## Archive for the Books Category

## golden glory [jatp]

Posted in Books, pictures, Travel with tags 1950, Golden Pavilion, Japan, Japanese literature, jatp, Kinkaku-ji, Kyoto, Rokuon-ji, The Temple of the Golden Pavilion, Yukio Mishima, zen buddhism on August 16, 2019 by xi'an## conditional noise contrastive estimation

Posted in Books, pictures, University life with tags Charlie Geyer, conference, ICML 2018, intractable constant, logistic regression, machine learning, noise contrasting estimation, Stockholm, Sweden on August 13, 2019 by xi'an**A**t ICML last year, Ciwan Ceylan and Michael Gutmann presented a new version of noise constrative estimation to deal with intractable constants. While noise contrastive estimation relies upon a second independent sample to contrast with the observed sample, this approach uses instead a perturbed or noisy version of the original sample, for instance a Normal generation centred at the original datapoint. And eliminates the annoying constant by breaking the (original and noisy) samples into two groups. The probability to belong to one group or the other then does not depend on the constant, which is a very effective trick. And can be optimised with respect to the parameters of the model of interest. Recovering the score matching function of Hyvärinen (2005). While this is in line with earlier papers by Gutmann and Hyvärinen, this line of reasoning (starting with Charlie Geyer’s logistic regression) never ceases to amaze me!

## blackwing [book review]

Posted in Books, pictures with tags Blackwing, book review, crow, Ed McDonald, grimdark, heroic fantasy, Joe Abercrombie, raven, suspension of disbelief, tattoo on August 10, 2019 by xi'an**A**nother fantasy series of the gritty type, maybe not up to the level of the first ground-breaking Abercrombie’s but definitely great! With some reminiscence of Lawrence’s first series but with a better defined and more complex universe and a not so repulsive central character. Maybe even not repulsive at all when considered past and current actions as described from his perspective…

“I’ve run the equations on it. It took me two days to plot them. Bear in mind that this is far, far beyond any light matrix that I’ve seen calculated before.”

The whole book is indeed written from ‘s viewpoint. A bounty hunter for a post- and pre-apocalyptic society, returning fugitives’ head to the central authorities but governed by a Nameless deity on top of everything (?). Appearing as a raven, hence the compelling cover, hence me buying the book! The plot is unraveling at such a pace that it keeps the tension going, especially since it is rather unpredictable. As noted above, it creates a fairly original universe and while magic is heavily involved, there are limitations to the powers of the sorcerers, witches, half-gods and other entities that mean no deus-ex-machina last minute resolution, sort of. Actually (spoiler alert!) the machine at the core of the story is not doing too well… With repeated mentions made of mathematics governing the handling of the machine, including one over-the-top computation on the ceiling of a cell! It is only when I finished the book that I realised this was part of a series, as the story could have ended there. (Maybe should have, if the associated reviews for the next two volumes are to be trusted.)

## a problem that did not need ABC in the end

Posted in Books, pictures, Statistics, Travel with tags ABC, Approximate Bayesian computation, Colorado, cross validated, dawn, Denver, high rise, introductory opening lecture, jatp, JSM 2019, law of the hammer, multinomial distribution, predictive on August 8, 2019 by xi'an**W**hile in Denver, at JSM, I came across [across validated!] this primarily challenging problem of finding the posterior of the 10³ long probability vector of a Multinomial M(10⁶,p) when only observing the range of a realisation of M(10⁶,p). This sounded challenging because the distribution of the pair (min,max) is not available in closed form. (Although this allowed me to find a paper on the topic by the late Shanti Gupta, who was chair at Purdue University when I visited 32 years ago…) This seemed to call for ABC (especially since I was about to give an introductory lecture on the topic!, law of the hammer…), but the simulation of datasets compatible with the extreme values of both minimum and maximum, m=80 and M=12000, proved difficult when using a uniform Dirichlet prior on the probability vector, since these extremes called for both small and large values of the probabilities. However, I later realised that the problem could be brought down to a Multinomial with only three categories and the observation (m,M,n-m-M), leading to an obvious Dirichlet posterior and a predictive for the remaining 10³-2 realisations.

## in a house of lies [book review]

Posted in Books, Travel with tags Brexit, detective story, Edinburgh, Glasgow, Ian Rankin, PM, Rebus, retirement, Scotland on August 7, 2019 by xi'an**W**hile I found the latest Rankin’s Rebus novels a wee bit disappointing, this latest installment in the stories of the Edinburghian ex-detective is a true pleasure! Maybe because it takes the pretext of a “cold case” suddenly resurfacing to bring back to life characters met in earlier novels of the series. And the borderline practice of DI Rebus himself. Which should matter less at a stage when Rebus has been retired for 10 years (I could not believe it had been that long!, but I feel like I followed Rebus for most of his carreer…) The plot is quite strong with none of the last minute revelations found in some earlier volumes, with a secondary plot that is much more modern and poignant. I also suspect some of the new characters will reappear in the next books, as well as the consequences of a looming Brexit [pushed by a loony PM] on the Scottish underworld… (No,. I do not mean ~~Torys~~Tories!)

## prime suspects [book review]

Posted in Books, Kids, University life with tags Alexandre Grothendieck, book review, CHANCE, comics, François Schuiten, Gödel Escher and Bach, graphic novel, Jacques Tardi, José Muñoz, Kingman's coalescent, logicomix, NCIS, Nicolas Bourbaki, Persi Diaconis, Princeton University Press on August 6, 2019 by xi'an

**I** was contacted by Princeton University Press to comment on the comic book/graphic novel Prime Suspects (The Anatomy of Integers and Permutations), by Andrew Granville (mathematician) & Jennifer Granville (writer), and Robert Lewis (illustrator), and they sent me the book. I am not a big fan of graphic book entries to mathematical even less than to statistical notions (Logicomix being sort of an exception for its historical perspective and nice drawing style) and this book did nothing to change my perspective on the subject. First, the plot is mostly a pretense at introducing number theory concepts and I found it hard to follow it for more than a few pages. The [noires maths] story is that “forensic maths” detectives are looking at murders that connects prime integers and permutations… The ensuing NCIS-style investigation gives the authors the opportunity to skim through the whole cenacle of number theorists, plus a few other mathematicians, who appear as more or less central characters. Even illusory ones like Nicolas Bourbaki. And Alexander Grothendieck as a recluse and clairvoyant hermit [who in real life did not live in a Pyrénées cavern!!!]. Second, I [and nor is Andrew who was in my office when the book arrived!] am not particularly enjoying the drawings or the page composition or the colours of this graphic novel, especially because I find the characters drawn quite inconsistently from one strip to the next, to the point of being unrecognisable, and, if it matters, hardly resembling their real-world equivalent (as seen in the portrait of Persi Diaconis). To be completely honest, the drawings look both ugly and very conventional to me, in that I do not find much of a characteristic style to them. To contemplate what Jacques Tardi, François Schuiten or José Muñoz could have achieved with the same material… (Or even Edmond Baudoin, who drew the strips for the graphic novels he coauthored with Cédric Villani.) The graphic novel (with a prime 181 pages) is postfaced with explanations about the true persons behind the characters, from Carl Friedriech Gauß to Terry Tao, and of course on the mathematical theory for the analogies between the prime and cycles frequencies behind the story. Which I find much more interesting and readable, obviously. (With a surprise appearance of Kingman’s coalescent!) But also somewhat self-defeating in that so much has to be explained on the side for the links between the story, the characters and the background heavily loaded with “obscure references” to make sense to more than a few mathematician readers. Who may prove to be the core readership of this book.

There is also a bit of a Gödel-Escher-and-Bach flavour in that a piece by Robert Schneider called Réverie in Prime Time Signature is included, while an Escher’s infinite stairway appears in one page, not far from what looks like Milano Vittorio Emmanuelle gallery (On the side, I am puzzled by the footnote on p.208 that “I should clarify that selecting a random permutation and a random prime, as described, can be done easily, quickly, and correctly”. This may be connected to the fact that the description of Bach’s algorithm provided therein is incomplete.)

*[Disclaimer about potential self-plagiarism: this post or an edited version will eventually appear in my Books Review section in CHANCE. As appropriate for a book about Chance!]*

## unbiased product of expectations

Posted in Books, Statistics, University life with tags ABC, g-and-k distributions, importance sampling, latent variable models, NP-complete problem, permanent of a matrix, pseudo-marginal MCMC, recycling, University of Warwick on August 5, 2019 by xi'an**W**hile I was not involved in any way, or even aware of this research, Anthony Lee, Simone Tiberi, and Giacomo Zanella have an incoming paper in Biometrika, and which was partly written while all three authors were at the University of Warwick. The purpose is to design an efficient manner to approximate the product of n unidimensional expectations (or integrals) all computed against the same reference density. Which is not a real constraint. A neat remark that motivates the method in the paper is that an improved estimator can be connected with the permanent of the n x N matrix A made of the values of the n functions computed at N different simulations from the reference density. And involves N!/ (N-n)! terms rather than N to the power n. Since it is NP-hard to compute, a manageable alternative uses random draws from constrained permutations that are reasonably easy to simulate. Especially since, given that the estimator recycles most of the particles, it requires a much smaller version of N. Essentially N=O(n) with this scenario, instead of O(n²) with the basic Monte Carlo solution, towards a similar variance.

This framework offers many applications in latent variable models, including pseudo-marginal MCMC, of course, but also for ABC since the ABC posterior based on getting each simulated observation close enough from the corresponding actual observation fits this pattern (albeit the dependence on the chosen ordering of the data is an issue that can make the example somewhat artificial).