Archive for BiPS

controlled SMC

Posted in Books, pictures, Statistics, University life with tags , , , , , on December 18, 2017 by xi'an

At the end of [last] August, Jeremy Heng, Adrian Bishop†, George Deligiannidis and Arnaud Doucet arXived a paper on controlled sequential Monte Carlo (SMC). That we read today at the BiPs reading group in Paris-Saclay, when I took these notes. The setting is classical SMC, but with a twist in that the proposals at each time iteration are modified by an importance function. (I was quite surprised to discover that this was completely new in that I was under the false impression that it had been tried ages ago!) This importance sampling setting can be interpreted as a change of measures on both the hidden Markov chain and on its observed version. So that the overall normalising constant remains the same. And then being in an importance sampling setting there exists an optimal choice for the importance functions. That results in a zero variance estimated normalising constant, unsurprisingly. And the optimal solution is actually the backward filter familiar to SMC users.

A large part of the paper actually concentrates on figuring out an implementable version of this optimal solution. Using dynamic programming. And projection of each local generator over a simple linear space with Gaussian kernels (aka Gaussian mixtures). Which becomes feasible through the particle systems generated at earlier iterations of said dynamic programming.

The paper is massive, both in terms of theoretical results and of the range of simulations, and we could not get through it within the 90 minutes Sylvain LeCorff spent on presenting it. I can only wonder at this stage how much Rao-Blackwellisation or AMIS could improve the performances of the algorithm. (A point I find quite amazing in Proposition 1 is that the normalising constant Z of the filtering distribution does not change along observations when using the optimal importance function, which translates into the estimates being nearly constant after a few iterations.)

Alan Gelfand in Paris

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , on May 11, 2017 by xi'an

Alan Gelfand (Duke University) will be in Paris on the week of May 15 and give several seminars, including one at AgroParisTech on May 16:

Modèles hiérarchiques

and on at CREST (BiPS)  on May 18, 2pm:

Scalable Gaussian processes for analyzing space and space-time datasets

zig, zag, and subsampling

Posted in Books, Statistics, University life with tags , , , , , , , , , on December 29, 2016 by xi'an

ENSAE, Nov. 17, 2010Today, I alas missed a seminar at BiPS on the Zig-Zag (sub-)sampler of Joris Bierkens, Paul Fearnhead and Gareth Roberts, presented here in Paris by James Ridgway. Fortunately for me, I had some discussions with Murray Pollock in Warwick and then again with Changye Wu in Dauphine that shed some light on this complex but highly innovative approach to simulating in Big Data settings thanks to a correct subsampling mechanism.

The zig-zag process runs a continuous process made of segments that turn from one diagonal to the next at random times driven by a generator connected with the components of the gradient of the target log-density. Plus a symmetric term. Provided those random times can be generated, this process is truly available and associated with the right target distribution. When the components of the parameter are independent (an unlikely setting), those random times can be associated with an inhomogeneous Poisson process. In the general case, one needs to bound the gradients by more manageable functions that create a Poisson process that can later be thinned. Next, one needs to simulate the process for the upper bound, a task that seems hard to achieve apart from linear and piecewise constant upper bounds. The process has a bit of a slice sampling taste, except that it cannot be used as a slice sampler but requires continuous time integration, given that the length of each segment matters. (Or maybe random time subsampling?)

A highly innovative part of the paper concentrates on Big Data likelihoods and on the possibility to subsample properly and exactly the original dataset. The authors propose Zig-Zag with subsampling by turning the gradients into random parts of the gradients. While remaining unbiased. There may be a cost associated with this gain of one to n, namely that the upper bounds may turn larger as they handle all elements in the likelihood at once, hence become (even) less efficient. (I am more uncertain about the case of the control variates, as it relies on a Lipschitz assumption.) While I still miss an easy way to implement the approach in a specific model, I remain hopeful for this new approach to make a major dent in the current methodologies!

Rémi Bardenet’s seminar

Posted in Kids, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , , on April 7, 2016 by xi'an

Grand Palais from Esplanade des Invalides, Paris, Dec. 07, 2012Next week, Rémi Bardenet is giving a seminar in Paris, Thursday April 14, 2pm, in ENSAE [room 15] on MCMC methods for tall data. Unfortunately, I will miss this opportunity to discuss with Rémi as I will be heading to La Sapienza, Roma, for Clara Grazian‘s PhD defence the next day.  And on Monday afternoon, April 11, Nicolas Chopin will give a talk on quasi-Monte Carlo for sequential problems at Institut Henri Poincaré.

Dan Simpson’s seminar at CREST

Posted in Kids, Mountains, Statistics, Travel, University life with tags , , , , , , , , , on April 18, 2014 by xi'an

Daniel Simpson gave a seminar at CREST yesterday on his recently arXived paper, “Penalising model component complexity: A principled, practical  approach to constructing priors” written with Thiago Martins, Andrea Riebler, Håvard Rue, and Sigrunn Sørbye. Paper that he should also have given in Banff last month had he not lost his passport in København airport…  I have already commented at length on this exciting paper, hopefully to become a discussion paper in a top journal!, so I am just pointing out two things that came to my mind during the energetic talk delivered by Dan to our group. The first thing is that those penalised complexity (PC) priors of theirs rely on some choices in the ordering of the relevance, complexity, nuisance level, &tc. of the parameters, just like reference priors. While Dan already wrote a paper on Russian roulette, there is also a Russian doll principle at work behind (or within) PC priors. Each shell of the Russian doll corresponds to a further level of complexity whose order need be decided by the modeller… Not very realistic in a hierarchical model with several types of parameters having only local meaning.

My second point is that the construction of those “politically correct” (PC) priors reflects another Russian doll structure, namely one of embedded models, hence would and should lead to a natural multiple testing methodology. Except that Dan rejected this notion during his talk, by being opposed to testing per se. (A good topic for one of my summer projects, if nothing more, then!)