## MCMC, variational inference, invertible flows… bridging the gap?

Posted in Books, Mountains, Running, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , , on October 2, 2020 by xi'an

Two weeks ago, my friend [see here when climbing Pic du Midi d’Ossau in 2005!] and coauthor Éric Moulines gave a very interesting on-line talk entitled MCMC, Variational Inference, Invertible Flows… Bridging the gap?, which was merging MCMC, variational autoencoders, and variational inference. I paid close attention as I plan to teach an advanced course on acronyms next semester in Warwick. (By acronyms, I mean ABC+GAN+VAE!)

The notion in this work is that variational autoencoders are based on over-simple mean-field variational distributions, that usually produce a poor approximation of the target distribution. Éric and his coauthors propose to introduce a Metropolis step in the VAE. This leads to a more general notion of Markov transitions and a global balance condition. Hamiltonian Monte Carlo can be used as well and it improves the latent distribution approximation, namely the encoder, which is surprising to me. The steps of the Markov kernel produce a manageable transform of the initial mean field approximation, a random version of the original VAE. Manageable provided not too many MCMC steps are implemented. (Now, the flow of slides was much too fast for me to get a proper understanding of the implementation of the method, of the degree of its calibration, and of the computing cost. I need to read the associated papers.)

Once the talk was over, I went back to changing tires and tubes, as two bikes of mine had flat tires, the latest being a spectacular explosion (!) that seemingly went through the tire (although I believe the opposite happened, namely the tire got slashed and induced the tube to blow out very quickly). Blame the numerous bits of broken glass over bike paths.

## structure and uncertainty, Bristol, Sept. 26

Posted in Books, pictures, R, Running, Statistics, Travel, University life, Wines with tags , , , , , , , , , , , , , , on September 27, 2012 by xi'an

Another day full of interesting and challenging—in the sense they generated new questions for me—talks at the SuSTain workshop. After another (dry and fast) run around the Downs; Leo Held started the talks with one of my favourite topics, namely the theory of g-priors in generalized linear models. He did bring a new perspective on the subject, introducing the notion of a testing Bayes factor based on the residual statistic produced by a classical (maximum likelihood) analysis, connected with earlier works of Vale Johnson. While I did not truly get the motivation for switching from the original data to this less informative quantity, I find this perspective opening new questions for dealing with settings where the true data is replaced with one or several classical statistics. With possible strong connections to ABC, of course. Incidentally, Leo managed to produce a napkin with Peter Green’s intro to MCMC dating back from their first meeting in 1994: a feat I certainly could not reproduce (as I also met both Peter and Leo for the first time in 1994, at CIRM)… Then Richard Everit presented his recent JCGS paper on Bayesian inference on latent Markov random fields, centred on the issue that simulating the latent MRF involves an MCMC step that is not exact (as in our earlier ABC paper for Ising models with Aude Grelaud). I already discussed this paper in an earlier blog and the only additional question that comes to my mind is whether or not a comparison with the auxiliary variable approach of Møller et al. (2006) would make sense.

In the intermission, I had a great conversation with Oliver Ratman on his talk of yesterday on the surprising feature that some models produce as “data” some sample from a pseudo-posterior.. Opening once again new vistas! The following talks were more on the mathematical side, with James Cussens focussing on the use of integer programming for Bayesian variable selections, then Éric Moulines presenting a recent work with a PhD student of his on PAC-Bayesian bounds and the superiority of combining experts. Including a CRAN package. Éric concluded his talk with the funny occurence of Peter’s photograph on Éric’s Microsoft Research Profile own page, due to Éric posting our joint photograph at the top of Pic du Midi d’Ossau in 2005… (He concluded with a picture of the mountain that was the exact symmetry of mine yesterday!)

The afternoon was equally superb with Gareth Roberts covering fifteen years of scaling MCMC algorithms, from the mythical 0.234 figure to the optimal temperature decrease in simulated annealing, John Kent playing the outlier with an EM algorithm—however including a formal prior distribution and raising the challenge as to why Bayesians never had to constrain the posterior expectation, which prompted me to infer that (a) the prior distribution should include all constraints and (b) the posterior expectation was not the “right” tool in non-convex parameters spaces—. Natalia Bochkina presented a recent work, joint with Peter Green, on connecting image analysis with Bayesian asymptotics, reminding me of my early attempts at reading Ibragimov and Has’minskii in the 1990’s. Then a second work with Vladimir Spoikoini on Bayesian asymptotics with misspecified models, introducing a new notion of effective dimension. The last talk of the day was by Nils Hjort about his coming book on “Credibility, confidence and likelihood“—not yet advertised by CUP—which sounds like an attempt at resuscitating Fisher by deriving distributions in the parameter space from frequentist confidence intervals. I already discussed this notion in an earlier blog, so I am fairly skeptical about it, but the talk was representative of Nils’ highly entertaining and though-provoking style! Esp. as he sprinkled the talk with examples where MLE (and some default Bayes estimators) did not work. And reanalysed one of Chris Sims‘ example presented during his Nobel Prize talk…

## CNRS awards

Posted in Mountains, Statistics, University life with tags , , , on September 11, 2010 by xi'an

﻿Congratulations to my friend Éric Moulines who just received the Silver medal from the national scientific research centre CNRS for the Institut des sciences de l’ingénierie et des systèmes (INSIS). Besides conducting top edge research in a wide spectrum of topics in statistics, probability and signal processing, including his influential book on Hidden Markov Models with Olivier Cappé and Tobias Rydén, (a paperback version is now available!) he has been intensely involved in driving national research policy for many years. This (prestigious) reward is thus well-deserved! (Congratulations to Alice Guionnet, too, for her Silver﻿ medal for the Institut national des sciences mathématiques et de leurs interactions (INSMI)!)