Archive for interacting particle systems
Cristina Toninelli, CEREMADE CNRS silver medallist [congrats!]
Posted in pictures, University life with tags bootstrap percolation, CEREMADE, CNRS, CNRS Silver Medal, glass, interacting particle systems, La Sapienza, probability theory, PSL Research University, Roma, statistical mechanics, Université Paris Dauphine on April 29, 2026 by xi'an
mostly MCMC’s back
Posted in Statistics, University life with tags interacting particle systems, Langevin MCMC algorithm, latent variable models, MCMC, Mostly MCMC seminar, Paris, PariSanté campus, Porte de Versailles, proximal interacting particle Langevin algorithms, PSL, SDEs, seminar, Université Paris Dauphine on September 13, 2024 by xi'an
séminaire parisien de statistique [09/01/23]
Posted in Books, pictures, Statistics, University life with tags Flatiron Institute, Gibbs distribution, Harris recurrence, IHP, Institut Henri Poincaré, interacting particle systems, Kac's theorem, KitKat, Mark Kac, matcha tea, McKean-Vlasov SDE, NeurIPS 2021, Panthéon, SDEs, sequential Monte Carlo, small set, SMC on January 22, 2023 by xi'an
I had missed the séminaire parisien de statistique for most of the Fall semester, hence was determined to attend the first session of the year 2023, the more because the talks were close to my interest. To wit, Chiara Amorino spoke about particle systems for McKean-Vlasov SDEs, when those are parameterised by several parameters, when observing repeatedly discretised versions, hereby establishing the consistence of a contrast estimator of these estimators. I was initially confused by the mention of interacting particles, since the work is not at all about related with simulation. Just wondering whether this contrast could prove useful for a likelihood-free approach in building a Gibbs distribution?
Valentin de Bortoli then spoke on diffusion Schrödinger bridges for generative models, which allowed me to better my understanding of this idea presented by Arnaud at the Flatiron workshop last November. The presentation here was quite different, using a forward versus backward explanation via a sequence of transforms that end up approximately Gaussian, once more reminiscent of sequential Monte Carlo. The transforms are themselves approximate Gaussian versions relying on adiscretised Ornstein-Ulhenbeck process, with a missing score term since said score involves a marginal density at each step of the sequence. It can be represented [as below] as an expectation conditional on the (observed) variate at time zero (with a connection with Hyvärinen’s NCE / score matching!) Practical implementation is done via neural networks.
Last but not least!, my friend Randal talked about his Kick-Kac formula, which connects with the one we considered in our 2004 paper with Jim Hobert. While I had heard earlier version, this talk was mostly on probability aspects and highly enjoyable as he included some short proofs. The formula is expressing the stationary probability measure π of the original Markov chain in terms of explorations between two visits to an accessible set C, more general than a small set. With at first an annoying remaining term due to the set not being Harris recurrent but which eventually cancels out. Memoryless transportation can be implemented because C is free for the picking, for instance the set where the target is bounded by a manageable density, allowing for an accept-reject step. The resulting chain is non-reversible. However, due to the difficulty to simulate from the target restricted to C, a second and parallel Markov chain is instead created. Performances, unsurprisingly, depend on the choice of C, but it can be adapted to the target on the go.
yet another opportunity in a summer of Briton conferences, free of charge!
Posted in Statistics with tags Bretagne, Brittany, Henri Lebesgue, interacting particle systems, mini-courses, Rennes, simulation, simulation and probability on April 10, 2018 by xi'an
bouncy particle sampler
Posted in pictures, Statistics, Travel, University life with tags curse of dimensionality, Gibbs sampler, Hamiltonian Monte Carlo, interacting particle systems, Monte Carlo Statistical Methods, particle, pinball sampler, Teneriffe on October 30, 2015 by xi'an
Alexandre Bouchard-Coté, Sebastian Vollmer and Arnaud Doucet just arXived a paper with the above title, which reminded me of a proposal Kerrie Mengersen and I made at Valencia 7, in Tenerife, the [short-lived!] pinball sampler. This sampler was a particle (MCMC) sampler where we used the location of the other particles to avoid their neighbourhood, by bouncing away from them according to a delayed rejection principle, with an overall Gibbs justification since the resulting target was the product of copies of the target distribution. The difficulty in implementing the (neat!) idea was in figuring out the amount of bouncing or, in more physical terms, the energy allocated to the move.
In the current paper, inspired from an earlier paper in physics, the Markov chain (or single particle) evolves by linear moves, changing directions according to a Poisson process, with intensity and direction depending on the target distribution. A local version takes advantage of a decomposition of the target into a product of terms involving only some components of the whole parameter to be simulated. And hence allowing for moves in subspaces. An extension proposed by the authors is to bounce along the Hamiltonian isoclines. The method is demonstrably ergodic and irreducible. In practice, I wonder at the level of calibration or preliminary testing required to facilitate the exploration of the parameter space, particularly in the local version that seems to multiply items to be calibrated.
