Archive for hypocoercivity

computational statistics and molecular simulation [18w5023]

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , , on November 16, 2018 by xi'an

This Thursday, our X fertilisation workshop at the interface between molecular dynamics and Monte Carlo statistical methods saw a wee bit of reduction in the audience as some participants had already left Oaxaca. Meaning they missed the talk of Christophe Andrieu on hypocoercivity which could have been another hand-on lecture, given the highly pedagogical contents of the talk. I had seen some parts of the talk in MCqMC 2018 in Rennes and at NUS, but still enjoyed the whole of it very much, and so did the audience given the induced discussion. For instance, previously, I had not seen the connection between the guided random walks of Gustafson and Diaconis, and continuous time processes like PDMP. Which Christophe also covered in his talk. (Also making me realise my colleague Jean Dolbeault in Dauphine was strongly involved in the theoretical analysis of PDMPs!) Then Samuel Power gave another perspective on PDMPs. With another augmentation, connected with time, what he calls trajectorial reversibility. This has the impact of diminishing the event rate, but creates some kind of reversibility which seems to go against the motivation for PDMPs. (Remember that all talks are available as videos on the BIRS webpage.) A remark in the talk worth reiterating is the importance of figuring out which kinds of approximations are acceptable in these approximations. Connecting somewhat with the next talk by Luc Rey-Bellet on a theory of robust approximations. In the sense of Poincaré, Gibbs, Bernstein, &tc. concentration inequalities and large deviations. With applications to rare events.The fourth and final “hand-on” session was run by Miranda Holmes-Certon on simulating under constraints. Motivated by research on colloids. For which the overdamp Langevin diffusion applies as an accurate model, surprisingly. Which makes a major change from the other talks [most of the workshop!] relying on this diffusion. (With an interesting intermede on molecular velcro made of DNA strands.) Connected with this example, exotic energy landscapes are better described by hard constraints. (Potentially interesting extension to the case when there are too many constraints to explore all of them?) Now, the definition of the measure projected on the manifold defined by the constraints is obviously an important step in simulating the distribution, which density is induced by the gradient of the constraints ∇q(x). The proposed algorithm is in the same spirit as the one presented by Tony the previous day, namely moving along the tangent space then on the normal space to get back to the manifold. A solution that causes issues when the gradient is (near) zero. A great hand-on session which induced massive feedback from the audience.

In the afternoon session, Gersende Fort gave a talk on a generalisation of the Wang-Landau algorithm, which modifies the true weights of the elements of a partition of the sampling space, to increase visits to low [probability] elements and jumps between modes. The idea is to rely on tempered versions of the original weights, learned by stochastic approximation. With an extra layer of adaptivity. Leading to an improvement with parameters that depends on the phase of the stochastic approximation. The second talk was by David Sanders on a recent paper in Chaos about importance sampling for rare events of (deterministic) billiard dynamics. With diffusive limits which tails are hard to evaluate, except by importance sampling. And the last talk of the day was by Anton Martinsson on simulated tempering for a molecular alignment problem. With weights of different temperatures proportional to the inverse of the corresponding normalising constants, which themselves can be learned by a form of bridge sampling  if I got it right.

On a very minor note, I heard at breakfast a pretty good story from a fellow participant having to give a talk at a conference that was moved to a very early time in the morning due to an official appearing at a later time and as a result “enjoying” a very small audience to the point that a cleaning lady appeared and started cleaning the board as she could not conceive the talks had already started! Reminding me of this picture at IHP.

IMS workshop [day 3]

Posted in pictures, R, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , , , , on August 30, 2018 by xi'an

I made the “capital” mistake of walking across the entire NUS campus this morning, which is quite green and pretty, but which almost enjoys an additional dimension brought by such an intense humidity that one feels having to get around this humidity!, a feature I have managed to completely erase from my memory of my previous visit there. Anyway, nothing of any relevance. oNE talk in the morning was by Markus Eisenbach on tools used by physicists to speed up Monte Carlo methods, like the Wang-Landau flat histogram, towards computing the partition function, or the distribution of the energy levels, definitely addressing issues close to my interest, but somewhat beyond my reach for using a different language and stress, as often in physics. (I mean, as often in physics talks I attend.) An idea that came out clear to me was to bypass a (flat) histogram target and aim directly at a constant slope cdf for the energy levels. (But got scared away by the Fourier transforms!)

Lawrence Murray then discussed some features of the Birch probabilistic programming language he is currently developing, especially a fairly fascinating concept of delayed sampling, which connects with locally-optimal proposals and Rao Blackwellisation. Which I plan to get back to later [and hopefully sooner than later!].

In the afternoon, Maria de Iorio gave a talk about the construction of nonparametric priors that create dependence between a sequence of functions, a notion I had not thought of before, with an array of possibilities when using the stick breaking construction of Dirichlet processes.

And Christophe Andrieu gave a very smooth and helpful entry to partly deterministic Markov processes (PDMP) in preparation for talks he is giving next week for the continuation of the workshop at IMS. Starting with the guided random walk of Gustafson (1998), which extended a bit later into the non-reversible paper of Diaconis, Holmes, and Neal (2000). Although I had a vague idea of the contents of these papers, the role of the velocity ν became much clearer. And premonitory of the advances made by the more recent PDMP proposals. There is obviously a continuation with the equally pedagogical talk Christophe gave at MCqMC in Rennes two months [and half the globe] ago,  but the focus being somewhat different, it really felt like a new talk [my short term memory may also play some role in this feeling!, as I now remember the discussion of Hilderbrand (2002) for non-reversible processes]. An introduction to the topic I would recommend to anyone interested in this new branch of Monte Carlo simulation! To be followed by the most recently arXived hypocoercivity paper by Christophe and co-authors.