Archive for piecewise deterministic
Scalable Monte Carlo for Bayesian Learning [not yet a book review]
Posted in Books, Statistics, University life with tags 1⁰ North, Bayesian learning, book review, Cambridge University Press, continuous time MCMC, convergence diagnostics, cup, Gelman-Rubin statistic, Hamiltonian Monte Carlo, IMS Monographs, kernel Stein discrepancy descent, Markov chain Monte Carlo, MCMC, Metropolis adjusted Langevin algorithm, non-reversible MCMC, North, PDMP, piecewise deterministic, scalable Bayesian learning, scalable MCMC, stochastic differential equation, stochastic gradient MCMC on May 11, 2025 by xi'an
more than mostly MC
Posted in Kids, pictures, Statistics, Travel, University life with tags casino, cross-entropy method, diffusion sampler, EDF, Gaussian mixture, group picture, importance sampling, modes of a mixture, Monaco, Monte Carlo, Monte-Carlo casino, multimodality, nuclear energy, nuclear plant, ODE, Paris, PariSanté campus, PDEs, PDMP, piecewise deterministic, rare events, SDEs, simulated annealing on December 27, 2024 by xi'an
The session of last Friday (and last one of 2024!) proved most interesting, with two (fully) Monte Carlo talks. The first one by Louis Grenioux was about an improvement on diffusion sampler, following a recent arXival by Maxime Noble and co-authors. Which brought me back to the long-standing multimodal challenge in Monte Carlo methods. When all modes of a target distribution are known, even roughly, this is not much of an issue since samplers can be arm-bent into visiting all these modes. But the problem becomes much harder when the location and a fortiori the number of modes are not known. The paper aims at adapting diffusion samplers towards a better exploration of the modes, albeit their location is known. Otherwise, using MCMC as a starting (reference) distribution would risk missing some of them. Which also explains why the authors can rely on the classical Gaussian mixtures proposal as a cheap substitute to neural networks (EBM). Since, within diffusion models, both intermediary distributions and their scores are intractable, they also introduce a variational parametric approximation that can be optimised.
The second talk was given by Guillaume Chennetier, in connection with his recent PhD thesis, developing a form of X-entropy sampling for rare events. As in nuclear plant major accidents. It took me a while to realise that PDMPs were not used as a simulation tool, as in the zigzag sampler and its avatars, The proposal involved creating a graph structure on the space of PDMP trajectories and designing the optimal importance process (yes, the one with zero variance!) using so-called committor functions that modify jump intensity and kernel, in a sequential way reminiscent of X-entropy. The approach recycles past trajectories as Monte Carlo elements if missing an adaptive mixture importance sampling (AMIS!) version that would bring more stability. The talk also included an interesting pointer to the availability of the distribution of the PDMP path, thus treated as a likelihood. (!). The signage at the entrance of the Monte-Carlo (mind the hyphen!) casino also made an appearance, reminding me of our memorable group picture on the same spot, eons ago! (But not of whom took the picture!)
mostly M[ay]C
Posted in Books, Statistics, Travel, University life with tags conditional expectations, free energy, HMC, importance sampling, MCMC, multimodality, Ocean, PariSanté campus, PDMP, piecewise deterministic, reversible jump, seminar, variational autoencoders, Zig-Zag on May 22, 2024 by xi'an
With the details from the second speaker:
Adaptive MCMC sampling using a Metropolized PDMP sampler combined with a No-U-Turn criterion
Augustin Chevallier, Université de Strasbourg
Adaptivity in MCMC algorithms is hard to achieve. In Hamiltonian Monte Carlo, for example, it is possible to tune the path length using the No-U-Turn sampler, but the numerical step size cannot be adapted; it can only be tuned. We propose here a new class of algorithm based on Metropolizing a numerical approximation of a PDMP sampler. Like HMC, these samplers require two parameters: a numerical step size and a path length. Unlike HMC, both parameters can be adapted. This paves the way for more robust sampling algorithms, especially for difficult target densities.
Mostly Monte Carlo Se[a]minar
Posted in Kids, pictures, Statistics, University life with tags approximate Bayesian inference, École Polytechnique, Bayesian inference, Monte Carlo methods, Oradour-sur-Glane, Paris, PariSanté campus, PDMP, piecewise deterministic, postdocs, PSL Research University, scoring rule, seminar, Université Paris Dauphine, Zig-Zag on October 6, 2023 by xi'an
A brand new monthly series of Parisian seminars on the theory and practice of Monte Carlo in statistics and data science, in conjunction with our ERC OCEAN project. To kick start the series the organisers, Joshua Bon and Andrea Bertazzi, first postdocs in the project, will present some of their work on Friday 13 October, 4PM – 6PM, Room 7, PariSanté Campus 2 Rue d’Oradour-sur-Glane, Paris 15. The following seminars are planned on Friday 17 November and Friday 15 December.
4pm/16h CEST: Piecewise deterministic sampling with splitting schemes
Andrea Bertazzi, CMAP – École Polytechnique
Piecewise deterministic Markov processes (PDMPs) received substantial interest in recent years as an alternative to classical Markov chain Monte Carlo algorithms. While theoretical properties of PDMPs have been studied extensively, their practical implementation remains limited to specific applications in which bounds on the gradient of the negative log-target can be derived. In order to address this problem, we propose to approximate PDMPs using splitting schemes, that means simulating the deterministic dynamics and the random jumps in two different stages. We show that symmetric splittings of PDMPs are of second order. Then we focus on the Zig-Zag sampler (ZZS) and show how to remove the bias of the splitting scheme with a skew reversible Metropolis filter. Finally, we illustrate with numerical simulations the advantages of our proposed scheme over competitors.
5pm/17h CEST: Bayesian score calibration for approximate models
Joshua Bon, Ceremade – Université Paris Dauphine-PSL
Scientists continue to develop increasingly complex mechanistic models to reflect their knowledge more realistically. Statistical inference using these models can be challenging since the corresponding likelihood function is often intractable and model simulation may be computationally burdensome. Fortunately, in many of these situations, it is possible to adopt a surrogate model or approximate likelihood function. It may be convenient to base Bayesian inference directly on the surrogate, but this can result in bias and poor uncertainty quantification. In this paper we propose a new method for adjusting approximate posterior samples to reduce bias and produce more accurate uncertainty quantification. We do this by optimizing a transform of the approximate posterior that maximizes a scoring rule. Our approach requires only a (fixed) small number of complex model simulations and is numerically stable. We demonstrate good performance of the new method on several examples of increasing complexity.
ISBA 2021.3
Posted in Kids, Mountains, pictures, Running, Statistics, Travel, University life, Wines with tags ABC, Adam and the Ants, Approximate Bayesian computation, Bayes factors, Bayesian model choice, boar, Cap Morgiou, CIRM, conference, coupling from the past, COVID-19, Dennis Lindley, Euro 2021, evidence, forensic statistics, GANs, gather.town, HMM, ISBA, ISBA 2021, j-ISBA, Luminy, Marseille, MCMC, mirror workshop, mixtures of distributions, Mont Puget, New Wave, optimal transport, organisers, Parc National des Calanques, PDMP, piecewise deterministic, The American Statistician, workshop, Zig-Zag on July 1, 2021 by xi'an
Now on the third day which again started early with a 100% local j-ISBA session. (After a group run to and around Mont Puget, my first real run since 2020!!!) With a second round of talks by junior researchers from master to postdoc level. Again well-attended. A talk about Bayesian non-parametric sequential taxinomy by Alessandro Zito used the BayesANT acronym, which reminded me of the new vave group Adam and the Ants I was listening to forty years ago, in case they need a song as well as a logo! (Note that BayesANT is also used for a robot using Bayesian optimisation!) And more generally a wide variety in the themes. Thanks to the j-organisers of this 100% live session!
The next session was on PDMPs, which I helped organise, with Manon Michel speaking from Marseille, exploiting the symmetry around the gradient, which is distribution-free! Then, remotely, Kengo Kamatani, speaking from Tokyo, who expanded the high-dimensional scaling limit to the Zig-Zag sampler, exhibiting an argument against small refreshment rates, and Murray Pollock, from Newcastle, who exposed quite clearly the working principles of the Restore algorithm, including why coupling from the past was available in this setting. A well-attended session despite the early hour (in the USA).
Another session of interest for me [which I attended by myself as everyone else was at lunch in CIRM!] was the contributed C16 on variational and scalable inference that included a talk on hierarchical Monte Carlo fusion (with my friends Gareth and Murray as co-authors), Darren’s call to adopt functional programming in order to save Bayesian computing from extinction, normalising flows for modularisation, and Dennis’ adversarial solutions for Bayesian design, avoiding the computation of the evidence.
Wes Johnson’s lecture was about stories with setting prior distributions based on experts’ opinions. Which reminded me of the short paper Kaniav Kamary and myself wrote about ten years ago, in response to a paper on the topic in the American Statistician. And could not understand the discrepancy between two Bayes factors based on Normal versus Cauchy priors, until I was told they were mistakenly used repeatedly.
Rushing out of dinner, I attended both the non-parametric session (live with Marta and Antonio!) and the high-dimension computational session on Bayesian model choice (mute!). A bit of a schizophrenic moment, but allowing to get a rough picture in both areas. At once. Including an adaptive MCMC scheme for selecting models by Jim Griffin. Which could be run directly over the model space. With my ever-going wondering at the meaning of neighbour models.
