Professors in charge of the option:
Vincent Bansaye - Probabilités
Email: bansaye@cmap.polytechnique.fr
Eric Moulines - Statistics
Email: eric.moulines@polytechnique.edu
Aymeric Dieuleveut - Machine Learning
Email: aymeric.dieuleveut@polytechnique.edu
Secretariat of the Applied Mathematics Department
Tel: 01 69 33 46 07
Fax: 01 69 33 46 46
Email: leyla.marzuk@polytechnique.edu
"Probability Modeling and Statistics" internships are generally about building and studying probabilistic models designed to describe and analyse physics, biological, computing or economy phenomena. Depending on the intended goals, models can be from machine learning (statistical learning), used as a tool to analysing data and proposing predictions (estimation, tests, prediction...), or to be analysed with probabilistical mehtods in order to grasp their behaviors and limits. Note that with the global rise of AI, big data or not, and the design of macine learning algorithms adapted are at the center of many intenships proposed.
The range of applications of these methods is very broad: biology (population dynamics, genetic heritage transmission, phylogenetic selection, biological regulation network...), communication network (traffic characterization, probabilistic analysis of protocols, congestion control), insurance (pricing, prediction of reserves), economy (analysis and prediction of macroeconomic aggregates...), etc.
These internships are particularly designed to students who have taken the Applied Mathematics PA (notably the course of "Process and estimate", "Communication network, algorithms and probabilities", "Statistical learning", "Random models in ecology and evolution").
Example of internships of the earlier years:
IN FRANCE
- EDF
Uncertainty about prediction of electricity consumption.
Analysis of the use of electrical interconnextions in Europe. - VEOLIA
Biodiversity modelisation in basin of activated sludges. - SCHLUMBERGER
Uncertainty assessment for CO2 geological storage integrity. - THOMSON
Navigability with a bias. - TELECOM PARISTECH
Dynamical share of bandwidth in the Internet. - INRIA
Probabilistic methods for the Poisson-Boltzmann equation in molecular dynamics. - INRA
Cyclostationary analysis of the Caledonian climate.
Statistical models for the analysis of biological interaction network.
Study of regrowth dynamics outside crop plots in an agro-ecosystem. - ORANGE
Random walk in the city.
ABROAD
- UNIVERSITY OF CALIFORNIA (Berkeley)
Development of flow model based algorithms for highway traffic estimation (Mobile Millenium).
Using mobile phones to estimate travel times in urban networks through the STARMA model.
Traffic forecasting using statistical machine learning. - COLUMBIA UNIVERSITY (New York)
Verification / testing of statistical decadal forecasts.
Subnational Carbon Emissions from Selected Countries. - IMPERIAL COLLEGE (London)
Influence in on-line social networks.
Dissemination of Information in Distributed Networks. - EPFL (Lausanne)
Stabilité des réseaux d'accès sans fil: impact de la topologie. - CMM-UNIVERSITY OF CHILE (Santiago)
Mathematical modeling and analysis of metabolic interaction networks. - UNIVERSITA ROMA 3 (Rome)
Mixing time for reversible Markov Chains and applications. - UNIVERSITY OF WATERLOO (Canada).
Bandwidth allocation policies in Wireless Networks. - NRS (Montréal)
Qualité de service et tarification des réseaux IP.
Course language: French
- Teaching coordinator: Dieuleveut Aymeric
- Teaching coordinator: Gerin Lucas