simulation as optimization [by kernel gradient descent]

Yesterday, which proved an unseasonal bright, warm, day, I biked (with a new wheel!) to the east of Paris—in the Gare de Lyon district where I lived for three years in the 1980’s—to attend a Mokaplan seminar at INRIA Paris, where Anna Korba (CREST, to which I am also affiliated) talked about sampling through optimization of discrepancies.
This proved a most formative hour as I had not seen this perspective earlier (or possibly had forgotten about it). Except through some of the talks at the Flatiron Institute on Transport, Diffusions, and Sampling last year. Incl. Marilou Gabrié’s and Arnaud Doucet’s.
The concept behind remains attractive to me, at least conceptually, since it consists in approximating the target distribution, known up to a constant (a setting I have always felt standard simulation techniques was not exploiting to the maximum) or through a sample (a setting less convincing since the sample from the target is already there), via a sequence of (particle approximated) distributions when using the discrepancy between the current distribution and the target or gradient thereof to move the particles. (With no randomness in the Kernel Stein Discrepancy Descent algorithm.)
Ana Korba spoke about practically running the algorithm, as well as about convexity properties and some convergence results (with mixed performances for the Stein kernel, as opposed to SVGD). I remain definitely curious about the method like the (ergodic) distribution of the endpoints, the actual gain against an MCMC sample when accounting for computing time, the improvement above the empirical distribution when using a sample from π and its ecdf as the substitute for π, and the meaning of an error estimation in this context.

“exponential convergence (of the KL) for the SVGD gradient flow does not hold whenever π has exponential tails and the derivatives of ∇ log π and k grow at most at a polynomial rate”

the (forty-)seven samurai (赤穂浪士)

During my vacations in Japan, I read the massive (1096p) book by Osaragi Jiro on the  Akō incident, with occidental title the 47 rōnins. Which I had bought in Paris before leaving. This is a romancized version of an historical event that took part in 1701 in the Genroku era. Where 47 rōnin (leaderless samurai) avenged the death of their former master Takumi no Kami ordered by the current Shôgun after Takumi no Kami stuck an official Kira Yoshinaka who had insulted him publicly. And were also condemned to commit sepuku. (As I suspected while reading the book, it was initially published in 1927-1928 as a series, which explains for its length.) This is a very famous story in the Japanese culture and there exist many versions in novels, plays, movies, one featuring the fabulous Toshirō Mifune (and another one commissioned by the Japanese military during WWII), and prints, including some by Hiroshige and Hokusai. Not only it is a great read, with a very classical style (in the French translation) and enough plots and subplots to deserve the 1096 pages!, but it also reflects [much more than in Yoshikawa’s Musashi] upon the transition from feudal to modern Japan, with the samurai class slowly dwindling out for the merchant class and a central administration. Which the central characters in the book mostly bemoan and hence praise the chivaleresque action of the 47 rōnins, fighting against superior forces, except for some who reflect on the uselessness of a warrior class (and go as far as assassinating random samurai). Interestingly, the conclusion of the real story, namely the suicide of the 47 rōnins, is not included in the book. Which links the head of the revenge to famous characters of the time, including a scholar anticipating the Meiji rise of Japanese nationalism by removing cultural and religious links to China, including the preeminence of Shintoism over Buddhism. The book is also the attention paid to seasons and gardens throughout, which is a feature I found in many Japanese books. Somewhat unsurprisingly, the story involves very few female central characters and, except for one spy, very passive roles.