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.”

launch of ELLIS

The European Laboratory for Learning and Intelligent Systems (ELLIS) is a network (inspired by the Canadian LMB CIFAR network ) that has been recently created to keep European research in artificial intelligence and machine learning at the forefront, to keep up with North America and China where the AI investments are far superior. It has currently 30 units and will be officially launched this Tuesday, 15 September with live streaming. (I am part of the Paris Ellis Unit, directed by Gabiel Peyré.) It also organizes PhD and postdoc exchange programs.

coauthorship and citation networks

As I discovered (!) the Annals of Applied Statistics in my mailbox just prior to taking the local train to Dauphine for the first time in 2017 (!), I started reading it on the way, but did not get any further than the first discussion paper by Pengsheng Ji and Jiashun Jin on coauthorship and citation networks for statisticians. I found the whole exercise intriguing, I must confess, with little to support a whole discussion on the topic. I may have read the paper too superficially as a métro pastime, but to me it sounded more like a post-hoc analysis than a statistical exercise, something like looking at the network or rather at the output of a software representing networks and making sense of clumps and sub-networks a posteriori. (In a way this reminded of my first SAS project at school, on the patterns of vacations in France. It was in 1983 on pinched cards. And we spent a while cutting & pasting in a literal sense the 80 column graphs produced by SAS on endless listings.)

It may be that part of the interest in the paper is self-centred. I do not think analysing a similar dataset in another field like deconstructionist philosophy or Korean raku would have attracted the same attention. Looking at the clusters and the names on the pictures is obviously making sense, if more at a curiosity than a scientific level, as I do not think this brings much in terms of ranking and evaluating research (despite what Bernard Silverman suggests in his preface) or understanding collaborations (beyond the fact that people in the same subfield or same active place like Duke tend to collaborate). Speaking of curiosity, I was quite surprised to spot my name in one network and even more to see that I was part of the “High-Dimensional Data Analysis” cluster, rather than of the “Bayes” cluster.  I cannot fathom how I ended up in that theme, as I cannot think of a single paper of mines pertaining to either high dimensions or data analysis [to force the trait just a wee bit!]. Maybe thanks to my joint paper with Peter Mueller. (I tried to check the data itself but cannot trace my own papers in the raw datafiles.)

I also wonder what is the point of looking at solely four major journals in the field, missing for instance most of computational statistics and biostatistics, not to mention machine learning or econometrics. This results in a somewhat narrow niche, if obviously recovering the main authors in the [corresponding] field. Some major players in computational stats still make it to the lists, like Gareth Roberts or Håvard Rue, but under the wrong categorisation of spatial statistics.

intractable likelihoods (even) for Alan

In connection with the official launch of the Alan Turing Institute (or ATI, of which Warwick is a partner), it funded an ATI Scoping workshop yesterday a week ago in Warwick around the notion(s) of intractable likelihood(s) and how this could/should fit within the themes of the Institute [hence the scoping]. This is one among many such scoping workshops taking place at all partners, as reported on the ATI website. Workshop that was quite relaxed and great fun, if only for getting together with most people (and friends) in the UK interested in the topic. But also pointing out some new themes I had not previously though of as related to ilike. For instance, questioning the relevance of likelihood for inference and putting forward decision theory under model misspecification, connecting with privacy and ethics [hence making intractable “good”!], introducing uncertain likelihood, getting more into network models, RKHS as a natural summary statistic, swarm of solutions for consensus inference… (And thanks to Mark Girolami for this homage to the iconic LP of the Sex Pistols!, that I played maniacally all over 1978…) My own two-cents into the discussion were mostly variations of other discussions, borrowing from ABC (and ABC slides) to call for a novel approach to approximate inference:

Topological sensitivity analysis for systems biology

Michael Stumpf sent me Topological sensitivity analysis for systems biology, written by Ann Babtie and Paul Kirk,  en avant-première before it came out in PNAS and I read it during the trip to NIPS in Montréal. (The paper is published in open access, so everyone can read it now!) The topic is quite central to a lot of debates about climate change, economics, ecology, finance, &tc., namely to assess the impact of using the wrong model to draw conclusions and make decisions about a real phenomenon. (Which reminded me of the distinction between mechanical and phenomenological models stressed by Michael Blum in his NIPS talk.) And it is of much interest from a Bayesian point of view since assessing the worth of a model requires modelling the “outside” of a model, using for instance Gaussian processes as in the talk Tony O’Hagan gave in Warwick earlier this term. I would even go as far as saying that the issue of assessing [and compensating for] how wrong a model is, given available data, may be the (single) most under-assessed issue in statistics. We (statisticians) have yet to reach our Boxian era.

In Babtie et al., the space or universe of models is represented by network topologies, each defining the set of “parents” in a semi-Markov representation of the (dynamic) model. At which stage Gaussian processes are also called for help. Alternative models are ranked in terms of fit according to a distance between simulated data from the original model (sounds like a form of ABC?!). Obviously, there is a limitation in the number and variety of models considered this way, I mean there are still assumptions made on the possible models, while this number of models is increasing quickly with the number of nodes. As pointed out in the paper (see, e.g., Fig.4), the method has a parametric bootstrap flavour, to some extent.

What is unclear is how one can conduct Bayesian inference with such a collection of models. Unless all models share the same “real” parameters, which sounds unlikely. The paper mentions using uniform prior on all parameters, but this is difficult to advocate in a general setting. Another point concerns the quantification of how much one can trust a given model, since it does not seem models are penalised by a prior probability. Hence they all are treated identically. This is a limitation of the approach (or an indication that it is only a preliminary step in the evaluation of models) in that some models within a large enough collection will eventually provide an estimate that differs from those produced by the other models. So the assessment may become altogether highly pessimistic for this very reason.

“If our parameters have a real, biophysical interpretation, we therefore need to be very careful not to assert that we know the true values of these quantities in the underlying system, just because–for a given model–we can pin them down with relative certainty.”

In addition to its relevance for moving towards approximate models and approximate inference, and in continuation of yesterday’s theme, the paper calls for nested sampling to generate samples from the posterior(s) and to compute the evidence associated with each model. (I realised I had missed this earlier paper by Michael and co-authors on nested sampling for system biology.) There is no discussion in the paper on why nested sampling was selected, compared with, say, a random walk Metropolis-Hastings algorithm. Unless it is used in a fully automated way,  but the paper is rather terse on that issue… And running either approach on 10⁷ models in comparison sounds like an awful lot of work!!! Using importance [sampling] nested sampling as we proposed with Nicolas Chopin could be a way to speed up this exploration if all parameters are identical between all or most models.