information and the underlying computational properties of natural languages.
Moreover, NLP is a fast evolving domain, in which cutting-edge research can nowadays be introduced in large scale applications in a couple of years.
The course focuses on modern and statistical approaches to NLP: using large corpora, statistical models for acquisition, disambiguation, parsing, understanding and translation. An important part will be dedicated to deep-learning models for NLP.
- Introduction to NLP, the main tasks, issues and peculiarities - Sequence tagging: models and applications - Computational Semantics - Syntax and Parsing - Deep Learning for NLP: introduction and basics - Deep Learning for NLP: advanced architectures - Deep Learning for NLP: Machine translation, a case study
Pré-requis recommandés :
pytorch
Compétences à acquérir :
- Skills in Natural Language Processing using deep-learning
- Understand new architectures
Bibliographie-lectures recommandées
References - Costa-jussà, M. R., Allauzen, A., Barrault, L., Cho, K., & Schwenk, H. (2017). Introduction to the special issue on deep learning approaches for machine translation. Computer Speech & Language, 46, 367-373. - Dan Jurafsky and James H. Martin. Speech and Language Processing (3rd ed. draft): web.stanford.edu/~jurafsky/slp3/ - Yoav Goldberg. A Primer on Neural Network Models for Natural Language Processing: u.cs.biu.ac.il/~yogo/nnlp.pdf - Ian Goodfellow, Yoshua Bengio, and Aaron Courville. Deep Learning: www.deeplearningbook.org
- Deep learning for image analysis
Deep learning for image analysis
Ects : 4
Enseignant responsable :
- Etienne DECENCIERE
Volume horaire : 24
Description du contenu de l'enseignement :
Deep learning has achieved formidable results in the image analysis field in recent years, in many cases exceeding human performance. This success opens paths for new applications, entrepreneurship and research, while making the field very competitive.
This course aims at providing the students with the theoretical and practical basis for understanding and using deep learning for image analysis applications.
Program to be followed The course will be composed of lectures and practical sessions. Moreover, experts from industry will present practical applications of deep learning. Lectures will include:
- Artificial neural networks, back-propagation algorithm - Convolutional neural networks - Design and optimization of a neural architecture - Analysis of neural network function - Image classification and segmentation - Auto-encoders and generative networks - Transformers - Current research trends and perspectives
During the practical sessions, the students will code in Python, using Keras or Pytorch. They will be confronted with the practical problems linked to deep learning: architecture design; optimization schemes and hyper-parameter selection; analysis of results.
Pré-requis obligatoire :
- Linear algebra, basic probability and statistics
- Python
Compétences à acquérir :
Deep learning for image analysis: theoretical foundations and applications
Mode de contrôle des connaissances :
Practical session and exam
- Data acquisition, extraction and storage
Data acquisition, extraction and storage
Ects : 4
Enseignant responsable :
Volume horaire : 24
Description du contenu de l'enseignement :
The objective of this course is to present the principles and techniques used to acquire, extract, integrate, clean, preprocess, store, and query datasets, that may then be used as input data to train various artificial intelligence models. The course will consist on a mix of lectures and practical sessions. We will cover the following aspects:
- Web data acquisition (Web crawling, Web APIs, open data, legal issues)
- Information extraction from semi-structured data
- Data cleaning and data deduplication
- Data formats and data models
- Storing and processing data in databases, in main memory, or in plain files
- Introduction to large-scale data processing with MapReduce and Spark
- Ontology-based data access
Pré-requis obligatoire :
Basics of computer science and computer engineering (algorithms, databases, programming, logics, complexity).
Compétences à acquérir :
Understanding:
- how to acquire data from a variety of sources and in a variety of formats
- how to extract structured data from unstructured or semi-structured data
- how to format, integrate, clean data sets
- how to store and access data sets
Mode de contrôle des connaissances :
Project (50% of the grade) and in-class written assessment (50% of the grade)
En savoir plus sur le cours :
PSL Week
Bloc stage
- Stage
Stage
Ects : 10
Modalités pédagogiques
A compter de janvier 2025, les cours seront dispensés au 16 bis rue de l'Estrapade, 75005 Paris.
La formation démarre en septembre et la présence en cours est obligatoire.
Stages et projets tutorés
L'étudiant(e) choisit librement un stage proposé par l'un des enseignants, un stage en entreprise proposé dans le cadre de la "bourse des stages", ou un stage d'origine différente ayant reçu l'agrément du responsable du Master. Le stage doit être effectué après inscription du Master. Il doit présenter un enjeu scientifique réel et le développement applicatif d'un des thèmes développés dans le master.
La durée est de quatre mois minimum, entre avril et septembre de l'année universitaire en cours. Sauf dérogation exceptionnelle, le stage doit se terminer au plus tard fin septembre.
Des programmes nourris par la recherche
Les formations sont construites au contact des programmes de recherche de niveau international de Dauphine, qui leur assure exigence et innovation.
La recherche est organisée autour de 6 disciplines toutes centrées sur les sciences des organisations et de la décision.
En savoir plus sur la recherche à Dauphine