one World ABC seminar [term #2]

The on-line One World ABC seminar continues on-line this semester! With talks every other Thursday at 11:30 UK time (12:30 central European time). Incoming speakers are

• Marko Järvenpää, on Batch simulations and uncertainty quantification in Gaussian process surrogate ABC, on the first of October
• David Frazier, on a minimum distance approach to ABC, on 15 October [Warning: 10:30 UK time, 11:30 EU time, 8:30 Victoria time!!!]
• David Nott, on Marginally calibrated deep distributional regression, on 12 November
• Matti Vihola, on the use of approximate Bayesian computation Markov chain Monte Carlo with inflated tolerance and post-correction, on 10 December

with presenters to be confirmed for 29 October. Anyone interested in presenting at this webinar in a near future should not hesitate in contacting Massimiliano Tamborrino in Warwick or any of the other organisers of the seminar!

Elves to the ABC rescue!

Marko Järvenpää, Michael Gutmann, Arijus Pleska, Aki Vehtari, and Pekka Marttinen have written a paper on Efficient Acquisition Rules for Model-Based Approximate Bayesian Computation soon to appear in Bayesian Analysis that gives me the right nudge to mention the ELFI software they have been contributing to for a while. Where the acronym stands for engine for likelihood-free inference. Written in Python, DAG based, and covering methods like the

• ABC rejection sampler
• Sequential Monte Carlo ABC sampler
• Bayesian Optimization for Likelihood-Free Inference (BOLFI) framework
• Bayesian Optimization (not likelihood-free)
• No-U-Turn-Sampler (not likelihood-free)

[Warning: I did not experiment with the software! Feel free to share.]

“…little work has focused on trying to quantify the amount of uncertainty in the estimator of the ABC posterior density under the chosen modelling assumptions. This uncertainty is due to a finite computational budget to perform the inference and could be thus also called as computational uncertainty.”

The paper is about looking at the “real” ABC distribution, that is, the one resulting from a realistic perspective of a finite number of simulations and acceptances. By acquisition, the authors mean an efficient way to propose the next value of the parameter θ, towards minimising the uncertainty in the ABC density estimate. Note that this involves a loss function that must be chosen by the analyst and then available for the minimisation program. If this sounds complicated…

“…our interest is to design the evaluations to minimise the uncertainty in a quantity that itself describes the uncertainty of the parameters of a costly simulation model.”

it indeed is and it requires modelling choices. As in Guttman and Corander (2016), which was also concerned by designing the location of the learning parameters, the modelling is based here on a Gaussian process for the discrepancy between the observed and the simulated data. Which provides an estimate of the likelihood, later used for selecting the next sampling value of θ. The final ABC sample is however produced by a GP estimation of the ABC distribution.As noted by the authors, the method may prove quite time consuming: for instance, one involved model required one minute of computation time for selecting the next evaluation location. (I had a bit of a difficulty when reading the paper as I kept hitting notions that are local to the paper but not immediately or precisely defined. As “adequation function” [p.11] or “discrepancy”. Maybe correlated with short nights while staying at CIRM for the Masterclass, always waking up around 4am for unknown reasons!)

ABC in Stockholm [on-board again]

After a smooth cruise from Helsinki to Stockholm, a glorious sunrise over the Ålend Islands, and a morning break for getting an hasty view of the city, ABC in Helsinki (a.k.a. ABCruise) resumed while still in Stockholm. The first talk was by Laurent Calvet about dynamic (state-space) models, when the likelihood is not available and replaced with a proximity between the observed and the simulated observables, at each discrete time in the series. The authors are using a proxy predictive for the incoming observable and derive an optimal—in a non-parametric sense—bandwidth based on this proxy. Michael Gutmann then gave a presentation that somewhat connected with his talk at ABC in Roma, and poster at NIPS 2014, about using Bayesian optimisation to reduce the rejections in ABC algorithms. Which means building a model of a discrepancy or distance by Bayesian optimisation. I definitely like this perspective as it reduces the simulation to one of a discrepancy (after a learning step). And does not require a threshold. Aki Vehtari expanded on this idea with a series of illustrations. A difficulty I have with the approach is the construction of the acquisition function… The last session while pretty late was definitely exciting with talks by Richard Wilkinson on surrogate or emulator models, which goes very much in a direction I support, namely that approximate models should be accepted on their own, by Julien Stoehr with clustering and machine learning tools to incorporate more summary statistics, and Tim Meeds who concluded with two (small) talks!, centred on the notion of deterministic algorithms that explicitly incorporate the random generators within the comparison, resulting in post-simulation recentering à la Beaumont et al. (2003), plus new advances with further incorporations of those random generators turned deterministic functions within variational Bayes inference…

On Wednesday morning, we will land back in Helsinki and head back to our respective homes, after another exciting ABC in… workshop. I am terribly impressed by the way this workshop at sea operated, providing perfect opportunities for informal interactions and collaborations, without ever getting claustrophobic or dense. Enjoying very long days also helped. While it seems unlikely we can repeat this successful implementation, I hope we can aim at similar formats in the coming occurrences. Kitos paljon to our Finnish hosts!

never mind the big data here’s the big models [workshop]

Maybe the last occurrence this year of the pastiche of the iconic LP of the Sex Pistols!, made by Tamara Polajnar. The last workshop as well of the big data year in Warwick, organised by the Warwick Data Science Institute. I appreciated the different talks this afternoon, but enjoyed particularly Dan Simpson’s and Rob Scheichl’s. The presentation by Dan was so hilarious that I could not resist asking him for permission to post the slides here:

Not only hilarious [and I have certainly missed 67% of the jokes], but quite deep about the meaning(s) of modelling and his views about getting around the most blatant issues. Ron presented a more computational talk on the ways to reach petaflops on current supercomputers, in connection with weather prediction models used (or soon to be used) by the Met office. For a prediction area of 1 km². Along with significant improvements resulting from multiscale Monte Carlo and quasi-Monte Carlo. Definitely impressive! And a brilliant conclusion to the Year of Big Data (and big models).