## Archive for Université Paris Dauphine

## Dauphine blocked for a few hours

Posted in Statistics with tags blockade, coronavirus epidemics, French politics, Paris, protest, reform, student, Université Paris Dauphine on March 14, 2020 by xi'an## course PSL 2020

Posted in Running, University life with tags bois de Boulogne, coronavirus epidemics, course PSL, Paris Sciences et Lettres, road race, Université Paris Dauphine on March 14, 2020 by xi'an## unbiased MCMC with couplings [4pm, 26 Feb., Paris]

Posted in Books, pictures, Statistics, University life with tags AgroParisTech, All about that Bayes, burns, Claude Bernard, Harvard University, maximal coupling, MCMC, Paris, PSL, seminar, unbiased MCMC, Université Paris Dauphine on February 24, 2020 by xi'an**O**n Wednesday, 26 February, Pierre Jacob (Havard U, currently visiting Paris-Dauphine) is giving a seminar on unbiased MCMC methods with couplings at AgroParisTech, bvd Claude Bernard, Paris 5ième, Room 32, at 4pm in the All about that Bayes seminar.

MCMC methods yield estimators that converge to integrals of interest in the limit of the number of iterations. This iterative asymptotic justification is not ideal; first, it stands at odds with current trends in computing hardware, with increasingly parallel architectures; secondly, the choice of “burn-in” or “warm-up” is arduous. This talk will describe recently proposed estimators that are unbiased for the expectations of interest while having a finite computing cost and a finite variance. They can thus be generated independently in parallel and averaged over. The method also provides practical upper bounds on the distance (e.g. total variation) between the marginal distribution of the chain at a finite step and its invariant distribution. The key idea is to generate “faithful” couplings of Markov chains, whereby pairs of chains coalesce after a random number of iterations. This talk will provide an overview of this line of research.

## Irène Waldspurger, CNRS bronze medal

Posted in Statistics with tags bois de Boulogne, CNRS, CNRS Bronze Medal, inverse problems, La Défense, machine learning, Université Paris Dauphine on February 14, 2020 by xi'an**M**y colleague at Paris Dauphine, Irène Waldspurger, got one of the prestigious CNRS bronze medals this year. Irène is working on inverse problems and machine learning, with applications to sensing and imaging. Congrats!

## mean field Langevin system & neural networks

Posted in Statistics with tags Bayesian GANs, convex optimisation, Fokker-Planck, Hamiltonian, Langevin diffusion, Metropolis-Hastings GANs, seminar, Université Paris Dauphine on February 4, 2020 by xi'an**A** colleague of mine in Paris Dauphine, Zhenjie Ren, recently gave a talk on recent papers of his connecting neural nets and Langevin. Estimating the parameters of the NNs by mean-field Langevin dynamics. Following from an earlier paper on the topic by Mei, Montanari & Nguyen in 2018. Here are some notes I took during the seminar, not necessarily coherent as I was a bit under the weather that day. And had no previous exposure to most notions.

Fitting a one-layer network is turned into a minimisation programme over a measure space (when using loads of data). A reformulation that makes the problem convex. Adding a regularisation by the entropy and introducing derivatives of a functional against the measure. With a necessary and sufficient condition for the solution to be unique when the functional is convex. This reformulation leads to a Fokker-Planck equation, itself related with a Langevin diffusion. Except there is a measure in the Langevin equation, which stationary version is the solution of the original regularised minimisation programme.

A second paper contains an extension to deep NN, re-expressed as a problem in a random environment. Or with a marginal constraint (one marginal distribution being constrained). With a partial derivative wrt the marginal measure. Turning into a Langevin diffusion with an extra random element. Using optimal control produces a new Hamiltonian. Eventually producing the mean-field Langevin system as backward propagation. Coefficients being computed by chain rule, equivalent to a Euler scheme for Langevin dynamics.

This approach holds consequence for GANs with *discriminator* as one-layer NN and *generator* minimised over two measures. The discriminator is the invariant measure of the mean-field Langevin dynamics. Mentioning Metropolis-Hastings GANs which seem to require one full run of an MCMC algorithm at each iteration of the mean-field Langevin.

## too many marginals

Posted in Kids, Statistics with tags blackboard, CEREMADE, compatible conditional distributions, Gibbs sampling, joint distribution, marginal density, mathematical puzzle, Université Paris Dauphine on February 3, 2020 by xi'an**T**his week, the CEREMADE coffee room puzzle was about finding a joint distribution for (X,Y) such that (marginally) X and Y are both U(0,1), while X+Y is U(½,1+½). Beyond the peculiarity of the question, there is a larger scale problem, as to how many (if any) compatible marginals h¹(X,Y), h²(X,Y), h³(X,Y), …, need one constrains the distribution to reconstruct the joint. And wondering if any Gibbs-like scheme is available to simulate the joint.

## Couplings and Monte Carlo [advanced graduate course at Dauphine by Pierre Jacob]

Posted in Kids, pictures, Statistics, Travel with tags coupling, graduate course, Monte Carlo methods, optimal transport, Paris, Pierre Jacob, Université Paris Dauphine on January 20, 2020 by xi'an**A**s a visiting professor at Paris-Dauphine next month, Pierre Jacob will give a series of lectures on coupling and Monte Carlo. Next month on Feb. 13, 14, 25 27, at Université Paris-Dauphine, the first two starting at 8:30 (room E) and the last two starting at 13:45 (room F and D201, respectively). Attendance is open to all and material will be made available on the lecture webpage.