Archive for machine learning

Bayesian gan [gan style]

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , , , , , , on June 26, 2018 by xi'an

In their paper Bayesian GANS, arXived a year ago, Saatchi and Wilson consider a Bayesian version of generative adversarial networks, putting priors on both the model and the discriminator parameters. While the prospect seems somewhat remote from genuine statistical inference, if the following statement is representative

“GANs transform white noise through a deep neural network to generate candidate samples from a data distribution. A discriminator learns, in a supervised manner, how to tune its parameters so as to correctly classify whether a given sample has come from the generator or the true data distribution. Meanwhile, the generator updates its parameters so as to fool the discriminator. As long as the generator has sufficient capacity, it can approximate the cdf inverse-cdf composition required to sample from a data distribution of interest.”

I figure the concept can also apply to a standard statistical model, where x=G(z,θ) rephrases the distributional assumption x~F(x;θ) via a white noise z. This makes resorting to a prior distribution on θ more relevant in the sense of using potential prior information on θ (although the successes of probabilistic numerics show formal priors can be used on purely numerical ground).

The “posterior distribution” that is central to the notion of Bayesian GANs is however unorthodox in that the distribution is associated with the following conditional posteriors

where D(x,θ) is the “discriminator”, that is, in GAN lingo, the probability to be allocated to the “true” data generating mechanism rather than to the one associated with G(·,θ). The generative conditional posterior (1) then aims at fooling the discriminator, i.e. favours generative parameter values that raise the probability of wrong allocation of the pseudo-data. The discriminative conditional posterior (2) is a standard Bayesian posterior based on the original sample and the generated sample. The authors then iteratively sample from these posteriors, effectively implementing a two-stage Gibbs sampler.

“By iteratively sampling from (1) and (2) at every step of an epoch one can, in the limit, obtain samples from the approximate posteriors over [both sets of parameters].”

What worries me about this approach is that  just cannot work, in the sense that (1) and (2) cannot be compatible conditional (posterior) distributions. There is no joint distribution for which (1) and (2) would be the conditionals, since the pseudo-data appears in D for (1) and (1-D) in (2). This means that the convergence of a Gibbs sampler is at best to a stationary σ-finite measure. And hence that the meaning of the chain is delicate to ascertain… Am I missing any fundamental point?! [I checked the reviews on NIPS webpage and could not spot this issue being raised.]

rage against the [Nature] Machine [Intelligence]

Posted in Books, Statistics, University life with tags , , , , , , , , , on May 15, 2018 by xi'an

Yesterday evening, my friend and colleague Pierre Alquier (CREST-ENSAE) got interviewed (for a few seconds on-line!, around minute 06) by the French national radio, France Culture, about the recent call to boycott the incoming Nature Machine Intelligence electronic journal. Call to the machine learning community, based on the lack of paying journals among the major machine learnings journals, like JMLR. Meaning that related conferences like AISTATS and NIPS also get their accepted papers available on-line for free. As noted in the call

“Machine learning has been at the forefront of the movement for free and open access to research. For example, in 2001 the Editorial Board of the Machine Learning Journal resigned en masse to form a new zero-cost open access journal, the Journal of Machine Learning Research (JMLR).”

Imperial postdoc in Bayesian nonparametrics

Posted in pictures, R with tags , , , , , , , , on April 27, 2018 by xi'an

Here is another announcement for a post-doctoral position in London (UK) to work with Sarah Filippi. In the Department of Mathematics at Imperial College London. (More details on the site or in this document. Hopefully, the salary is sufficient for staying in London, if not in South Kensington!)

The post holder will work on developing a novel Bayesian Non-Parametric Test for Conditional Independence. This is at the core of modern causal discovery, itself of paramount importance throughout the sciences and in Machine Learning. As part of this project, the post holder will derive a Bayesian non-parametric testing procedure for conditional independence, scalable to high-dimensional conditioning variable. To ensure maximum impact and allow experimenters in different fields to easily apply this new methodology, the post holder will then create an open-source software package available on the R statistical programming platform. Doing so, the post holder will investigate applying this approach to real-world data from our established partners who have a track record of informing national and international bodies such as Public Health England and the World Health Organisation.

a postdoc with Christian Robert

Posted in Statistics with tags , , , , , , on April 12, 2018 by xi'an

[Here is another call for a postdoctoral position in Lyon, under the supervision of my homonym Christian Robert:]

Post-Doctoral Position in Data Science and Machine Learning

Chair Data Analytics and Models for Insurance – 20182020

DAMI is a research chair funded by BNP Paribas Cardif, and is interested in problems related to Data Science and Models for Insurance.

Description

A post-doctoral fellowship in the areas of data science and machine learning is available at the DAMI research chair at the Claude Bernard Lyon 1 University. The post-doctoral fellow, in collaboration with the industry partner, will conduct research of advanced analytics and machine learning algorithms for actuarial sciences and insurance, and in particular, for improving risk-based pricing, and for developing predictive analytics.

The position is for one year (possibly two years), starting in September/October 2018.

Required Professional Expertise

–        A recent PhD (received within the past 5 years) in Computer Science, Computer Engineering, Applied Statistics and Mathematics, or related fields.

–        Excellent research capabilities and competitive development skills

–        Strong knowledge/expertise in machine learning and data analytics including data pre-processing, model building, and model evaluation

–        Experience with Python and/or R

Interested candidates are invited to submit their CV, list of publications, and contact information of two references to Christian ROBERT at univ-lyon1.fr.

gender gaps

Posted in Statistics, University life with tags , , , , , , , , , , on March 31, 2018 by xi'an

Two of my colleagues [and co-authors] at Dauphine, Elyès Jouini and Clotilde Napp, published a paper in Science last week (and an associated tribune in Le Monde which I spotted first) about explaining differences in national gender inequalities in maths (as measured by PISA) in terms of the degree of overall inequality in the respective countries. Gaps in the highest maths performer sex ratio. While I have no qualm about the dependency or the overall statistical cum machine learning analysis (supported by our common co-author Jean-Michel Marin), and while I obviously know nothing about the topic!, I leisurely wonder at the cultural factor (which may also partly explain for the degree of inequality) when considering that the countries at the bottom of the above graphs are rather religious (and mostly catholic). I also find it most intriguing that the gender gap is consistently reversed when considering higher performer sex ratio for reading, because mastering the language should be a strong factor in power structures and hence differences therein should also lead to inequalities…

1500 nuances of gan [gan gan style]

Posted in Books, Statistics, University life with tags , , , , , , , , , , , on February 16, 2018 by xi'an

I recently realised that there is a currently very popular trend in machine learning called GAN [for generative adversarial networks] that strongly connects with ABC, at least in that it relies mostly on the availability of a generative model, i.e., a probability model that can be generated as in x=G(ϵ;θ), to draw inference about θ [or predictions]. For instance, there was a GANs tutorial at NIPS 2016 by Ian Goodfellow and many talks on the topic at recent NIPS, the 1500 in the title referring to the citations of the GAN paper by Goodfellow et al. (2014). (The name adversarial comes from opposing true model to generative model in the inference. )

If you remember Jeffreys‘s famous pique about classical tests as being based on improbable events that did not happen, GAN, like ABC,  is sort of the opposite in that it generates events until the one that was observed happens. More precisely, by generating pseudo-samples and switching parameters θ until these samples get as confused as possible between the data generating (“true”) distribution and the generative one. (In its original incarnation, GAN is indeed an optimisation scheme in θ.) A basic presentation of GAN is that it constructs a function D(x,ϕ) that represents the probability that x came from the true model p versus the generative model, ϕ being the parameter of a neural network trained to this effect, aimed at minimising in ϕ a two-term objective function

E[log D(x,ϕ)]+E[log(1D(G(ϵ;θ),ϕ))]

where the first expectation is taken under the true model and the second one under the generative model.

“The discriminator tries to best distinguish samples away from the generator. The generator tries to produce samples that are indistinguishable by the discriminator.” Edward

One ABC perception of this technique is that the confusion rate

E[log(1D(G(ϵ;θ),ϕ))]

is a form of distance between the data and the generative model. Which expectation can be approximated by repeated simulations from this generative model. Which suggests an extension from the optimisation approach to a ABCyesian version by selecting the smallest distances across a range of θ‘s simulated from the prior.

This notion relates to solution using classification tools as density ratio estimation, connecting for instance to Gutmann and Hyvärinen (2012). And ultimately with Geyer’s 1992 normalising constant estimator.

Another link between ABC and networks also came out during that trip. Proposed by Bishop (1994), mixture density networks (MDN) are mixture representations of the posterior [with component parameters functions of the data] trained on the prior predictive through a neural network. These MDNs can be trained on the ABC learning table [based on a specific if redundant choice of summary statistics] and used as substitutes to the posterior distribution, which brings an interesting alternative to Simon Wood’s synthetic likelihood. In a paper I missed Papamakarios and Murray suggest replacing regular ABC with this version…

machine learning methods are useful for ABC [or my first PCI Evol Biol!]

Posted in Books, Kids, pictures, Statistics, University life with tags , , , , , , on November 23, 2017 by xi'an

While I am still working on setting a PCI [peer community in] Comput Stats, having secure sponsorship of some societies (ASA, KSS, RSS, SFdS, and hopefully ISBA), my coauthors Jean-Michel Marin and Louis Raynal submitted our paper ABC random forests for Bayesian parameter inference to PCI Evol Biol. And after a few months of review, including a revision accounting for the reviewers’ requests, our paper stood the test and the recommendation by Michael Blum and Dennis Prangle got published there. Great news, and hopefully helpful for our submission within the coming days!