International Graduate Program: Big Data & Data Science

Multiple testing issue, False Discovery Rate (FDR), usual method (Bonferroni, local FDR, Benjamini-Hochberg,..), case of correlated data

Penalised regression: LASSO, RIDGE, ELASTICNET

Decision trees and random forest, variable importance

Criteria of model selection: AIC, BIC, …

Criteria of goodness of it: RMSE, confusion table ROC curve

Variable selection: Cross validation, knockoffs, stability selection

Classification

Dimensionality Reduction

Feature Extraction & Feature Learning

Deep Learning

High Availability, High Troughput, Distributed Storage

Scalable Distributed Computing

MapReduce

NoSQL

Symbolic data mining

Knowledge representation

Pattern extraction

Formal Concept Analysis

Theoretical results for unconstrained and contrained optimisation

Gradient methods

Penalization, duality

Formal Concept Analysis

Data compression. The case of Kolmogorov complexity. The case of the Shannon entropy.

Main results on Shannon information: chain rule, data treatment inequality;

Lossy data compression: what is the maximum compression rate that you can achieve for a signal up to a certain tolerable distorsion?

Kullback-Leibler divergence and large deviation theory: how surprising is a result with respect to a given belief?

The Cramér-Rao bound: in statistics, this is a fundamental limit on how much information you can get about a hidden parameter.

Information theory as a tool for model selection: justification for the AIC and BIC criteria.

Point processes (Poisson, Cox, Gibbs).

Markovianity and integrability. Hammersley Clifford theorem. Campbell Mecke theorem. Palm distributions.

- Exploratory statistics tools. Simulation algorithms (Metropolis-Hastings, Gibbs, CFTP). Bayesian inference.

- Applications : geosciences, image analysis, astrophysics.

1 week dedicated to the development of a project proposed by a company or an organization

About twenty workshops are offered each year, one day a week between September and April.