Archive for Université Paris Dauphine
unusual view of my office [jatp]
Posted in pictures, Travel with tags bois de Boulogne, flight, Italia, La Défense, office, Paris, Seine, Université Paris Dauphine, Venezia on October 18, 2017 by xi'anwhat is your favorite teacher?
Posted in Kids, Statistics, University life with tags American Statistical Association, Amstat News, ASA, bootstrap, estimation class, GlivenkoCantelli Theorem, mathematics and statistics, teaching, Université Paris Dauphine on October 14, 2017 by xi'anWhen JeanLouis Foulley pointed out to me this page in the September issue of Amstat News, about nominating a favourite teacher, I told him it had to be an homonym statistician! Or a practical joke! After enquiry, it dawned on me that this completely underserved inclusion came from a former student in my undergraduate Estimation course, who was very enthusiastic about statistics and my insistence on modelling rather than mathematical validation. He may have been the only one in the class, as my students always complain about not seeing the point in slides with no mathematical result. Like earlier this week when after 90mn on introducing the bootstrap method, a student asked me what was new compared with the GlivenkoCantelli theorem I had presented the week before… (Thanks anyway to David for his vote and his kind words!)
Le Monde puzzle [#1024]
Posted in Books, Kids with tags Bertrand's paradox, competition, Le Monde, mathematical puzzle, Monty Hall problem, R, random walk, Université Paris Dauphine on October 10, 2017 by xi'anThe penultimate and appropriately somewhat Monty Hallesque Le Monde mathematical puzzle of the competition!
A dresser with 5×5 drawers contains a single object in one of the 25 drawers. A player opens a drawer at random and, after each choice, the object moves at random to a drawer adjacent to its current location and the drawer chosen by the player remains open. What is the maximum number of drawers one need to open to find the object?
In a dresser with 9 drawers in a line, containing again a single object, the player opens drawers one at a time, after which the open drawer is closed and the object moves to one of the drawers adjacent to its current location. What is the maximum number of drawers one need to open to find the object?
For the first question, setting a pattern of exploration and, given this pattern, simulating a random walk trying to avoid the said pattern as long as possible is feasible, returning a maximum number of steps over many random walks [and hence a lower bound on the true maximum]. As in the following code
sefavyd=function(pater=seq(1,49,2)%%25+1){ fild=matrix(0,5,5) m=pater[1];i=fild[m]=1 t=sample((1:25)[m],1) nomove=FALSE while (!nomove){ i=i+1 m=pater[i];fild[m]=1 if (t==m){ nomove=TRUE}else{ muv=NULL if ((t1)%%5>0) muv=c(muv,t1) if (t%%5>0) muv=c(muv,t+1) if ((t1)%/%5>0) muv=c(muv,t5) if (t%/%5<4) muv=c(muv,t+5) muv=muv[fild[muv]==0] nomove=(length(muv)==0) if (!nomove) t=sample(rep(muv,2),1)} } return(i)}
But a direct reasoning starts from the observation that, while two adjacent drawers are not opened, a random walk can, with nonzero probability, switch indefinitely between both drawers. Hence, a sure recovery of the object requires opening one drawer out of two. The minimal number of drawers to open on a 5×5 dresser is 2+3+2+3+2=12. Since in 12 steps, those drawers are all open, spotting the object may require up to 13 steps.
For the second case, unless I [again!] misread the question, whatever pattern one picks for the exploration, there is always a nonzero probability to avoid discovery after an arbitrary number of steps. The [wrong!] answer is thus infinity. To crosscheck this reasoning, I wrote the following R code that mimics a random pattern of exploration, associated by an opportunistic random walk that avoids discovery whenever possible (even with very low probability) bu pushing the object towards the centre,
drawl=function(){ i=1;t=5;nomove=FALSE m=sample((1:9)[t],1) while (!nomove){ nextm=sample((1:9),1) muv=c(t1,t+1) muv=muv[(muv>0)&(muv<10)&(muv!=nextm)] nomove=(length(muv)==0)(i>1e6) if (!nomove) t=sample(rep(muv,2),1, prob=1/(5.5rep(muv,2))^4) i=i+1} return(i)}
which returns unlimited values on repeated runs. However, I was wrong and the R code unable to dismiss my a priori!, as later discussions with Robin and Julien at ParisDauphine exhibited ways of terminating the random walk in 18, then 15, then 14 steps! The idea was to push the target to one of the endpoints because it would then have no option but turning back: an opening pattern like 2, 3, 4, 5, 6, 7, 8, 8 would take care of a hidden object starting in an even drawer, while the following 7, 6, 5, 4, 3, 2 openings would terminate any random path starting from an odd drawer. To double check:
grawl=function(){ len=0;muvz=c(3:8,8:1) for (t in 1:9){ i=1;m=muvz[i];nomove=(t==m) while (!nomove){ i=i+1;m=muvz[i];muv=c(t1,t+1) muv=muv[(muv>0)&(muv<10)&(muv!=m)] nomove=(length(muv)==0) if (!nomove) t=sample(rep(muv,2),1)} len=max(len,i)} return(len)}
produces the value 14.
Journée algorithmes stochastiques
Posted in Books, pictures, Statistics, University life with tags Jussieu, La Défense, Monte Carlo Statistical Methods, PACBayesian, Paris, PSL, stochastic algorithms, Université Paris Dauphine, Université Pierre et Marie Curie, workshop on September 27, 2017 by xi'anOn December 1, 2017, we will hold a day workshop on stochastic algorithms at Université ParisDauphine, with the following speakers

Rémi Bardenet – CNRS Lille / CRISTAL [10:00]

Nicolas Chopin – ENSAE / CREST [11:00]

Aymeric Dieuleveut – ENS / DI & INRIA [14:00]

Aude Genevay – Dauphine / CEREMADE & INRIA [15:00]

Pierre Monmarché – UPMC / LJLL [16:30]
Details and abstracts of the talks are available on the workshop webpage. Attendance is free, but registration is requested towards planning the morning and afternoon coffee breaks. Looking forward seeing ‘Og’s readers there, at least those in the vicinity!
And while I am targetting Parisians, cryptoBayesians, and nearlyParisians, there is another day workshop on Bayesian and PACBayesian methods on November 16, at Université Pierre et Marie Curie (campus Jussieu), with invited speakers
and a similar request for (free) registration.
the HMC algorithm meets the exchange algorithm
Posted in Mountains, pictures, Statistics, Travel, University life with tags doubly intractable problems, Dublin, estimating constants, exchange algorithm, Hamiltonian Monte Carlo, leapfrog generator, Université Paris Dauphine, University College Dublin, University of Warwick on July 26, 2017 by xi'anJulien Stoehr (now in Dublin, soon to join us as a new faculty in ParisDauphine!), Alan Benson and Nial Friel (both at UCD) arXived last week a paper entitled Noisy HMC for doublyintractable distributions. Which considers solutions for adapting Hamiltonian Monte Carlo to target densities that involve a missing constant. In the sense of our workshop last year in Warwick. And in the theme pursued by Nial in the past years. The notion is thus to tackle a density π(θ)∞exp(V(Xθ)/Z(θ) when Z(θ) is intractable. In that case the gradient of log Z(θ) can be estimated as the expectation of the gradient of V(Xθ) [as a standard exponential family identity]. And the ratio of the Z(θ)’s appearing in the Metropolis ratio can be derived by Iain Murray’s exchange algorithm, based on simulations from the sampling distribution attached to the parameter in the denominator.
The resulting algorithm proposed by the authors thus uses N simulations of auxiliary variables at each step þ of the leapfrog part, towards an approximation of the gradient term, plus another N simulations for approximating the ratio of the normalising constants Z(θ)/Z(θ’). While justified from an importance sampling perspective, this approximation is quite poor when θ and θ’ differ. A better solution [as shown in the paper] is to take advantage of all leapfrog steps and of associated auxiliary simulations to build a telescopic product of ratios where the parameter values θ and θ’ are much closer. The main difficulty is in drawing a comparison with the exchange algorithm, since the noisy HMC version is computationally more demanding. (A secondary difficulty is in having an approximate algorithm that no longer leaves the target density stationary.)
ParisDauphine in Nature
Posted in Statistics with tags Abel Prize, bois de Boulogne, France, Higgs boson, La Défense, Nature, Paris, Université Paris Dauphine, wavelets, Yves Meyer on April 25, 2017 by xi'anSince this is an event unlikely to occur that frequently, let me point out that Université ParisDauphine got a nominal mention in Nature of two weeks ago, through an article covering the recent Abel Prize of Yves Meyer and his work on wavelets through a collection of French institutions, including ParisDauphine where he was a professor in the maths department (CEREMADE) from 1985 till 1996. (Except for including a somewhat distantly related picture of an oscilloscope and a mention of the Higgs boson, the Nature article is quite nice!)