off to Edinburgh [and SMC 2024]

Today I am off to Edinburgh for the SMC 2024 workshop run by the ICMS. Looking forward meeting with long time friends and new ones, and learning about novel directions in the field. And returning to Edinburgh I last visited in 2019 for the opening of the Bayes Centre. Hoping to enjoy the nearby Arthur’s Seat volcano and maybe farther away Munroes, depending on the program, train schedules, and…weather forecasts!

maths as catchy background [and no further future for humanity]

connection between tempering & entropic mirror descent

The next One World ABC webinar is this  Thursday,  the 2nd May, at 9am UK time, with Francesca Crucinio (King’s College London, formerly CREST and even more formerly Warwick) presenting

“A connection between Tempering and Entropic Mirror Descent”.

a joint work with Nicolas Chopin and Anna Korba (both from CREST) whose abstract follows:

This work explores the connections between tempering (for Sequential Monte Carlo; SMC) and entropic mirror descent to sample from a target probability distribution whose unnormalized density is known. We establish that tempering SMC corresponds to entropic mirror descent applied to the reverse Kullback-Leibler (KL) divergence and obtain convergence rates for the tempering iterates. Our result motivates the tempering iterates from an optimization point of view, showing that tempering can be seen as a descent scheme of the KL divergence with respect to the Fisher-Rao geometry, in contrast to Langevin dynamics that perform descent of the KL with respect to the Wasserstein-2 geometry. We exploit the connection between tempering and mirror descent iterates to justify common practices in SMC and derive adaptive tempering rules that improve over other alternative benchmarks in the literature.

travel woes

On my last trip to Warwick, the local (RER) train I boarded broke on its way to the CDG airport, after hitting something in a tunnel just three stops short of the airport, with so much delay and misleading communication that I missed my flight. While a minor issue for me, since I managed to work (and blog) in an airport lounge for most of the day—where I crossed path with Numerobis—, while waiting for the only flight to B’ham, this made me to reflect anew on the very poor state of the transportation network in Paris and its suburbs, with such incidents (power failures, broken rails, vetust engines, stolen cables, idiots on the tracks, &tc., even without mentioning the strikes) more and more the norm. And to wonder at how the ancient and bursting network is going to cope with the incoming flow of visitors attending the Olympics this summer… Actually, when compared with the other cities with a fairly reasonably efficient airport connection I experienced, it remains a mystery to me why the Greater Paris conurbation—whose president, Valérie Pécresse, was apparently deemed the main culprit for our train break by an incensed fellow passenger that morning!—has kept for years postponing the construction of a dedicated rail line between the airport and central Paris, as the unpredictable and uncomfortable suburban train is not delivering the intended message to Paris visitors and their still-growing contribution to the French GNP. But with the growing public opposition to any new infrastructure, incl. trains, this is unlikely to happen!

d≥3 strikes again

Yesterday, Bálint Tóth (University of Bristol and Alfréd Rényi Institute of Mathematics) came to Paris Dauphine for a seminar on the Botlzmann-Grad limit and the existence of a central (double) limit theory. Which was somewhat related with the above video of an earlier seminar, albeit without the first part on the historical roots of the problem. This was a brilliant talk as quite accessible to the entirety of the lab, while providing detailed entries on the mechanism leading to the CLT, in particular the substitution of the physical process by a Markovian(ised) process that stayed closed enough to the original for long enough, a sort of (anti-)coupling idea I had never met before. The other (personally) striking feature of the seminar was the occurrence of the boundary d=3 on the dimension of the process, The same boundary as in the Stein phenomenon (and the difference from recurrent to transient in random walks). But I could not see a clear connection with the present challenge.