deep learning in Toulouse [post-doc position]

An opening for an ERC post-doc position on Bayesian deep learning with Cédric Févotte in Toulouse.

tenure track position in Clermont, Auvergne

My friend Arnaud Guillin pointed out this opening of a tenure-track professor position at his University of Clermont Auvergne, in Central France. With specialty in statistics and machine-learning, especially deep learning. The deadline for applications is 12 May 2019. (Tenure-track positions are quite rare in French universities and this offer includes a limited teaching load over three years, potential tenure and titularisation at the end of a five year period, and is restricted to candidates who did their PhD or their postdoc abroad.)

deep and embarrassingly parallel MCMC

Diego Mesquita, Paul Blomstedt, and Samuel Kaski (from Helsinki, like the above picture) just arXived a paper on embarrassingly parallel MCMC. Following a series of papers discussed on this ‘og in the past. They use a deep learning approach of Dinh et al. (2017) to the computation of the probability density of a convoluted and non-volume-preserving transform of a given random variable to turn multiple samples from sub-posteriors [corresponding to the k k-th roots of the true posterior] into a sample from the true posterior. If I understand correctly the argument [on page 4], the deep neural network provides a density estimate that apparently does better than traditional non-parametric density estimates. Maybe by being more efficient than a Parzen-Rosenblat estimator which is of order the number of simulations… For any value of θ, the estimate of the true target is the product of these estimates and for a value of θ simulated from one of the subposteriors an importance weight naturally ensues. However, for a one-dimensional transform of θ, h(θ), I would prefer estimating first the density of h(θ) for each sample and then construct an importance weight. If only to avoid the curse of dimension.

On various benchmarks, like the banana-shaped 2D target above, the proposed method (NAP) does better. Even in relatively high dimensions. Given that the overall computing times are not produced, with only the calibration that the same number of subsamples were produced for all methods, it would be interesting to test the same performances on even higher dimensions and larger population sizes.

ICM 2018

While I am not following the International Congress of Mathematicians which just started in Rio, and even less attending, I noticed an entry on their webpage on my friend and colleague Maria Esteban which I would have liked to repost verbatim but cannot figure how. (ICM 2018 also features a plenary lecture by Michael Jordan on gradient based optimisation [which was also Michael’s topic at ISBA 2018] and another one by Sanjeev Arora on the maths deep learning, two talks broadly related with statistics, which is presumably a première at this highly selective maths conference!)

JSM 2018 [#1]

As our direct flight from Paris landed in the morning in Vancouver,  we found ourselves in the unusual situation of a few hours to kill before accessing our rental and where else better than a general introduction to deep learning in the first round of sessions at JSM2018?! In my humble opinion, or maybe just because it was past midnight in Paris time!, the talk was pretty uninspiring in missing the natural question of the possible connections between the construction of a prediction function and statistics. Watching improving performances at classifying human faces does not tell much more than creating a massively non-linear function in high dimensions with nicely designed error penalties. Most of the talk droned about neural networks and their fitting by back-propagation and the variations on stochastic gradient descent. Not addressing much rather natural (?) questions about choice of functions at each level, of the number of levels, of the penalty term, or regulariser, and even less the reason why no sparsity is imposed on the structure, despite the humongous number of parameters involved. What came close [but not that close] to sparsity is the notion of dropout, which is a sort of purely automated culling of the nodes, and which was new to me. More like a sort of randomisation that turns the optimisation criterion in an average. Only at the end of the presentation more relevant questions emerged, presenting unsupervised learning as density estimation, the pivot being the generative features of (most) statistical models. And GANs of course. But nonetheless missing an explanation as to why models with massive numbers of parameters can be considered in this setting and not in standard statistics. (One slide about deterministic auto-encoders was somewhat puzzling in that it seemed to repeat the “fiducial mistake”.)

ISBA 18 tidbits

Among a continuous sequence of appealing sessions at this ISBA 2018 meeting [says a member of the scientific committee!], I happened to attend two talks [with a wee bit of overlap] by Sid Chib in two consecutive sessions, because his co-author Ana Simoni (CREST) was unfortunately sick. Their work was about models defined by a collection of moment conditions, as often happens in econometrics, developed in a recent JASA paper by Chib, Shin, and Simoni (2017). With an extension about moving to defining conditional expectations by use of a functional basis. The main approach relies on exponentially tilted empirical likelihoods, which reminded me of the empirical likelihood [BCel] implementation we ran with Kerrie Mengersen and Pierre Pudlo a few years ago. As a substitute to ABC. This problematic made me wonder on how much Bayesian the estimating equation concept is, as it should somewhat involve a nonparametric prior under the moment constraints.

Note that Sid’s [talks and] papers are disconnected from ABC, as everything comes in closed form, apart from the empirical likelihood derivation, as we actually found in our own work!, but this could become a substitute model for ABC uses. For instance, identifying the parameter θ of the model by identifying equations. Would that impose too much input from the modeller? I figure I came with this notion mostly because of the emphasis on proxy models the previous day at ABC in ‘burgh! Another connected item of interest in the work is the possibility of accounting for misspecification of these moment conditions by introducing a vector of errors with a spike & slab distribution, although I am not sure this is 100% necessary without getting further into the paper(s) [blame conference pressure on my time].

Another highlight was attending a fantastic poster session Monday night on computational methods except I would have needed four more hours to get through every and all posters. This new version of ISBA has split the posters between two sites (great) and themes (not so great!), while I would have preferred more sites covering all themes over all nights, to lower the noise (still bearable this year) and to increase the possibility to check all posters of interest in a particular theme…

Mentioning as well a great talk by Dan Roy about assessing deep learning performances by what he calls non-vacuous error bounds. Namely, through PAC-Bayesian bounds. One major comment of his was about deep learning models being much more non-parametric (number of parameters rising with number of observations) than parametric models, meaning that generative adversarial constructs as the one I discussed a few days ago may face a fundamental difficulty as models are taken at face value there.

On closed-form solutions, a closed-form Bayes factor for component selection in mixture models by Fũqene, Steel and Rossell that resemble the Savage-Dickey version, without the measure theoretic difficulties. But with non-local priors. And closed-form conjugate priors for the probit regression model, using unified skew-normal priors, as exhibited by Daniele Durante. Which are product of Normal cdfs and pdfs, and which allow for closed form marginal likelihoods and marginal posteriors as well. (The approach is not exactly conjugate as the prior and the posterior are not in the same family.)

And on the final session I attended, there were two talks on scalable MCMC, one on coresets, which will require some time and effort to assimilate, by Trevor Campbell and Tamara Broderick, and another one using Poisson subsampling. By Matias Quiroz and co-authors. Which did not completely convinced me (but this was the end of a long day…)

All in all, this has been a great edition of the ISBA meetings, if quite intense due to a non-stop schedule, with a very efficient organisation that made parallel sessions manageable and poster sessions back to a reasonable scale [although I did not once manage to cross the street to the other session]. Being in unreasonably sunny Edinburgh helped a lot obviously! I am a wee bit disappointed that no one else follows my call to wear a kilt, but I had low expectations to start with… And too bad I missed the Ironman 70.3 Edinburgh by one day!

Bayesian program synthesis

Last week, I—along with Jean-Michel Marin—got an email from a journalist working for Science & Vie, a French sciences journal that published a few years ago a special issue on Bayes’ theorem. (With the insane title of “the formula that deciphers the World!”) The reason for this call was the preparation of a paper on Gamalon, a new AI company that relies on (Bayesian) probabilistic programming to devise predictive tools. And spent an hour skyping with him about Bayesian inference, probabilistic programming and machine-learning, at the general level since we had not heard previously of this company or of its central tool.

“the Gamalon BPS system learns from only a few examples, not millions. It can learn using a tablet processor, not hundreds of servers. It learns right away while we play with it, not over weeks or months. And it learns from just one person, not from thousands.”

Gamalon claims to do much better than deep learning at those tasks. Not that I have reasons to doubt that claim, quite the opposite, an obvious reason being that incorporating rules and probabilistic models in the predictor is going to help if these rule and models are even moderately realistic, another major one being that handling uncertainty and learning by Bayesian tools is usually a good idea (!), and yet another significant one being that David Blei is a member of their advisory committee. But it is hard to get a feeling for such claims when the only element in the open is the use of probabilistic programming, which is an advanced and efficient manner of conducting model building and updating and handling (posterior) distributions as objects, but which does not enjoy higher predictives abilities by default. Unless I live with a restricted definition of what probabilistic programming stands for! In any case, the video provided by Gamalon and the presentation given by its CEO do not help in my understanding of the principles behind this massive gain in efficiency. Which makes sense given that the company would not want to give up their edge on the competition.

Incidentally, the video in this presentation comparing the predictive abilities of the four major astronomical explanations of the solar system is great. If not particularly connected with the difference between deep learning and Bayesian probabilistic programming.