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!

transport Monte Carlo

Read this recent arXival by Leo Duan (from UF in Gainesville) on transport approaches to approximate Bayesian computation, in connection with normalising flows. The author points out a “lack of flexibility in a large class of normalizing flows”  to bring forward his own proposal.

“…we assume the reference (a multivariate uniform distribution) can be written as a mixture of many one-to-one transforms from the posterior”

The transportation problem is turned into defining a joint distribution on (β,θ) such that θ is marginally distributed from the posterior and β is one of an infinite collection of transforms of θ. Which sounds quite different from normalizing flows, to be sure. Reverting the order, if one manages to simulate β from its marginal the resulting θ is one of the transforms. Chosen to be a location-scale modification of β, s⊗β+m. The weights when going from θ to β are logistic transforms with Dirichlet distributed scales. All with parameters to be optimised by minimising the Kullback-Leibler distance between the reference measure on β and its inverse mixture approximation, and resorting to gradient descent. (This may sound a wee bit overwhelming as an approximation strategy and I actually had to make a large cup of strong macha to get over it, but this may be due to the heat wave occurring at the same time!) Drawing θ from this approximation is custom-made straightforward and an MCMC correction can even be added, resulting in an independent Metropolis-Hastings version since the acceptance ratio remains computable. Although this may defeat the whole purpose of the exercise by stalling the chain if the approximation is poor (hence suggesting this last step being used instead as a control.)

The paper also contains a theoretical section that studies the approximation error, going to zero as the number of terms in the mixture, K, goes to infinity. Including a Monte Carlo error in log(n)/n (and incidentally quoting a result from my former HoD at Paris 6, Paul Deheuvels). Numerical experiments show domination or equivalence with some other solutions, e.g. being much faster than HMC, the remaining $1000 question being of course the on-line evaluation of the quality of the approximation.

right place, wrong version

adaptive ABC tolerance

“There are three common approaches for selecting the tolerance sequence (…) [they] can lead to inefficient sampling”

Umberto Simola, Jessi Cisewski-Kehe, Michael Gutmann and Jukka Corander recently arXived a paper entitled Adaptive Approximate Bayesian Computation Tolerance Selection. I appreciate that they start from our ABC-PMC paper, i.e., Beaumont et al. (2009) [although the representation that the ABC tolerances are fixed in advance is somewhat incorrect in that we used in our codes quantiles of the distances to set our tolerances.] This is also the approach advocated for the initialisation step by the current paper.  Although remaining a wee bit vague. Subsequent steps are based on the proximity between the resulting approximations to the ABC posteriors, more exactly with a quantile derived from the maximum of the ratio between two estimated successive ABC posteriors. Mimicking the Accept-Reject step if always one step too late.  The iteration stops when the ratio is almost one, possibly missing the target due to Monte Carlo variability. (Recall that the “optimal” tolerance is not zero for a finite sample size.)

“…the decrease in the acceptance rate is mitigated by the improvement in the proposed particles.”

A problem is that it depends on the form of the approximation and requires non-parametric hence imprecise steps. Maybe variational encoders could help. Interesting approach by Sugiyama et al. (2012), of which I knew nothing, the core idea being that the ratio of two densities is also the solution to minimising a distance between the numerator density and a variable function times the bottom density. However since only the maximum of the ratio is needed, a more focused approach could be devised. Rather than first approximating the ratio and second maximising the estimated ratio. Maybe the solution of Goffinet et al. (1992) on estimating an accept-reject constant could work.

A further comment is that the estimated density is not properly normalised, which lessens the Accept-Reject analogy since the optimum may well stand above one. And thus stop “too soon”. (Incidentally, the paper contains the mixture example of Sisson et al. (2007), for which our own graphs were strongly criticised during our Biometrika submission!)

PhD position for research in ABC in Chalmers University

[Posting a call for PhD candidates from Umberto Piccini as the deadline is June 1, next Monday!]

A PhD student position in mathematical statistics on simulation-based inference methods for models with an “intractable” likelihood is available at the Dept. Mathematical Sciences, Chalmers University, Gothenburg (Sweden).

You will be part of an international collaboration to create new methodology bridging between simulation-based inference (such as approximate Bayesian computation and other likelihood-free methods) and deep neuronal networks. The goal is to ease inference for stochastic modelling.

Details on the project and the essential requirements are at https://www.chalmers.se/en/departments/math/research/research-groups/AIMS/Pages/ai-project-5.aspx

The PhD student position is fully funded and is up to 5 years, in the dynamic and international city of Gothenburg, the second largest city in Sweden, https://www.goteborg.com/en/ As a PhD student in Mathematical Sciences you will have opportunities for many inspiring conversations, a lot of autonomous work and some travel.

The position will be supervised by Assoc. Prof. Umberto Picchini.

Apply by 01 June 2020 following the instructions at
https://www.chalmers.se/en/about-chalmers/Working-at-Chalmers/Vacancies/Pages/default.aspx?rmpage=job&rmjob=8556

For informal enquiries, please get in touch with Umberto Picchini