horsy new year!
Posted in pictures, Travel with tags ⾺, Cambodia, China, Chinese zodiac, Fire Horse, horse, Japan, Lunar New Year, lunisolar calendar, North Korea, Singapore, South Korea, Year of the Horse on February 17, 2026 by xi'anmostly Monte Carlo [20/02]
Posted in Statistics with tags #ERCSyG, École Polytechnique, ERC, federated learning, machine learning model, MCMC, Ocean, Palaiseau, Paris, PariSanté campus, privacy, Scaffold algorithm, seminar, stochastic gradient on February 16, 2026 by xi'anA new episode of our mostly Monte Carlo seminar, very soon coming near you (if in Paris):
On Friday 20/02/26, from 3-5pm at PariSanté Campus
Paul Mangold (École Polytechnique, Palaiseau)
Convergence and Linear Speed-Up in Stochastic Federated Learning
In federated learning, multiple users collaboratively train a machine learning model without sharing local data. To reduce communication, users perform multiple local stochastic gradient steps that are then aggregated by a central server. However, due to data heterogeneity, local training introduces bias. In this talk, I will present a novel interpretation of the Federated Averaging algorithm, establishing its convergence to a stationary distribution. By analyzing this distribution, we show that the bias consists of two components: one due to heterogeneity and another due to gradient stochasticity. I will then extend this analysis to the Scaffold algorithm, demonstrating that it effectively mitigates heterogeneity bias but not stochasticity bias. Finally, we show that both algorithms achieve linear speed-up in the number of agents, a key property in federated stochastic optimization.
Alain Durmus (École Polytechnique, Palaiseau)
TBA
X de Sceaux turns 50
Posted in Running, pictures with tags 5K, Cross de Sceaux, Parc de Sceaux, Paris suburbs, poster, training on February 15, 2026 by xi'anfirst man below the 6:00:00 barrier on the 5000m?!
Posted in Kids, Mountains, Running, Statistics, University life with tags Isaac Newton Institute, Jakob Ingebrigtsen, Milano, Norway, Salt Lake City, speed skating, University of Cambridge, Winter Olympics, World record on February 14, 2026 by xi'anWhen I spotted this arXiv posting by Nils Hjort, Six-Minute Man Sander Eitrem 5:58.52 – first man below the 6:00.00 barrier, discussing Sander Eitrem‘s massive gain from the month-old previous record by Frenchman Timothy Loubineaud in Salt Lake City, just above 6’00”.. I was incredulous, not because I am knowledgeable in speed skating records, but because I was thinking of running… Where the World record is twice as large (12:35.36). Beyond my own personal interests, which drove the way I read this title, I was also stuck back in the past, with my last conversation with Nils being about long-distance running and record prediction, which happened quite a while ago when visiting the Isaac Newton Institute in Cambridge! (Nils’ note holds a reference to another famous Norwegian [runner], Jakob Ingebrigtsens.) Sander Eitrem also became the Olympic champion in Milano, breaking the Olympic record as well.
When Is Generalized Bayes Bayesian?
Posted in Books, Statistics, University life with tags ABC, Bayes factors, Bayesian model choice, coherence, decision theory, generalised Bayesian inference, loss functions, marginal likelihood, normalising constant on February 13, 2026 by xi'anI spotted this title in the new arXiv postings on Monday. When Is Generalized Bayes Bayesian? A Decision-Theoretic Characterization of Loss-Based Updating by Kenichiro McAlinn & Kōsaku Takanashi is discussing decision-theoretic consequences of generalized Bayes approaches based on losses and show that decisions based on a loss-based posterior coincides with those of ordinary Bayes if and only if the loss is essentially a negative log-likelihood (leading to a belief posterior). This is not very surprising in that, otherwise, there is no Bayesian update delivering the generalised Bayes pseudo-posteriors (which can be traced back to a 2007 result of Catoni). The authors also demonstrate that generalized marginal likelihoods are not delivering evidence for decision posteriors, and thus that Bayes factors are not well-defined in this context, which reminds me of our warning for ABC model choice. However, the reason here is much more mundane, as it is due to the decision posterior failing to identify the normalising constant Z(x). Outside belief posteriors. The paper concludes with a coherence book, which is a table reproduced above.
Xi'an's Og