Propagation of uncertainty

October - December 2015

The propagation of uncertainty concerns the way the uncertainty on input data propagates in the computations based on a model. It is in general non-linear and difficult to analyse, although of major concern in practice. This first axis will focus on the way it is already handled in certain fields (e.g. fluid mechanics, geophysics,...) and how the solutions proposed in these areas can be applied to the management of financial risks.

Lectures
All lectures take place at the Institut Henri Poincaré from 9am to 11am.
⚬ October 9: L. Tamellini, Introduction and Polynomial Chaos Expansion, Sparse grids. (slides)
⚬ October 16: F. Nobile, Sparse grids approximation, Sparse grids. (slides)
⚬ November 6: G. Migliorati, Random L2 regression methods. (slides)
⚬ November 13: Raul Tempone, Sparse grids in option pricing of basket options. Multilevel Monte Carlo-Multi index Monte Carlo. (slides part 1, slides part 2)
⚬ November 20: Alvaro Moraes, Pure jump processes and Multilevel Monte Carlo. (slides)

Workshop (To download : Program, Abstracts, Slides)
The one day workshop will take place on December 11, 2015, at the Amphithéâtre Hermite of the Institute Henri Poincaré, Paris. Registration is free but compulsory, to register please write to Registration before December 1st.

Particle methods for the management of risks

January - March 2016

Particle methods are widely used in Bayesian statistics or signal processing under the label of sequential Monte-Carlo methods, but also in optimization, calibration, to estimate models with hidden components (particle filtering), for rare events (selection-mutation algorithms), more recently for the resolution of non-linear dynamic programming equations.

Lectures
Lectures are given P. Del Moral on An introduction to Feynman-Kac integration and genealogical tree based particle models.
All lectures take place at the Institut Henri Poincaré from 9am to 11am, January 15, 22, 29, and February 12, 2016.

Abstract: In the last three decades, there has been a dramatic increase in the use of Feynman-Kac type particle methods as a powerful tool in real-world applications of Monte Carlo simulation in computational physics, population biology, computer sciences, and statistical machine learning. Ideally suited to parallel and distributed computation, these advanced particle algorithms include quantum and diffusion Monte Carlo methods, resampled Monte Carlo methods; genetic and evolutionary type algorithms; sequential Monte Carlo methods; interacting Markov chain Monte Carlo models and particle filters. This series of lectures presents a comprehensive treatment of these models. We shall discuss the mathematical foundations of these particle stochastic models as well as their applications in rare event analysis, signal processing, mathematical finance and Bayesian statistical inference.

Slides: Lecture 1, Lecture 2, Lecture 3, Lecture 4.
Labs (.sce): Lab 1, Lab 2

Workshop (To download : Program, Slides)
The one day workshop will take place on April 1, 2016, at Telecom ParisTech, Paris. Registration is free but compulsory, to register please write to Registration before March 25.
Confirmed speakers: José Blanchet (Columbia), Arnaud Guyader (UPMC), Julien Guyon (Bloomberg), Tony Lelièvre (CERMICS), Gareth Peters (University College London), Michael Pitt (Warwick).

Stochastic Algorithms for Big Data

June 2016.

Stochastic algorithms for optimization have recently gain a lot of attention with the development of big data sets, because of their effective performance. It can be understood theoretically for strongly convex optimization problems, but they are also very efficient in many non-convex situations (e.g. in deep-learning). We will try to investigate the reasons of this success from a mathematical point of view.

Workshop (To download : Program and abstracts, Slides)
A one day workshop will take place at Amphithéâtre Herpin in the Esclangon building (see map) of Université Pierre et Marie Curie, on June 17, 2016. Welcome of participants will start at 9am. A program will be available soon. Registration is free but compulsory, to register please write to Registration before June 10.
Confirmed speakers: Patrick Gallinari (UPMC-LIP6), Vianey Perchet (UPD-LPMA), Gersende Fort (CNRS-Télécom ParisTech), Benedikt Wilbertz (Trendiction, Luxembourg), Mark Schmidt (Univ. of British Columbia), Jeremy Harroch (QuantMetry).

Final conference

July 2016.

The closing conference will take place at Les Cordeliers, July 5 to 8, 2016. Registrations are now open on the dedicated web site (access here). Young researchers can submit a poster (see Poster (submission call ) here ).