Arnaud Guillin and Manon Michel from the Université Clermont-Auvergne are currently looking for PhD candidates interested in the mathematical analysis of neural networks via the tool of mean-field analysis. With full funding available. Candidates can contact Arnaud Guillin at uca.fr.

## Archive for the Mountains Category

## mathematical understanding of neural networks through mean-field analysis [PhD studenship]

Posted in Kids, Mountains, pictures, Running, Statistics, Travel, University life, Wines with tags ANR, Auvergne, Clermont-Ferrand, mean field analysis, neural network, PhD fellowship on June 26, 2020 by xi'an## non-reversible guided Metropolis–Hastings

Posted in Mountains, pictures, Statistics, Travel with tags arXiv, compacity, group action, Haar measure, Hamiltonian Monte Carlo, Japan, Kii peninsula, Markov chain, Metropolis-Hastings algorithm, Mount Koya, non-reversible diffusion, non-reversible MCMC, Osaka on June 4, 2020 by xi'an**K**engo Kamatani and Xiaolin Song, whom I visited in Osaka last summer in what seems like another reality!, just arXived another paper on a non-reversible Metropolis version. That exploits a group action and the associated Haar measure.

Following a proposal of Gustafson (1998), a ∆-guided Metropolis–Hastings kernel is based on a statistic ∆ that is totally ordered and determine the acceptance of a proposed value y~Q(x,.) by adding a direction (-,+) to the state space and moving from x if ∆x≤∆y in the positive direction and if ∆y≤∆x in the negative direction [with the standard Metropolis–Hastings acceptance probability]. The sign of the direction switches in case of a rejection. And the statistic ∆ is such that the proposal kernel Q(x,.) is unbiased, i.e., agnostic to the sign, i.e., it gives the same probability to ∆x≤∆y and ∆y≤∆x. This modification reduces the asymptotic variance compared with the original Metropolis–Hastings kernel.

To construct a random walk proposal that is unbiased, the authors assume that the ∆ transform takes values in a topological group, G, with Q further being invariant under the group actions. This can be constructed from a standard proposal by averaging the transforms of Q under all elements of the group over the associated right Haar measure. (Which I thought implied that the group is compact, except I forgot to account for the data update into a posterior..!) The worked-out example is based on a multivariate autoregressive kernel with ∆x being a rescaled non-central chi-squared variate. In dimension 24. The results show a clear improvement in effective sample size per second evaluation over off-the-shelf random walk and Hamiltonian Monte Carlo versions.

Seeing the Haar measure appearing in the setting of Markov chain Monte Carlo is fun!, as my last brush with it was not algorithmic. I would think the proposal only applies to settings where the components of the simulated vector are somewhat homogeneous in that the determinationthe determination of both the group action and a guiding statistic seem harder in cases where these components take different meaning (or live in a weird topology). I also lazily wonder if selecting the guiding statistic as a gradient of the log-target would have any interest.

## first 8000

Posted in Mountains with tags 8000's, Annapurna, Annapurna Premier 8000, Carnets de Vertige, climbing, Gaston Rebuffat, Himalayas, La Piste des Cimes, Les conquérants de l'inutile, Lionel Terray, Louis Lachenal, Maurice Herzog, Nepal, sherpas on June 3, 2020 by xi'an## running in circles

Posted in Mountains, pictures, Running, Travel with tags coronavirus epidemics, COVID-19, France, jogging, lockdown, Paris suburbs, road running, sunrise, swimming pool on May 31, 2020 by xi'an**A**s lockdown rules concerning outdoor activities were rather restrictive (run alone, away from other people, at most one hour and at most 1km away from home), I used the network of streets around my house to design a 13km circuit that was never replicating more than intersecting previously visited roads. And I ran it every one of the 60 days of the lockdown.

This was a purely urban run on pavement only, but offered nice views of the neighbouring suburbs, with three hills to climb.

And hardly anyone in the streets, except for the occasional soul walking her dog. And never a single control of the laisser-passer I had to print every morn.

Going by the park and the local swimming pool every day and unrealistically wishing they would open soon…