a journal of the [experienced] plague and pestilence year

Read The Cybernetic Tea Shop, by Meredith Katz, which is a short and rather clever (if YA) novel about the hazy boundary between humans and humanoids. Plus involving tea addicts! (Which is presumably why Amazon suggested it to me following my reading A Psalm for the Wide Built). And further read over a few sleepless nights the terrible Isandor series starting with City of Strife, by Claudie Arseneault, which had an interesting built of characters and fantasy universe, only to collapse into the usual cracks of super-evil villeins, a massive imbalance of power and a focus on the mundane (like foods and romantic attractions) when their society is under attack. The writing style is also heavily handed, to the point that I found myself skipping more and more paragraphs as the story unfolded. And will definitely not consider the incoming volume.

Went smoothly through my first (?) COVID positivity, which only caused a mild fever over one single day, amidst common cold symptom. Luckily did not pass it to anyone in my immediate vicinity, and resumed running if not swimming almost immediately (if not hard enough to train for the Argentan 1/2 marathon!). But sadly missed the 800th anniversary conference in Padova, as I was still testing positive the day before. I may have gotten infected in Britain or Belgium, despite my constant use of a mask (except in restaurants!).

Watched three more episodes of House of the Dragon, with great characters but a definitive lack of scope (when compared with Game of Thrones). The story remains at a highly local level of power fights and bickering, with existential threats inexistent. Still relatively enjoyable.

Finite mixture models do not reliably learn the number of components

When preparing my talk for Padova, I found that Diana Cai, Trevor Campbell, and Tamara Broderick wrote this ICML / PLMR paper last year on the impossible estimation of the number of components in a mixture.

“A natural check on a Bayesian mixture analysis is to establish that the Bayesian posterior on the number of components increasingly concentrates near the truth as the number of data points becomes arbitrarily large.” Cai, Campbell & Broderick (2021)

Which seems to contradict [my formerly-Glaswegian friend] Agostino Nobile  who showed in his thesis that the posterior on the number of components does concentrate at the true number of components, provided the prior contains that number in its support. As well as numerous papers on the consistency of the Bayes factor, including the one against an infinite mixture alternative, as we discussed in our recent paper with Adrien and Judith. And reminded me of the rebuke I got in 2001 from the late David McKay when mentioning that I did not believe in estimating the number of components, both because of the impact of the prior modelling and of the tendency of the data to push for more clusters as the sample size increased. (This was a most lively workshop Mike Titterington and I organised at ICMS in Edinburgh, where Radford Neal also delivered an impromptu talk to argue against using the Galaxy dataset as a benchmark!)

“In principle, the Bayes factor for the MFM versus the DPM could be used as an empirical criterion for choosing between the two models, and in fact, it is quite easy to compute an approximation to the Bayes factor using importance sampling” Miller & Harrison (2018)

This is however a point made in Miller & Harrison (2018) that the estimation of k logically goes south if the data is not from the assumed mixture model. In this paper, Cai et al. demonstrate that the posterior diverges, even when it depends on the sample size. Or even the sample as in empirical Bayes solutions.

off to Padova??? [for its 800th anniversary]

γ-ABC

An AISTATS 2021 paper by Masahiro Fujisawa,Takeshi Teshima, Issei Sato and Masashi Sugiyama (RIKEN, Tokyo) just appeared on arXiv.  (AISTATS 2021 is again virtual this year.)

“ABC can be sensitive to outliers if a data discrepancy measure is chosen inappropriately (…) In this paper, we propose a novel outlier-robust and computationally-efficient discrepancy measure based on the γ-divergence”

The focus is on measure of robustness for ABC distances as those can be lethal if insufficient summarisation is used. (Note that a referenced paper by Erlis Ruli, Nicola Sartori and Laura Ventura from Padova appeared last year on robust ABC.) The current approach mixes the γ-divergence of Fujisawa and Eguchi, with a k-nearest neighbour density estimator. Which may not prove too costly, of order O(n log n), but also may be a poor if robust approximation, even if it provides an asymptotic unbiasedness and almost surely convergent approximation. These properties are those established in the paper, which only demonstrates convergence in the sample size n to an ABC approximation with the true γ-divergence but with a fixed tolerance ε, when the most recent results are rather concerned with the rates of convergence of ε(n) to zero. (An extensive simulation section compares this approach with several ABC alternatives, incl. ours using the Wasserstein distance. If I read the comparison graphs properly, it does not look as if there is a huge discrepancy between the two approaches under no contamination.) Incidentally, the paper contains a substantial survey section and has a massive reference list, if missing the publication more than a year earlier of our Wasserstein paper in Series B.

discussione a Padova

Here are the slides of my talk in Padova for the workshop Recent Advances in statistical inference: theory and case studies (very similar to the slides for the Varanasi and Gainesville meetings, obviously!, with Peter Müller commenting [at last!] that I had picked the wrong photos from Khajuraho!)

The worthy Padova addendum is that I had two discussants, Stefano Cabras from Universidad Carlos III in Madrid, whose slides are :

and Francesco Pauli, from Trieste, whose slides are:

These were kind and rich discussions with many interesting openings: Stefano’s idea of estimating the pivotal function h is opening new directions, obviously, as it indicates an additional degree of freedom in calibrating the method. Esp. when considering the high variability of the empirical likelihood fit depending on the the function h. For instance, one could start with a large collection of candidate functions and build a regression or a principal component reparameterisation from this collection… (Actually I did not get point #1 about ignoring f: the empirical likelihood is by essence ignoring anything outside the identifying equation, so as long as the equation is valid..) Point #2: Opposing sample free and simulation free techniques is another interesting venue, although I would not say ABC is “sample free”. As to point #3, I will certainly get a look at Monahan and Boos (1992) to see if this can drive the choice of a specific type of pseudo-likelihoods. I like the idea of checking the “coverage of posterior sets” and even more “the likelihood must be the density of a statistic, not necessarily sufficient” as it obviously relates with our current ABC model comparison work… Esp. when the very same paper is mentioned by Francesco as well. Grazie, Stefano! I also appreciate the survey made by Francesco on the consistency conditions, because I think this is an important issue that should be taken into consideration when designing ABC algorithms. (Just pointing out again that, in the theorem of Fearnhead and Prangle (2012) quoting Bernardo and Smith (1992), some conditions are missing for the mathematical consistency to apply.) I also like the agreement we seem to reach about ABC being evaluated per se rather than an a poor man’s Bayesian method. Francesco’s analysis of Monahan and Boos (1992) as validating or not empirical likelihood points out a possible link with the recent coverage analysis of Prangle et al., discussed on the ‘Og a few weeks ago. And an unsuspected link with Larry Wasserman! Grazie, Francesco!