M1 - Statistics and Data Science (SSD)

The first part of this course covers additional probability theory topics: conditional expectation, Gaussian vectors. The second part introduces one of the main families of discrete-time stochastic processes: Markov chains. These are sequences of dependent random variables, whose dependency relationship is relatively simple since each variable depends only on the previous one. They are also a very powerful modeling tool. We will study the main properties of these processes, as well as their long-term behavior and the estimation of their parameters.

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Statistical data continues to grow in volume. Before modeling it, it is essential to explore it and reduce its size while losing as little information as possible. This is the objective of this course in multidimensional exploratory statistics. Methodologically, the tools used are essentially those of Euclidean geometry. Statistical problems and concepts will therefore be translated into the language of Euclidean geometry before being addressed within this framework. The two families of exploratory methods that will be covered in this course are:

1) automatic classification methods, which group observations into classes and reduce their disparity to the disparity between these classes;

2) Component analysis methods, which seek out the main directions of disparity between observations and provide interpretable images of this disparity in reduced dimensions.

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This course is a continuation of the optimization course from the second semester of L3.

After reviewing the results and numerical methods for first- and second-order optimization problems, without constraints and under equality and inequality constraints, the course focuses on issues of current interest in industrial optimization, in particular robust, multi-criteria optimization in the presence of uncertainty.

The course then illustrates the role of optimization in the main mathematical learning algorithms (machine learning). These issues are illustrated by examples of classification and regression problems in supervised learning. These examples provide an opportunity to discuss issues of metrics and procedures for evaluating learning, validation, and inference (crossfold, overfitting, etc.).

The course presents the different types of learning: unsupervised, supervised, transfer learning, reinforcement learning, incremental learning, etc.

Issues surrounding database management are addressed: generation, allocation, visualization, and segmentation.

The course presents the links between transfer learning and numerical simulation to address issues such as synthetic database generation, imputation, non-intrusive prediction, rapid inference, etc.

The course includes a significant amount of ongoing IT projects. All sessions take place in a computerized environment and allow for immediate implementation of theoretical concepts.

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This course focuses on discovering best practices for professional-level coding.
The language used is Python, but some elements of bash and git will also be useful.
A particular emphasis will be placed on data processing and visualization at the heart of the course.
We will focus mainly on the basic concepts of programming, as well as discovering Python's scientific libraries, including "numpy, scipy, pandas, matplotlib, seaborn."
Beyond knowledge of these fundamental packages, we will introduce modern coding practices: (unit) testing, version control (git), automatic documentation generation, etc.

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The importance of statistical science in the process of scientific discovery and industrial advancement lies in its ability to formulate inferences about phenomena of interest that can be associated with risks of error or degrees of confidence. The calculation of these risks of error is based on probability theory, but the principles and methods used to associate these risks with inferences constitute a theoretical corpus that serves as the basis for all statistical methodologies.

This module aims to provide a fairly comprehensive presentation of these basic principles and the mathematical tools, results, and theorems used in inferential statistics. It develops the concepts of point and interval estimation, hypothesis testing, and fundamental concepts such as exponential families, the maximum likelihood principle, and the use of p-values.
For the implementation of certain applications, the appropriate tools from the R software will be presented.

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Statistical modeling is based on two fundamental concepts: information (which must be extracted from data) and decision-making (which must be based on this data). This course introduces the theoretical formalization of these two concepts. It is therefore logically placed at the beginning of the curriculum, as many other courses use these concepts and results later on.

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This course is an introduction to stochastic control. In this type of problem
, we seek to modify the natural trajectory of a process in order to fulfill a certain objective
. We will focus on discrete-time Markov decision processes, where we can
choose an action at each time step. We will see how to formalize stochastic control problems in this framework, and how to solve them theoretically and numerically.

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This introductory course on time series, i.e., a sequence of observations made over time, provides an essential toolkit for processing this type of data, which is frequently encountered in a wide range of applications: pollutant concentration in the air over time, blood glucose levels over time, sales of a product in a supermarket, stock market prices, etc. This course focuses both on the mathematical presentation of concepts and on the more technical aspects of implementing methods. Numerical illustrations are provided using R software.

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Nonparametric methods are important in many statistical applications because they allow us to move away from traditional approaches that require the specification of valid statistical models. However, establishing the validity of such a model is a complex undertaking. 

Nonparametric methods circumvent this problem by transforming the data into ranks and conditioning on certain quantities derived from the observed configuration of these ranks. The statistics thus constructed are independent of the distribution of the raw data, which makes it possible to construct statistical inference procedures that are free of the underlying model of the data. In addition, the loss of statistical efficiency is minimal.
 
This course provides a fairly comprehensive overview of non-parametric methods. It follows on from an introductory course on parametric inferential methods, adapting and developing the theory behind several advanced concepts such as conditional tests, comparative test power (efficiency measures), and the notion of "effect size." It emphasizes the practical application of these methodologies by providing an overview of the main R commands and their uses.

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The linear model is a simple yet powerful tool that forms the basis of many statistical methods. Mastering and understanding it is very useful both from a practical standpoint, for analyzing certain data sets in detail, and from a conceptual standpoint, for understanding the theoretical foundations of more advanced learning methods, including current ones.
 
This course offers an introduction to simple and multiple linear regression models, with quantitative or qualitative variables. It presents the formal derivation and theoretical study of least squares and maximum likelihood estimators in the Gaussian case. It also provides tools for validating and selecting variables in order to study the model's limitations. Finally, it introduces the practical use of this tool on simple data sets using the R software.

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Tutored projects carried out in groups under the supervision of a teacher.

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English tutorial course for students enrolled in the "M1 Statistics and Data Science" program who wish to achieve professional autonomy in English.

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This course introduces mathematical modeling of the behavior of actors seeking to optimize an individual objective in a competitive situation.

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This course introduces mathematical modeling of the behavior of actors seeking to optimize an individual objective in a competitive situation.

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The aim will be to understand the nature of the interrelationships between economies and to analyze the conditions for the effectiveness of economic policies in an open economy, taking into account the nature of the exchange rate regime on the one hand and the degree of capital openness on the other.

With this in mind, the balance of payments will be presented and analyzed; issues of competitiveness and attractiveness of economies will be discussed.

It will also be necessary to understand the impact of financial liberalization on exchange rate volatility and the options available to different types of economic actors to hedge against exchange rate risk.

Finally, the concepts of crisis will be presented (financial, currency). The endogenous nature of crises will be highlighted with an analysis of the last two crises: the 2008 financial crisis on the one hand and the health crisis on the other.

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The aim will be to understand the nature of the interrelationships between economies and to analyze the conditions for the effectiveness of economic policies in an open economy, taking into account the nature of the exchange rate regime on the one hand and the degree of capital openness on the other.

With this in mind, the balance of payments will be presented and analyzed; issues of competitiveness and attractiveness of economies will be discussed.

It will also be necessary to understand the impact of financial liberalization on exchange rate volatility and the options available to different types of economic actors to hedge against exchange rate risk.

Finally, the concepts of crisis will be presented (financial, currency). The endogenous nature of crises will be highlighted with an analysis of the last two crises: the 2008 financial crisis on the one hand and the health crisis on the other.

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This R programming course is intended for students who will need to know a programming language for advanced data processing in their professional practice. The aim is therefore to learn how to structure, comment, and debug code properly. This course is intended for both M1 SSD and M1 Bio-Info students. It is not intended for the use of packages as black boxes for the implementation of statistical methods.

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