Bangalore workshop [ಬೆಂಗಳೂರು ಕಾರ್ಯಾಗಾರ]

Posted in pictures, Running, Statistics, Travel, University life, Wines with tags , , , , , on July 30, 2014 by xi'an

iiscFirst day at the Indo-French Centre for Applied Mathematics and the get-together (or speed-dating!) workshop. The campus of the Indian Institute of Science of Bangalore where we all stay is very pleasant with plenty of greenery in the middle of a very busy city. Plus, being at about 1000m means the temperature remains tolerable for me, to the point of letting me run in the morning.Plus, staying in a guest house in the campus also means genuine and enjoyable south Indian food.

The workshop is a mix of statisticians and of mathematicians of neurosciences, from both India and France, and we are few enough to have a lot of opportunities for discussion and potential joint projects. I gave the first talk this morning (hence a fairly short run!) on ABC model choice with random forests and, given the mixed audience, may have launched too quickly into the technicalities of the forests. Even though I think I kept the statisticians on-board for most of the talk. While the mathematical biology talks mostly went over my head (esp. when I could not resist dozing!), I enjoyed the presentation of Francis Bach of a fast stochastic gradient algorithm, where the stochastic average is only updated one term at a time, for apparently much faster convergence results. This is related with a joint work with Éric Moulines that both Éric and Francis presented in the past month. And makes me wonder at the intuition behind the major speed-up. Shrinkage to the mean maybe?

Bangalore snapshot [ಬೆಂಗಳೂರು ಚಿತ್ರ]

Posted in pictures, Travel with tags , , , , , on July 29, 2014 by xi'an

storm

one hundred years ago, a telegram…

Posted in Books, Kids, pictures with tags , , , , on July 28, 2014 by xi'an

PMC for combinatoric spaces

Posted in Statistics, University life with tags , , , , , , , on July 28, 2014 by xi'an

I received this interesting [edited] email from Xiannian Fan at CUNY:

I am trying to use PMC to solve Bayesian network structure learning problem (which is in a combinatorial space, not continuous space).

In PMC, the proposal distributions qi,t can be very flexible, even specific to each iteration and each instance. My problem occurs due to the combinatorial space.

For importance sampling, the requirement for proposal distribution, q, is:

support (p) ⊂ support (q)             (*)

For PMC, what is the support of the proposal distribution in iteration t? is it

support (p) ⊂ U support(qi,t)    (**)

or does (*) apply to every qi,t?

For continuous problem, this is not a big issue. We can use random walk of Normal distribution to do local move satisfying (*). But for combination search, local moving only result in finite states choice, just not satisfying (*). For example for a permutation (1,3,2,4), random swap has only choose(4,2)=6 neighbor states.

Fairly interesting question about population Monte Carlo (PMC), a sequential version of importance sampling we worked on with French colleagues in the early 2000’s.  (The name population Monte Carlo comes from Iba, 2000.)  While MCMC samplers do not have to cover the whole support of p at each iteration, it is much harder for importance samplers as their core justification is to provide an unbiased estimator to for all integrals of interest. Thus, when using the PMC estimate,

1/n ∑i,t {p(xi,t)/qi,t(xi,t)}h(qi,t),  xi,t~qi,t(x)

this estimator is only unbiased when the supports of the qi,t “s are all containing the support of p. The only other cases I can think of are

  1. associating the qi,t “s with a partition Si,t of the support of p and using instead

    i,t {p(xi,t)/qi,t(xi,t)}h(qi,t), xi,t~qi,t(x)

  2. resorting to AMIS under the assumption (**) and using instead

    1/n ∑i,t {p(xi,t)/∑j,t qj,t(xi,t)}h(qi,t), xi,t~qi,t(x)

but I am open to further suggestions!

off to Bangalore [#2]

Posted in Mountains, pictures, Travel with tags , , , , on July 27, 2014 by xi'an

kurdis1While I was trying to find a proper window to take a picture of the mountains of Eastern Turkey, an Air France flight attendant suggested me to try the view from the pilots’ cockpit! I thought she was joking but, after putting a request to the captain, she came to walk me there and I had a fantastic five minutes with the pilots, chatting and taking unconstrained views of the region of Van, as we were nearing Turkey. I was actually most surprised at the very possibility of entering the cockpit as I thought it was now completely barred to passengers. Thanks then to the Air France crew that welcomed me there!

van

Ulam’s grave [STAN post]

Posted in Books, Kids, pictures, Travel, University life with tags , , , , , , , on July 27, 2014 by xi'an

ulamSince Stan Ulam is buried in Cimetière du Montparnasse, next to CREST, Andrew and I paid his grave a visit on a sunny July afternoon. Among elaborate funeral constructions, the Aron family tomb is sober and hidden behind funeral houses. It came as a surprise to me to discover that Ulam had links with France to the point of him and his wife being buried in Ulam’s wife family vault. Since we were there, we took a short stroll to see Henri Poincaré’s tomb in the Poincaré-Boutroux vault (missing Henri’s brother, the French president Raymond Poincaré). It came as a surprise that someone had left a folder with the cover of 17 equations that changed the World on top of the tomb). Even though the book covers Poincaré’s work on the three body problem as part of Newton’s formula. There were other mathematicians in this cemetery, but this was enough necrophiliac tourism for one day.

poincare

off to Bangalore

Posted in Statistics, Travel, University life with tags , , , on July 26, 2014 by xi'an

I am off to Bangalore for a few days, taking part in an Indo-French workshop on statistics and mathematical biology run by the Indo-French Centre for Applied Mathematics (IFCAM).

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