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.

See the full page

See the full page

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.

See the full page

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.

See the full page

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.

See the full page

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.

See the full page

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.

See the full page

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.

See the full page

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.

See the full page

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.

See the full page

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.

See the full page

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

See the full page

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

See the full page

See the full page

See the full page

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

See the full page

See the full page

See the full page

See the full page

See the full page

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

See the full page

See the full page

See the full page

See the full page

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.

See the full page

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.

See the full page

See the full page

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.

See the full page

This course presents some of the classical and modern methods for constructing nonparametric density or regression estimators. Both theoretical and practical aspects are covered.

See the full page

This course introduces the general framework of linear models, which seek to express a response variable as a function of a linear combination of predictors. By assuming both a specific relationship between the mean response and the predictors (link function) and a specific distribution of the random variation of the response around its mean, it is possible to represent binary data (e.g., presence/absence, mortality/survival) or count data (e.g., number of individuals, number of species). Thanks to this general framework, it is then possible to model non-normally distributed variables. The use and interpretation of logistic, binomial, and Poisson regression models will be detailed in particular.

See the full page

English tutorial course for students in the "M2 Statistics and Data Science" program who wish to achieve professional autonomy in English.

See the full page

See the full page

This course offers an introduction to parametric Bayesian statistics. After presenting the Bayesian paradigm, point and ensemble estimators will be considered, followed by a discussion of Bayesian model selection methodology. Binomial, Gaussian, and linear models will be used to illustrate the above topics.

For complex models, the issues of estimation and model selection in the Bayesian context require the use of advanced tools for approximating integrals. Therefore, the second part of the course will focus on Monte Carlo methods and Markov chain Monte Carlo algorithms.

See the full page

The size of statistical data continues to grow, particularly in terms of the richness of the description of statistical units. However, classical linear statistical modeling becomes invalid in high dimensions, i.e., when the number of variables exceeds the number of statistical units. This course presents the most common techniques used to regularize linear models in high dimensions.

See the full page

This course covers the framework of machine learning from a statistical perspective.
We will focus mainly on the supervised framework (regression and classification) and introduce some elements of the unsupervised framework through partitioning methods (clustering).
Beyond modeling and theory, the course will also cover some elements of optimization and implementation (sklearn, pytorch, etc.) of the methods introduced.

See the full page

The lifetime of an individual in biostatistics, or of a component in reliability analysis, is a quantity whose statistical analysis differs from that of usual data. On the one hand, it leads to considering quantities such as the hazard function, the mean residual lifetime, etc., which are not as interesting in other areas of statistics. On the other hand, it often involves a censoring mechanism, because the data are observed incompletely due to the length of the experiments in relation to the time we want to allocate to them.

The purpose of this module is to present the basics of survival analysis. The reasons for censoring data and the main mechanisms involved are discussed. Two main types of statistical approaches are presented: the parametric approach, which despite its limitations is often favored by users because "the parameters speak for themselves," and the non-parametric approach, which can reinforce and complement parametric analyses by giving them greater flexibility and depth when there is a large amount of data. The module also presents different models (Cox model, accelerated failure rate model, etc.) that link survival to explanatory factors, making it possible to determine which factors may impact survival. This information is particularly useful in a healthcare context, as it allows for the personalization of an individual's survival projections.

These methods will be implemented using R software.

See the full page

The supplementary courses provide an introduction to more specialized areas of statistics and stochastic modeling. Their content is subject to change from year to year. The topics covered may include the following:
- Analysis of biological sequences: Probabilistic models of biological sequence evolution, Phylogeny inference, Hidden Markov models for pattern detection, Graphical models and inference of gene regulation networks
     - Population dynamics: birth and death processes (definitions, properties, asymptotic behavior, parameter estimation, simulation), deterministic, stochastic, or hybrid approximations
- Biomedical statistics: Introduction to clinical research data, regulatory and methodological aspects, likelihood function and applications to biomedical data, review of survival data, competing risks models, U-statistic-based testing, fertility data analysis models, medical diagnosis and ROC curves as an application of a U-statistic, meta-analyses.
     - Extreme statistics and applications to the environment: Theory of univariate and multivariate extreme values: law of maxima and high threshold exceedances for random variables and vectors, extremal dependencies, estimation of extreme quantiles, risk analysis. Applications for environmental data: rainfall, wave height, temperatures, etc.
    - Spatial statistics: Introduction to the fundamentals of spatial prediction and applications. In order to cover a wide range of spatial statistics, this course will be divided into two parts: point processes and geostatistics.
- Mixed linear models: Extension of linear models to mixed linear models. Estimation of fixed effect parameters such as variance within these models. Implementation in various practical cases. Random effects in generalized linear models.

See the full page

The supplementary courses provide an introduction to more specialized areas of statistics and stochastic modeling. Their content is subject to change from year to year. The topics covered may include the following:
- Analysis of biological sequences: Probabilistic models of biological sequence evolution, Phylogeny inference, Hidden Markov models for pattern detection, Graphical models and inference of gene regulation networks
     - Population dynamics: birth and death processes (definitions, properties, asymptotic behavior, parameter estimation, simulation), deterministic, stochastic, or hybrid approximations
- Biomedical statistics: Introduction to clinical research data, regulatory and methodological aspects, likelihood function and applications to biomedical data, review of survival data, competing risks models, U-statistic-based testing, fertility data analysis models, medical diagnosis and ROC curves as an application of a U-statistic, meta-analyses.
     - Extreme statistics and applications to the environment: Theory of univariate and multivariate extreme values: law of maxima and high threshold exceedances for random variables and vectors, extremal dependencies, estimation of extreme quantiles, risk analysis. Applications for environmental data: rainfall, wave height, temperatures, etc.
    - Spatial statistics: Introduction to the fundamentals of spatial prediction and applications. In order to cover a wide range of spatial statistics, this course will be divided into two parts: point processes and geostatistics.
- Mixed linear models: Extension of linear models to mixed linear models. Estimation of fixed effect parameters such as variance within these models. Implementation in various practical cases. Random effects in generalized linear models.

See the full page

4- to 6-month internship in a company, EPIC (public industrial and commercial establishment), or research laboratory, supervised by a researcher, teacher-researcher, or research engineer.

See the full page

Many phenomena are only partially or indirectly observed, which complicates their analysis. Their statistical modeling must therefore include unobserved variables, known as latent variables, which are linked in some way to the observed variables. This course introduces the various ways of introducing latent variables into a model according to their type (qualitative or quantitative), and of estimating the model parameters.

See the full page

This course introduces the general framework of linear models, which seek to express a response variable as a function of a linear combination of predictors. By assuming both a specific relationship between the mean response and the predictors (link function) and a specific distribution of the random variation of the response around its mean, it is possible to represent binary data (e.g., presence/absence, mortality/survival) or count data (e.g., number of individuals, number of species). Thanks to this general framework, it is then possible to model non-normally distributed variables. The use and interpretation of logistic, binomial, and Poisson regression models will be detailed in particular.

See the full page

English tutorial course for students in the "M2 Statistics and Data Science" program who wish to achieve professional autonomy in English.

See the full page

See the full page

See the full page

The size of statistical data continues to grow, particularly in terms of the richness of the description of statistical units. However, classical linear statistical modeling becomes invalid in high dimensions, i.e., when the number of variables exceeds the number of statistical units. This course presents the most common techniques used to regularize linear models in high dimensions.

See the full page

This course covers the framework of machine learning from a statistical perspective.
We will focus mainly on the supervised framework (regression and classification) and introduce some elements of the unsupervised framework through partitioning methods (clustering).
Beyond modeling and theory, the course will also cover some elements of optimization and implementation (sklearn, pytorch, etc.) of the methods introduced.

See the full page

The lifetime of an individual in biostatistics, or of a component in reliability analysis, is a quantity whose statistical analysis differs from that of usual data. On the one hand, it leads to considering quantities such as the hazard function, the mean residual lifetime, etc., which are not as interesting in other areas of statistics. On the other hand, it often involves a censoring mechanism, because the data are observed incompletely due to the length of the experiments in relation to the time we want to allocate to them.

The purpose of this module is to present the basics of survival analysis. The reasons for censoring data and the main mechanisms involved are discussed. Two main types of statistical approaches are presented: the parametric approach, which despite its limitations is often favored by users because "the parameters speak for themselves," and the non-parametric approach, which can reinforce and complement parametric analyses by giving them greater flexibility and depth when there is a large amount of data. The module also presents different models (Cox model, accelerated failure rate model, etc.) that link survival to explanatory factors, making it possible to determine which factors may impact survival. This information is particularly useful in a healthcare context, as it allows for the personalization of an individual's survival projections.

These methods will be implemented using R software.

See the full page

4- to 6-month internship in a company, EPIC (public industrial and commercial establishment), or research laboratory, supervised by a researcher, teacher-researcher, or research engineer.

See the full page

See the full page

Many phenomena are only partially or indirectly observed, which complicates their analysis. Their statistical modeling must therefore include unobserved variables, known as latent variables, which are linked in some way to the observed variables. This course introduces the various ways of introducing latent variables into a model according to their type (qualitative or quantitative), and of estimating the model parameters.

See the full page

See the full page