approximate Bayesian inference [survey]

In connection with the special issue of Entropy I mentioned a while ago, Pierre Alquier (formerly of CREST) has written an introduction to the topic of approximate Bayesian inference that is worth advertising (and freely-available as well). Its reference list is particularly relevant. (The deadline for submissions is 21 June,)

simulation-based inference for neuroscience [One World ABC seminar]

The next One World ABC seminar will take place on Thursday at 11:30, UK time, and will broadcast a talk by Jakob Macke on Simulation-based inference for neuroscience. Here is the abstract

Neuroscience research makes extensive use of mechanistic models of neural dynamics — these models are often implemented through numerical simulators, requiring the use of simulation-based approaches to statistical inference. I will talk about our recent work on developing simulation based inference-methods using flexible density estimators parameterised with neural networks, our efforts on benchmarking these approaches, and applications to modelling problems in neuroscience.

Remember you need to register beforehand to receive the access code!

ABC on brain networks

Research Gate sent me an automated email pointing out a recent paper citing some of our ABC papers. The paper is written by Timothy West et al., neuroscientists in the UK, comparing models of Parkinsonian circuit dynamics. Using SMC-ABC. One novelty is the update of the tolerance by a fixed difference, unless the acceptance rate is too low, in which case the tolerance is reinitialised to a starting value.

“(…) the proposal density P(θ|D⁰) is formed from the accepted parameters sets. We use a density approximation to the marginals and a copula for the joint (…) [i.e.] a nonparametric estimation of the marginal densities overeach parameter [and] the t-copula(…) Data are transformed to the copula scale (unit-square) using the kernel density estimator of the cumulative distribution function of each parameter and then transformed to the joint space with the t-copula.”

The construct of the proposal is quite involved, as described in the above quote. The model choice approach is standard (à la Grelaud et al.) but uses the median distance as a tolerance.

“(…) test whether the ABC estimator will: a) yield parameter estimates that are unique to the data from which they have been optimized; and b) yield consistent estimation of parameters across multiple instances (…) test the face validity of the model comparison framework (…) [and] demonstrate the scalability of the optimization and model comparison framework.”

The paper runs a fairly extensive test of the above features, concluding that “the ABC optimized posteriors are consistent across multiple initializations and that the output is determined by differences in the underlying model generating the given data.” Concerning model comparison, the authors mix the ABC Bayes factor with a post-hoc analysis of divergence to discriminate against overfitting. And mention the potential impact of the summary statistics in the conclusion section, albeit briefly, and the remark that the statistics were “sufficient to recover known parameters” is not supporting their use for model comparison. The additional criticism of sampling strategies for approximating Bayes factors is somewhat irrelevant, the main issue with ABC model choice being a change of magnitude in the evidence.

“ABC has established itself as a key tool for parameter estimation in systems biology (…) but is yet to see wide adoption in systems neuroscience. It is known that ABC will not perform well under certain conditions (Sunnåker et al., 2013). Specifically, it has been shown that the
simplest form of ABC algorithm based upon an rejection-sampling approach is inefficient in the case where the prior densities lie far from the true posterior (…) This motivates the use of neurobiologically grounded models over phenomenological models where often the ranges of potential parameter values are unknown.”

the new DIYABC-RF

My friends and co-authors from Montpellier have released last month the third version of the DIYABC software, DIYABC-RF, which includes and promotes the use of random forests for parameter inference and model selection, in connection with Louis Raynal’s thesis. Intended as the earlier versions of DIYABC for population genetic applications. Bienvenue!!!

The software DIYABC Random Forest (hereafter DIYABC-RF) v1.0 is composed of three parts: the dataset simulator, the Random Forest inference engine and the graphical user interface. The whole is packaged as a standalone and user-friendly graphical application named DIYABC-RF GUI and available at https://diyabc.github.io. The different developer and user manuals for each component of the software are available on the same website. DIYABC-RF is a multithreaded software on three operating systems: GNU/Linux, Microsoft Windows and MacOS. One can use the program can be used through a modern and user-friendly graphical interface designed as an R shiny application (Chang et al. 2019). For a fluid and simplified user experience, this interface is available through a standalone application, which does not require installing R or any dependencies and hence can be used independently. The application is also implemented in an R package providing a standard shiny web application (with the same graphical interface) that can be run locally as any shiny application, or hosted as a web service to provide a DIYABC-RF server for multiple users.

ABC in Svalbard [#2]

The second day of the ABC wwworkshop got a better start than yesterday [for me] as I managed to bike to Dauphine early enough to watch the end of Gael’s talk and Matias Quiroz’ in full on the Australian side (of zoom). With an interesting take on using frequency-domain (pseudo-)likelihoods in complex models. Followed by two talks by David Frazier from Monash and Chris Drovandi from Brisbane on BSL, the first on misspecification with a finer analysis as to why synthetic likelihood may prove worse: the Mahalanobis distance behind it may get very small and the predictive distribution of the distance may become multimodal. Also pointing out the poor coverage of both ABC and BSL credible intervals. And Chris gave a wide-ranging coverage of summary-free likelihood-free approaches, with examples where they were faring well against some summary-based solutions. Olivier from Grenoble [with a co-author from Monash, keeping up the Australian theme] discussed dimension reductions which could possibly lead to better summary statistics, albeit unrelated with ABC!

Riccardo Corradin considered this most Milanese problem of all problems (!), namely how to draw inference on completely random distributions. The clustering involved in this inference being costly, the authors using our Wasserstein ABC approach on the partitions, with a further link to our ABC-Gibbs algorithm (which Grégoire had just presented) for the tolerance selection. Marko Järvenpää presented an approach related with a just-published paper in Bayesian Analysis. with a notion of noisy likelihood modelled as a Gaussian process. Towards avoiding evaluating the (greedy) likelihood too often, as in the earlier Korrakitara et al. (2014). And coining the term of Bayesian Metropolis-Hastings sampler (as the regular Metropolis (Rosenbluth) is frequentist)! And Pedro Rodrigues discussed using normalising flows in poorly identified (or inverse) models. Raising the issue of validating this approximation to the posterior and connecting with earlier talks.

The afternoon session was a reply of the earliest talks from the Australian mirrors. Clara Grazian gave the first talk yesterday on using and improving a copula-based ABC, introducing empirical likelihood, Gaussian processes and splines. Leading to a question as to whether or not the copula family could be chosen by ABC tools. David Nott raised the issue of conflicting summary statistics. Illustrated by a Poisson example where using the pair made by the empirical mean and the empirical variance  as summary: while the empirical mean is sufficient, conditioning on both leads to a different ABC outcome. Which indirectly relates to a work in progress in our Dauphine group. Anthony Ebert discussed the difficulty of handling state space model parameters with ABC. In an ABCSMC² version, the likelihood is integrated out by a particle filter approximation but leading to difficulties with the associated algorithm, which I somewhat associate with the discrete nature of the approximation, possibly incorrectly. Jacob Priddle’s talked about a whitening version of Bayesian synthetic likelihood. By arguing that the variance of the Monte Carlo approximation to the moments of the Normal synthetic likelihood is much improved when assuming that the components of the summary statistic are independent. I am somewhat puzzled by the proposal, though, in that the whitening matrix need be estimated as well.

Thanks to all colleagues and friends involved in building and running the mirrors and making some exchanges possible despite the distances and time differences! Looking forward a genuine ABC meeting in a reasonable future, and who knows?!, reuniting in Svalbard for real! (The temperature in Longyearbyen today was -14⁰, if this makes some feel better about missing the trip!!!) Rather than starting a new series of “ABC not in…”