Archive for Oscars (Academy Awards)

optimal mixture weights in multiple importance sampling

Posted in Statistics, University life with tags , , , , , , on December 12, 2014 by xi'an

Multiple importance sampling is back!!! I am always interested in this improvement upon regular importance sampling, even or especially after publishing a recent paper about our AMIS (for adaptive multiple importance sampling) algorithm, so I was quite eager to see what was in Hera He’s and Art Owen’s newly arXived paper. The paper is definitely exciting and set me on a new set of importance sampling improvements and experiments…

Some of the most interesting developments in the paper are that, (i) when using a collection of importance functions qi with the same target p, every ratio qi/p is a control variate function with expectation 1 [assuming each of the qi‘s has a support smaller than the support of p]; (ii) the weights of a mixture of the qi‘s can be chosen in an optimal way towards minimising the variance for a certain integrand; (iii) multiple importance sampling incorporates quite naturally stratified sampling, i.e. the qi‘s may have disjoint supports; )iv) control variates contribute little, esp. when compared with the optimisation over the weights [which does not surprise me that much, given that the control variates have little correlation with the integrands]; (v) Veach’s (1997) seminal PhD thesis remains a driving force behind those results [and in getting Eric Veach an Academy Oscar in 2014!].

One extension that I would find of the uttermost interest deals with unscaled densities, both for p and the qi‘s. In that case, the weights do not even sum up to a know value and I wonder at how much more difficult it is to analyse this realistic case. And unscaled densities led me to imagine using geometric mixtures instead. Or even harmonic mixtures! (Maybe not.)

Another one is more in tune with our adaptive multiple mixture paper. The paper works with regret, but one could also work with remorse! Besides the pun, this means that one could adapt the weights along iterations and even possible design new importance functions from the past outcome, i.e., be adaptive once again. He and Owen suggest mixing their approach with our adaptive sequential Monte Carlo model.

The Missing Picture nominated for the Oscars!

Posted in Books, pictures with tags , , , , on January 20, 2014 by xi'an

The Missing Picture (L’image manquante), a documentary movie by Rithy Panh whose text is read by my friend, co-author and former student Randal Douc, has just been nominated for the Oscars. (After winning a prize in Cannes.) As a foreign-language movie. This film is actually much much more than a documentary on the Red Khmer terror. The text is just gripping and the idea of depicting the horror of the camps by little clay figures made and painted in the movie gives them a strength and a life other representations would miss. The painstaking application of the sculptor into making those figures endows them with a soul that make their suffering the more real. The Missing Picture goes beyond the political and the ideological to translate the simple but absolute multiplication of lost destinies. Whether or not it stands a chance for the Oscars, a truly unique movie.