non-reversible guided Metropolis–Hastings

Kengo Kamatani and Xiaolin Song, whom I visited in Osaka last summer in what seems like another reality!, just arXived another paper on a non-reversible Metropolis version. That exploits a group action and the associated Haar measure.

Following a proposal of Gustafson (1998), a ∆-guided Metropolis–Hastings kernel is based on a statistic ∆ that is totally ordered and determine the acceptance of a proposed value y~Q(x,.) by adding a direction (-,+) to the state space and moving from x if ∆x≤∆y in the positive direction and if ∆y≤∆x in the negative direction [with the standard Metropolis–Hastings acceptance probability]. The sign of the direction switches in case of a rejection. And the statistic ∆ is such that the proposal kernel Q(x,.) is unbiased, i.e., agnostic to the sign, i.e., it gives the same probability to ∆x≤∆y and ∆y≤∆x. This modification reduces the asymptotic variance compared with the original Metropolis–Hastings kernel.

To construct a random walk proposal that is unbiased, the authors assume that the ∆ transform takes values in a topological group, G, with Q further being invariant under the group actions. This can be constructed from a standard proposal by averaging the transforms of Q under all elements of the group over the associated right Haar measure. (Which I thought implied that the group is compact, except I forgot to account for the data update into a posterior..!) The worked-out example is based on a multivariate autoregressive kernel with ∆x being a rescaled non-central chi-squared variate. In dimension 24. The results show a clear improvement in effective sample size per second evaluation over off-the-shelf random walk and Hamiltonian Monte Carlo versions.

Seeing the Haar measure appearing in the setting of Markov chain Monte Carlo is fun!, as my last brush with it was not algorithmic. I would think the proposal only applies to settings where the components of the simulated vector are somewhat homogeneous in that the determinationthe determination of both the group action and a guiding statistic seem harder in cases where these components take different meaning (or live in a weird topology). I also lazily wonder if selecting the guiding statistic as a gradient of the log-target would have any interest.

enjoy a cuppa for International Tea Day

It's an art.
It's culture.
It's heritage.
And it's a source of livelihood for millions.

🍵Tea isn't just a drink, it's so much more.

On this first #InternationalTeaDay, we celebrate the history of tea and the farmers that produce it!

👉https://t.co/Zb6CrSURPq pic.twitter.com/kckGVhQXzg

— FAO (@FAO) May 21, 2020

 

on an absurd climbing competition

The New York Times has a very interesting piece on why Adam Ondra, arguably the best sport climber in the World, who climbed the very first 9c route in 2018, with a supernatural move involving hanging head down, actually has little hope of winning the Olympics. Assuming there will be Olympics this year. It is essentially because there is only one single medal for the sport, merging the radically different skills of bouldering, lead climbing and the absurd addition of speed climbing, which involves a single route, always the same, not particularly hard (6b) but to be climbed as fast as possible. To be a top contender on two categories is already pretty rare, with Ondra an exception. To master all three… Only cumulated athletic categories like heptathlon or pentathlon compare, but they come on top of existing competitions for every single of the seven or five events they are made of. Ondra came second or first in bouldering and lead, but closer to last for speed climbing. At least he made it through the qualifications.

Rashomon, plus 47 ronins, plus…

Another chance encounter (on Amazon) led me to read a graphical novel entitled Rashōmon, by Victor Santos. Which uses the same short stories from Ryūnosuke Akutagawa as Akira Kurosawa in his superlative film, if not with the same intensity. (The very first sentences are inspired from the first pages of the book, though.) And in a second part builds upon the tale of the 47 rônins which I read last summer in Koyasan. Plus a possible appearance of Miyamato Mushashi, the great 17th Century swordsman (depicted in two wonderful novels by Eiji Yoshikawa). While this is historically impossible, since Rashōmon takes place in the 12th Century and the 47 rônins acted in 1702, the theme cementing the story is the presence of a detective named Heigo Kobayashi, who “solves” both crimes but is nonetheless outsmarted by the novel “femme fatale”… Without a clear explanation as to how she did it.

While I found the rendering rather entertaining, with an original if convoluted drawing style, I was rather disappointed at the simplistic and Westernised adaptation of the subtle stories into a detective story. Calling upon (anachronic) ninjas as if the historical setting per se was not exotic enough. And the oddly modified role of the main female character into an Hammet-like heroin kills the ambivalence that is central to both Akutagawa’s and Kurosawa’s versions.

夢幻花 [Dream flower]

Another Japanese mystery novel by Higashino Keigo, which I read in French under the title La fleur de l´illusion [on a sunny Sunday afternoon, under my fig tree] and enjoyed both for its original, convoluted (and mostly convincing) plot and for the well-rendered interaction between the young protagonists. And also for having a few connections with my recent trip, from one protagonist studying nuclear physics at the University of Osaka to a visit to the back country of Katsuura. (The author himself graduated from Osaka Prefecture University with a Bachelor of Engineering degree.) Spoiler warning: the only annoying part of the plot was the resolution of the mystery via a secret society run by a few families of civil servants, which as always sounds to me like a rather cheap way out. But not enough to ruin the entire novel.