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

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.

local mayhem, again and again and again…

The public transports in France and in particular in Paris have now been on strike for three weeks. In connection with a planned reform of the retirement conditions of workers with special status, like those in the train and metro companies, who can retire earlier than the legal age (62). As usual with social unrest in France, other categories joined the strike and the protest, including teachers and health service public workers, as well as police officers, fire-fighters and opera dancers, and even some students. Below are some figures from the OECD about average retirement conditions in nearby EU countries that show that these conditions are apparently better in France. (With the usual provision that these figures have been correctly reported.) In particular, the life expectancy at the start of retirement is the highest for both men and women. Coincidence (or not), my UCU affiliated colleagues in Warwick were also on strike a few weeks ago about their pensions…

Travelling through and around Paris by bike, I have not been directly affected by the strikes (as heavy traffic makes biking easier!), except for the morning of last week when I was teaching at ENSAE, when I blew up a tyre midway there and had to hop to the nearest train station to board the last train of the morning, arriving (only) 10mn late. Going back home was only feasible by taxi, which happened to be large enough to take my bicycle as well… Travelling to and from the airport for Vancouver and Birmingham was equally impossible by public transportation, meaning spending fair amounts of time in and money on taxis! And listening to taxi-drivers’ opinions or musical tastes. Nothing to moan about when considering the five to six hours spent by some friends of mine to get to work and back.

clothespin and bike woes

The past week at Warwick was a pleasant (pre)start of semester (with hardly any student around), pleasant except from a biking perspective, as I was essentially three days without a bike, from having to recover it at a friend’s at the end of my first morning run, where it had been kindly stored over the summer break, to facing once again a flat tyre, to running after a safe and dry storage location as my Department is about to move to a new and smaller building. Where bikes are not allowed indoor, apparently. (Sometimes, it feels like the University of Carwick!) And the new bike hub at Coventry train station had no free fob. Nothing major as I am living once again in the maths houses, quite a quick walk to the Department, but mildly annoying and disrupting my routine. As it happened, the flat tyre was the result of my riding over the spring of a clothes peg (or clothespin, as in the above sculpture in Phillie), lying the wrong way on the ground, which acted as a perfect caltrop! (My friend and bike wizzard Nick fixed the tyre and changed the tube as soon as I reached the  Department with the wheel, but annoying it was.)