Archive for Singapore

Le Monde puzzle [#1081]

Posted in Books, Kids, R, Travel with tags , , , , on January 24, 2019 by xi'an

A “he said-she said” Le Monde mathematical puzzle (again in the spirit of the famous Singapore high-school birthdate problem):

Abigail and Corentin are both given a positive integer, a and b, such that a+b is either 19 or 20. They are asked one after the other and repeatedly if they are sure of the other’s number. What is the maximum number of times they are questioned?

If Abigail is given a 19, b=1 necessarily. Hence if Abigail does not reply, a<19. This implies that, if Corentin is given b=1 or b=19, he can reply a+b=19 or a+b=20, necessarily. Else, 1<b<19 implies that, if a=1 or a=18, b=18 or b=2. And so on…which leads to a maximum of 20 questions, 10 for Abigail and 0 for Corentin. Here is my R implementation

az=bz=cbind(20-(1:19),19-(1:19))
qwz=0;at=TRUE;bt=FALSE
while ((max(az)>0)&(max(bz)>0)){
 if (at){ 
  for (i in 1:19){ 
   if (sum(az[i,]>0)==2){
   for (j in az[i,az[i,]>0]){ 
     if (sum(bz[j,]==0)==2) az[i,]=rep(0,2)}}
   if (sum(az[i,]>0)<2){ 
    az[i,]=rep(0,2)}}} 
  if (bt){ 
   for (i in 1:19){ 
    if (sum(bz[i,bz[i,]>0]>0)==2){
     for (j in bz[i,bz[i,]>0]){ 
      if (sum(az[j,]==0)==2) bz[i,]=rep(0,2)}}
     if (sum(bz[i,]>0)<2){ bz[i,]=rep(0,2)}}}
  bt=!bt;at=!at;qwz=qwz+1}

Le Monde puzzle [#1071]

Posted in Books, Kids with tags , , , , , , , , , , , on October 18, 2018 by xi'an

A “he said she said” Le Monde mathematical puzzle sixth competition problem that reminded me of the “Singapore birthday problem” (nothing to do with the original birthday problem!):

Arwen and Brandwein are privately and respectively given the day and month of Caradoc’s birthday [in the Gregorian calendar] with the information that the month number is at least the day number. Arwen starts by stating she knows Brandwein cannot deduce the birthday, followed by Brandwein who says the same about Arwen. If this “she says he says” goes on for the largest possible number of steps before Arwen says she knows, when is Caradoc’s birthday? Arwen and Brandwein are later given two numbers corresponding to Deirdre’s birthday with no indication of which one is the day and which one is the month. They know both numbers end up with the same digit and that the month number is strictly less than the day number. Arwen states she does not know the date and she knows Brandwein cannot know either. Then Brandwein says he indeed does not the date but he knows whether he got the day or the month. This prompts Arwen to conclude she knows, then Brandwein to do the same. When is Deirdre’s birthday?

Since this was a fairly easy puzzle (and since I had spent too much time debugging the previous R code!), I did not try coding this one but instead drew the possibilities and remove the impossibilities on a blackboard. The first question is quite simple actually since the day numbers stand between 1 and 12 and that each “I cannot know” excludes one of the remaining endpoints, removing first excludes 1 from both lists, then 12, then 2, then …. 8, ending up with 7. And 07/07 as Caradoc’s birthday. The second case sees 13,…,20,23,…,30 eliminated from Arwen’s numbers, then 3,…,10 as well, which eliminates the same numbers from Brandwein’s possibilities. That he knows whether it is a month or a day leaves only 1,2,21,22,31 as possible numbers. Then Arwen’s certainty reduces her numbers to be 2, 21, 22, or 31, and since Brandwein is also sure, the only possible cases are (2,22) and (22,2). Meaning Deirdre’s birthday is on 22/02. I dunno if this symmetry was to be expected! (And I cannot fathom why this puzzle is awarded so many points, when compared with the others.)

Le Monde puzzle [#1650]

Posted in Books, Kids, R with tags , , , , , , , , , on September 5, 2018 by xi'an

A penultimate Le Monde mathematical puzzle  before the new competition starts [again!]

For a game opposing 40 players over 12 questions, anyone answering correctly a question gets as reward the number of people who failed to answer. Alice is the single winner: what is her minimal score? In another round, Bob is the only lowest grade: what is his maximum score?

For each player, the score S is the sum δ¹s¹+…+δ⁸s⁸, where the first term is an indicator for a correct answer and the second term is the sum over all other players of their complementary indicator, which can be replaced with the sum over all players since δ¹(1-δ¹)=0. Leading to the vector of scores

worz <- function(ansz){
  scor=apply(1-ansz,2,sum)
  return(apply(t(ansz)*scor,2,sum))}

Now, running by brute-force a massive number of simulations confirmed my intuition that the minimal winning score is 39, the number of players minus one [achieved by Alice giving a single good answer and the others none at all], while the maximum loosing score appeared to be 34, for which I had much less of an intuition!  I would have rather guessed something in the vicinity of 80 (being half of the answers replied correctly by half of the players)… Indeed, while in SIngapore, I however ran in the wee hours a quick simulated annealing code from this solution and moved to 77.

And the 2018 version of Le Monde maths puzzle competition starts today!, for a total of eight double questions, starting with an optimisation problem where the adjacent X table is filled with zeros and ones, trying to optimise (max and min) the number of positive entries [out of 45] for which an even number of neighbours is equal to one. On the represented configuration, green stands for one (16 ones) and P for the positive entries (31 of them). This should be amenable to a R resolution [R solution], by, once again!, simulated annealing. Deadline for the reply on the competition website is next Tuesday, midnight [UTC+1]

IMS workshop [day 5]

Posted in Books, pictures, Statistics, Travel with tags , , , , , , , , on September 3, 2018 by xi'an

The last day of the starting workshop [and my last day in Singapore] was a day of importance [sampling] with talks by Matti Vihola opposing importance sampling and delayed acceptance and particle MCMC, related to several papers of his that I missed. To be continued in the coming weeks at the IMS, which is another reason to regret having to leave that early [as my Parisian semester starts this Monday with an undergrad class at 8:30!]

And then a talk by Joaquín Miguez on stabilizing importance sampling by truncation which reminded me very much of the later work by Andrew Gelman and Aki Vehtari on Pareto smoothed importance sampling, with further operators adapted to sequential settings and the similar drawback that when the importance sampler is poor, i.e., when the simulated points are all very far from the centre of mass, no amount of fudging with the weights will bring the points closer. AMIS made an appearance as a reference method, to be improved by this truncation of the weights, a wee bit surprising as it should bring the large weights of the earlier stages down.

Followed by an almost silent talk by Nick Whiteley, who having lost his voice to the air conditioning whispered his talk in the microphone. Having once faced a lost voice during an introductory lecture to a large undergraduate audience, I could not but completely commiserate for the hardship of the task. Although this made the audience most silent and attentive. His topic was the Viterbi process and its parallelisation, by using a truncated horizon (presenting connection with overdamped Langevin, eg Durmus and Moulines and Dalalyan).

And due to a pressing appointment with my son and his girlfriend [who were traveling through Singapore on that day] for a chili crab dinner on my way to the airport, I missed the final talk by Arnaud Doucet, where he was to reconsider PDMP algorithms without the continuous time layer, a perspective I find most appealing!

Overall, this was a quite diverse and rich [starting] seminar, backed by the superb organisation of the IMS and the smooth living conditions on the NUS campus [once I had mastered the bus routes], which would have made much more sense for me as part of a longer stay, which is actually what happened the previous time I visited the IMS (in 2005), again clashing with my course schedule at home… And as always, I am impressed with the city-state of Singapore, for the highly diverse food scene in particular, but also this [maybe illusory] impression of coexistence between communities. And even though the ecological footprint could certainly be decreased, measures to curb car ownership (with a 150% purchase tax) and use (with congestion charges).

IMS workshop [day 3]

Posted in pictures, R, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , , , , on August 30, 2018 by xi'an

I made the “capital” mistake of walking across the entire NUS campus this morning, which is quite green and pretty, but which almost enjoys an additional dimension brought by such an intense humidity that one feels having to get around this humidity!, a feature I have managed to completely erase from my memory of my previous visit there. Anyway, nothing of any relevance. oNE talk in the morning was by Markus Eisenbach on tools used by physicists to speed up Monte Carlo methods, like the Wang-Landau flat histogram, towards computing the partition function, or the distribution of the energy levels, definitely addressing issues close to my interest, but somewhat beyond my reach for using a different language and stress, as often in physics. (I mean, as often in physics talks I attend.) An idea that came out clear to me was to bypass a (flat) histogram target and aim directly at a constant slope cdf for the energy levels. (But got scared away by the Fourier transforms!)

Lawrence Murray then discussed some features of the Birch probabilistic programming language he is currently developing, especially a fairly fascinating concept of delayed sampling, which connects with locally-optimal proposals and Rao Blackwellisation. Which I plan to get back to later [and hopefully sooner than later!].

In the afternoon, Maria de Iorio gave a talk about the construction of nonparametric priors that create dependence between a sequence of functions, a notion I had not thought of before, with an array of possibilities when using the stick breaking construction of Dirichlet processes.

And Christophe Andrieu gave a very smooth and helpful entry to partly deterministic Markov processes (PDMP) in preparation for talks he is giving next week for the continuation of the workshop at IMS. Starting with the guided random walk of Gustafson (1998), which extended a bit later into the non-reversible paper of Diaconis, Holmes, and Neal (2000). Although I had a vague idea of the contents of these papers, the role of the velocity ν became much clearer. And premonitory of the advances made by the more recent PDMP proposals. There is obviously a continuation with the equally pedagogical talk Christophe gave at MCqMC in Rennes two months [and half the globe] ago,  but the focus being somewhat different, it really felt like a new talk [my short term memory may also play some role in this feeling!, as I now remember the discussion of Hilderbrand (2002) for non-reversible processes]. An introduction to the topic I would recommend to anyone interested in this new branch of Monte Carlo simulation! To be followed by the most recently arXived hypocoercivity paper by Christophe and co-authors.

IMS workshop [day 2]

Posted in pictures, Statistics, Travel with tags , , , , , , , , , , , , on August 29, 2018 by xi'an

Here are the slides of my talk today on using Wasserstein distances as an intrinsic distance measure in ABC, as developed in our papers with Espen Bernton, Pierre Jacob, and Mathieu Gerber:

This morning, Gael Martin discussed the surprising aspects of ABC prediction, expanding upon her talk at ISBA, with several threads very much worth weaving in the ABC tapestry, one being that summary statistics need be used to increase the efficiency of the prediction, as well as more adapted measures of distance. Her talk also led me ponder about the myriad of possibilities available or not in the most generic of ABC predictions (which is not the framework of Gael’s talk). If we imagine a highly intractable setting, it may be that the marginal generation of a predicted value at time t+1 requires the generation of the entire past from time 1 till time t. Possibly because of a massive dependence on latent variables. And the absence of particle filters. if this makes any sense. Therefore, based on a generated parameter value θ it may be that the entire series needs be simulated to reach the last value in the series. Even when unnecessary this may be an alternative to conditioning upon the actual series. In this later case, comparing both predictions may act as a natural measure of distance since one prediction is a function or statistic of the actual data while the other is a function of the simulated data. Another direction I mused about is the use of (handy) auxiliary models, each producing a prediction as a new statistic, which could then be merged and weighted (or even selected) by a random forest procedure. Again, if the auxiliary models are relatively well-behaved, timewise, this would be quite straightforward to implement.

off to Singapore [IMS workshop]

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , on August 26, 2018 by xi'an

Tonight I am off to the National University of Singapore, at the Institute for Mathematical Sciences [and not the Institute of Mathematical Statistics!], to take part in a (first) week workshop on Bayesian Computation for High-Dimensional Statistical Models, covering topics like Approximate Bayesian Computation, Markov chain Monte Carlo, Multilevel Monte Carlo and Particle Filters. Having just barely recovered from the time difference with Vancouver, I now hope I can switch with not too much difficulty to Singapore time zone! As well as face the twenty plus temperature gap with the cool weather this morning in the Parc…