Daniel Lacker (Columbia U) gave a talk at the probability seminar of Paris Dauphine this week which I happened to attend by happenstance, on a recent paper, Projected Langevin dynamics and a gradient flow for entropic optimal transport, written with Giovanni Conforti and, Soumik Pal. The talk was quite progressive and I hence could follow most of it. The core idea is in studying Langevin-type diffusion dynamics that sample from an entropy-regularized optimal transport, i.e. looking for an optimal distribution (in the sense of achieving entropy minimisation problem within a Wasserstein space, with regularisation) obtained via a gradient flow equation (as eg in variational inference) that couples two SDEs that are recentred by conditional expectation terms. Expectations in the equations are estimated by a Nadaraya-Watson estimate in optimal transport problem (reminding me of SMC), with no theoretical derivation of an optimal bandwidth, and they achieve quantitive bounds on the convergence, namely for exponential convergence, energy decay and new logarithmic Sobolev inequalities. From the talk and a quick glance at the paper, it is unclear to me there are direct algorithmic consequences, since the SDEs need be discretised, while the expectation approximations are costly, being repeated at each iteration of the discretised SDE.
Archive for NYC
gradient flow for projected Langevin dynamics
Posted in Books, Statistics, University life with tags Columbia University, coupling, gradient flow, Langevin diffusion, metro station, New York city, New York metro, NYC, optimal transport, SDEs, seminar, SMC, unadjusted Langevin algorithm, Université Paris Dauphine, variational inference on April 7, 2025 by xi'anfat tire [jatp]
Posted in Statistics with tags amber beer, Belgian beer, Colorado, delivery vans, Fat Tire, jatp, microbrewery, New Belgium, New York city, NYC, street view on January 20, 2023 by xi'an
leaves & masks [cover]
Posted in Books, Kids, pictures, Travel with tags cover, dead leaves, face mask, Fall, Fall sweep, New York, NYC, The New Yorker on December 13, 2022 by xi'an
New York City trip
Posted in pictures, Running, Travel with tags Donald Trump, electric bike, Flatiron building, Hudson river, Manhattan, matcha tea, NYC, Queensboro Bridge, Roosevelt Island, scooter, UN building on December 8, 2022 by xi'an
While the Sampling, Transport, Diffusion workshop at the Flatiron Institute kept me happily busy, and while I did not stay any longer, spending a few days in New York City was a treat and I took advantage of my early hours to go running along the river sides, first south of the Flatiron building, then north to the Queensboro Bridge and over it, and last north along the Hudson River. The East River side is much less convenient for running as the path is repeatedly blocked by construction / storage sites and Xing the Queensboro Bridge gave a great view of Manhattan, albeit at the risk of being hit by a bike / scooter / moppet, as the path was shared with [an endless flow of] speeding electric bicycles. As I had never been to this part of the city, I was unaware of the cable car / gondola to Roosevelt Island (surprisingly called tram), which I would have taken given an extra day. Came by uponchance over a Trump Tower, which I ignored was so inappropriately close to the UN Headquarters! Running on the uninterrupted Hudson River trail was much nicer (and busier) despite the freezing wind that day.
For once (!) I stayed in an hotel, reserved by the Flatiron, and for the three nights I was there it was most tolerable, except for the usual background noise found in hotels, both from heating fans and patrons discussing in the corridors after hours. But the staff was helpful to the point of purchasing a kettle for my early morning tea. As the workshop provided an enormous amount of food at all times (and there was a true matcha tea provider around the corner!), it did not matter in the least.
semi de Boulogne [1:29:33, 1243/8134, M5M 6/206, 8⁰+rain]
Posted in pictures, Running with tags Argentan half-marathon, bois de Boulogne, half-marathon, NYC, race, Seine, semi-marathon, training on December 1, 2022 by xi'an
First time back to the Boulogne half-marathon since 2008! With clearly a much degraded time, albeit better than the previous race in Argentan. The route has changed, with a longer part in the Bois de Boulogne, sharing the road with the hordes of Sunday cyclists that pile up loops at high speed. But still a very fast one (with a record at 1:00:11 in 2013). The number has alas considerably increased since my last visit, with 9800 registrations, which makes running in the first kilometers a challenge with hidden sidewalks, parked cars and moppets, &tc. And a permanent difficulty in passing other runners, especially on a rainy day. (The only good side was being protected from headwinds.)
Once on the road by the Seine River, I managed to pass a large group conglomerated around a (1:30) pace setter and moved at my own speed, till Km16 when I started to tire and realise I was alas missing some volume of training (as running in NYC was only a slow-paced jogging). Hence wasting about a minute on the final four kilometers… (Jogging back after the race to my car, parked 3km away, proved rather painful!) As the 1:30 time was my upper limit, I am still reasonably fine with the result (and the 4’14” per km) and hope I can train harder for the next race.
Xi'an's Og 