Le but de cet enseignement est de fournir une initiation à la recherche et développement en mathématiques appliquées, à travers la réalisation d’un projet.
Le projet consiste en l’étude d’un problème, motivé par les applications ou des
questions de nature mathématique, allant de la modélisation à l’implémentation
numérique et à l’analyse critique des résultats. Ce projet est effectué en binôme ou en trinôme, et constitue un véritable travail d’équipe.
L'évaluation sera basée sur la remise de deux rapports écrits et sur deux présentations orales, à mi-parcours puis à la fin du projet.
- Teaching coordinator: Breden Maxime
- Teaching coordinator: Gaubert Stéphane
- Teaching coordinator: Lehalle Charles-Albert
- Teaching coordinator: Lelievre Tony
- Teaching coordinator: Rey Clément
- Teaching coordinator: Rosenbaum Mathieu
- Teaching coordinator: Gouarin Loïc
Machine learning is a scientific discipline that is concerned with the design and development of algorithms that allow computers to learn from data. A major focus of machine learning is to automatically learn complex patterns and to make intelligent decisions based on them. The set of possible data inputs that feed a learning task can be very large and diverse, which makes modelling and prior assumptions critical problems for the design of relevant algorithms.
This course aims to complement the first Machine Learning course.
- Teaching coordinator: Capitaine Aymeric
- Teaching coordinator: Durmus Alain
- Teaching coordinator: Goudenege Ludovic
- Teaching coordinator: Le Pennec Erwan
- Teaching coordinator: Mangold Paul
- Teaching coordinator: Michel Manon
- Teaching coordinator: Simsekli Umut
- Stock data:
- Sequential stock data, in one dimension (prices, returns, realized and Parkinson volatilities, autocorrelation, serial information)
- Sequential stock data in higher dimension (correlation, Markowitz)
- Standard trading strategies and their backtest
- Market microstructure (order book, bid-ask spreads, liquidity risk)
- Derivatives and options data :
- Introduction/reminders on forward and future contracts, no-arbitrage principles
- Option prices (on a large equity index such as SP500), put-call parity.
- Black Scholes formula with some justification (without continuous time stochastic calculus), numerical evaluation of implied volatilities.
- Static no-arbitrage conditions on option prices and implied volatilities, fitting of a parametric implied volatility smile models (SVI, SSVI).
- Teaching coordinator: De Marco Stéfano
- Teaching coordinator: Garcin Matthieu
More and more companies are actively investing human and financial resources in data management technologies in order to improve and making effective decision making. This is mainly because a wide class of data analytics operations (e.g., statistical analysis, machine learning, ad-hoc queries) for supporting decision makers requires to process massive data sets in order to ensure high precision of analysis result. In addition, companies are more and more interested in extracting, transforming, store and analyse data involving massive and heterogeneous data collections coming from external sources (social networks, competitors' movements, market trends, etc.), typically made available by Web applications.
The main aim of this course is to give students a deep and solid understanding of the state of the art of Big Data systems and programming paradigms, and to enable them to devise and implement efficient algorithms for analysing massive data sets. The focus will be on paradigms based on distribution and shared-nothing parallelism, which are crucial to enable the implementation of algorithms that can be run on clusters of computers, scale as the size of input data increases, and can be safely executed even in the presence of system failures.
Lectures will give articular emphasis to the MapReduce paradigm and the internal aspects of its related runtime support Hadoop, as well as to MapReduce-based systems, with a particular focus on Spark that provides users with powerful programming tools and efficient execution support for performing operations related to complex data flows. The attention will be then given to mechanisms and algorithms for both both iterative and interactive data processing. A particular attention will be given to SQL-like data querying, graph analysis, and the development of machine learning algorithms.
A large part of the course consists of lab-sessions where students develop parallel algorithms for data querying and analysis, including algorithms for relational database operators, matrix operations, graph analysis, and clustering. Lab-sessions rely on the use of both desktop computers and Hadoop clusters on Google Cloud.
- Teaching coordinator: Colazzo Dario
- Teaching coordinator: Durmus Alain