Mathieu and I have just realised that the version of our SQMC paper made available on the RSS web site contains several unfortunate typos. In particular, the symbol for “small o” has been replaced by a “big O” by editors. For instance, Theorem 9 should state the QMC beats standard SMC; i.e. the MSE (mean square error) of an SQMC estimator is
but in the RSS version, it reads
Well, that’s a bummer. For now, I recommend anyone to read instead the arxiv version (updated on Monday).
Almost 10 months since my latest post? I guess bloggin’ ain’t my thing… In my defense, Mathieu Gerber and I were quite busy revising our SQMC paper. I am happy to announce that it has just been accepted as a read paper in JRSSB. If all goes as planned, we should present the paper at the RSS ordinary meeting on Dec 10. Everybody is welcome to attend, and submit an oral or written discussion (or both). More details soon, when the event is officially announced on the RSS web-site.
What is SQMC? It is a QMC (Quasi-Monte Carlo) version of particle filtering. For the same CPU cost, it typically generates much more accurate estimators. Interested? consider reading the paper here (more recent version coming soon), checking this video where I present SQMC, or, even better, attending our talk in London!
I presented an arxived paper of my postdoc at the big success Young Bayesian Conference in Vienna. The big picture of the talk is simple: there are situations in Bayesian nonparametrics where you don’t know how to sample from the posterior distribution, but you can only compute posterior expectations (so-called marginal methods). So e.g. you cannot provide credible intervals. But sometimes all the moments of the posterior distribution are available as posterior expectations. So morally, you should be able to say more about the posterior distribution than just reporting the posterior mean. To be more specific, we consider a hazard (h) mixture model
where is a kernel, and the mixing distribution is random and discrete (Bayesian nonparametric approach).
We consider the survival function which is recovered from the hazard rate by the transform
and some possibly censored survival data having survival . Then it turns out that all the posterior moments of the survival curve evaluated at any time can be computed.
The nice trick of the paper is to use the representation of a distribution in a [Jacobi polynomial] basis where the coefficients are linear combinations of the moments. So one can sample from [an approximation of] the posterior, and with a posterior sample we can do everything! Including credible intervals.
I’ve wrapped up the few lines of code in an R package called momentify (not on CRAN). With a sequence of moments of a random variable supported on [0,1] as an input, the package does two things:
- evaluates the approximate density
- samples from it
A package example for a mixture of beta and 2 to 7 moments gives that result:
With Alexandre Thiéry we’ve been working on non-negative unbiased estimators for a while now. Since I’ve been talking about it at conferences and since we’ve just arXived the second version of the article, it’s time for a blog post. This post is kind of a follow-up of a previous post from July, where I was commenting on Playing Russian Roulette with Intractable Likelihoods by Mark Girolami, Anne-Marie Lyne, Heiko Strathmann, Daniel Simpson, Yves Atchade.
It’s been a while I haven’t written about parallelization and GPUs. With colleagues Lawrence Murray and Anthony Lee we have just arXived a new version of Parallel resampling in the particle filter. The setting is that, on modern computing architectures such as GPUs, thousands of operations can be performed in parallel (i.e. simultaneously) and therefore the rest of the calculations that cannot be parallelized quickly becomes the bottleneck. In the case of the particle filter (or any sequential Monte Carlo method such as SMC samplers), that bottleneck is the resampling step. The article investigates this issue and numerically compares different resampling schemes.
Today I am going to introduce the moustache target distribution (moustarget distribution for brievety). Load some packages first.
library(wesanderson) # on CRAN library(RShapeTarget) # available on https://github.com/pierrejacob/RShapeTarget/ library(PAWL) # on CRAN
Let’s invoke the moustarget distribution.
shape <- create_target_from_shape( file_name=system.file(package = "RShapeTarget", "extdata/moustache.svg"), lambda=5) rinit <- function(size) matrix(rnorm(2*size), ncol = 2) moustarget <- target(name = "moustache", dimension = 2, rinit = rinit, logdensity = shape$logd, parameters = shape$algo_parameters)
This defines a target distribution represented by a SVG file using RShapeTarget. The target probability density function is defined on and is proportional to on the segments described in the SVG files, and decreases exponentially fast to away from the segments. The density function of the moustarget is plotted below, a picture being worth a thousand words.
There’s a nice exhibition open until May 26th at the British Library in London, entitled Beautiful Science: Picturing Data, Inspiring Insight. Various examples of data visualizations are shown, either historical or very modern, or even made especially for the exhibition. Definitely worth a detour if you happen to be in the area, you can see everything in 15 minutes.
In particular there are nice visualisations of historical climate data, gathered from the logbooks of the English East India company, whose ships were crossing every possible sea in the beginning of the 19th century. The logbooks contain locations and daily weather reports, handwritten by the captains themselves. Turns out the logbooks are kept at the British Library itself and some of them are on display at the exhibition. More info on that project here: oldweather.org.
Kudos to Rasmus for this very practical approach, potentially very impactful. Maybe someday people will have to specify if they want a frequentist approach and not the other way around! (I had a dream, etc).
I’m Joseph Dureau, I have been an avid reader of this blog for while now, and I’m very glad Pierre proposed me to share a few things. Until a few months ago, I used to work on Bayesian inference methods for stochastic processes, with applications to epidemiology. Along with fellow colleagues from this past life, I have now taken the startup path, founding Standard Analytics. We’re looking into how web technologies can be used to enhance browsability, transparency and impact of scientific publications. Here’s a start on what we’ve been up to so far.
Let me just make it clear that everything I’m presenting is fully open source, and available here. I hope you’ll find it interesting, and we’re very excited to hear from you! Here it goes..
To date, the Web has developed most rapidly as a medium of documents for people rather than for data and information that can be processed automatically.
Berners-Lee et al, 2001
Since this sentence was written, twelve years ago, ambitious and collective initiatives have been undertaken to revolutionize what machines can do for us on the web. When I make a purchase online, my email service is able to understand it from the purchase confirmation email, communicate to the online store service, authenticate, obtain information on the delivery, and provide me with a real-time representation of where the item is located. Machines now have the means to process data in a smarter way, and to communicate over it!
However, when it comes to exchanging quantitative arguments, be it in a blog post or in a scientific article, web technology does not bring us much further than what can be done with pen and paper. (more…)
A few days after the MCMSki conference, I start to see the main lessons gathered there.
- I should really read the full program before attending the next MCMSki. The three parallel sessions looked consistently interesting, and I really regret having missed some talks (in particular Dawn Woodard‘s and Natesh Pillai‘s) and some posters as well (admittedly, due to exhaustion on my part).
- Compared to the previous instance three years ago (in Utah), the main themes have significantly changed. Scalability, approximate methods, non-asymptotic results, 1/n methods … these keywords are now on everyone’s lips. Can’t wait to see if MCQMC’14 will feel that different from MCQMC’12.
- The community is rightfully concerned about scaling Monte Carlo methods to big data, with some people pointing out that models should also be rethought in this new context.
- The place of software developers in the conference, or simply references to software packages in the talks, is much greater than it used to be. It’s a very good sign towards reproducible research in our field. There’s still a lot of work to do, in particular in terms of making parallel computing easier to access (time to advertise LibBi a little bit). On a related note, many people now point out whether their proposed algorithms are parallel-friendly or not.
- Going from the Rockies to the Alps, the food drastically changed from cheeseburgers to just melted cheese. Bread could be found but ground beef and Budweiser were reported missing.
- It’s fun to have an international conference in your home country, but switching from French to English all the time was confusing.
Back in flooded Oxford now!