Archive for quasi-Monte Carlo methods
Congrats, Dr. Andral!
Posted in Books, pictures, Statistics, University life with tags adaptive Monte Carlo algorithm, ENSAE, history of Monte Carlo, importance MCMC, importance sampling, jury, normalizing flow, Paris, PDMP, PhD thesis, PSL Research University, quasi-Monte Carlo methods, thesis defence, Université Paris Dauphine on November 27, 2024 by xi'an
webinar on Monte Carlo Methods
Posted in Books, Statistics, University life with tags Art Owen, Gare du Nord, MCMC, Monte Carlo methods, Monte Carlo Statistical Methods, non-reversible MCMC, Persi Diaconis, quasi-Monte Carlo methods, simulated tempering, simulation, Stanford University, University of Warwick, webinar on October 7, 2024 by xi'an
Hey, there is a new international Monte Carlo webinar starting this semester! Taking place at 8:30 am PT, 11:30 am ET (which currently set it at 16:30 in Tórshavn time and 17:30 in Longyearbyen time!). The first speakers on the list are
- Persi Diaconis (who gave a talk last week)
- Mike Giles (tomorrow!)
- Art Owen (on quasi-Monte Carlo)
- Gareth O Roberts (Warwick)
Enjoy!
repulsive sampling
Posted in Books, Statistics, University life with tags Coulomb potential, determinantal point process, HMC, IHP, importance sampling, Institut Henri Poincaré, MCMC algorithms, Nikolai Bakhvalov, numerical integration, pinball sampler, quasi-Monte Carlo methods, repulsiveness, simulating copulas, slides, Sobol sequences, variance reduction on January 31, 2024 by xi'an
After a long absence from the monthly Séminaire Parisien de Statistique I attended one today at IHP, including a talk by Diala Hawat on repelled point processes for numerical integration by Hawat et al. The goal is to get (and prove) a universal variance improvement for numerical integration by applying a form of determinantal processes to initial simulations, as eg iid (Poisson process) sampling (without accounting for the O(N²) cost in moving these points). The repelled points are obtain by a single (why single?) move based on a force function (as shown in the slide below), inspired by a Coulomb potential (in the sense that said move appears as one gradient step along the potential). Which reminded me of the pinball sampler, even though the inverse norm was just there to create infinite repulsion near each point. A surprising feature of this repelling step is that it even modifies a (QMC) Sobol process with also an (empirical) improvement in the variance. I wonder if one could construct an MCMC algorithm that would target a joint distribution, maybe via a copula representation, maybe via an equivalent version of HMC.
As an aside, the Bakhvalov results on the existence of a worst case integrand for any deterministic or random sequence (see top slide) made me wonder what the shape of this worst case function is, esp. for a QMC sequence (eg, Sobol). And whether or not they are of any relevance as a counterfactor to the optimal importance functions.
combining normalizing flows and QMC
Posted in Books, Kids, Statistics with tags Arianna Rosenbluth, arXiv, Illya Sobol, importance sampling, inverse cdf, John Halton, MCM 2023, Metropolis-Hastings algorithm, mostly Monte Carlo seminar, normalizing flow, Python, quasi-Monte Carlo methods, scrambling, Sobol sequences on January 23, 2024 by xi'an
My PhD student Charly Andral [presented at the mostly Monte Carlo seminar and] arXived a new preprint yesterday, on training a normalizing flow network as an importance sampler (as in Gabrié et al.) or an independent Metropolis proposal, and exploiting its invertibility to call quasi-Monte Carlo low discrepancy sequences to boost its efficiency. (Training the flow is not covered by the paper.) This extends the recent study of He et al. (which was presented at MCM 2023 in Paris) to the normalising flow setting. In the current experiments, the randomized QMC samples are computed using the SciPy package (Roy et al. 2023), where the Sobol’ sequence is based on Joe and Kuo (2008) and on Matouˇsek (1998) for the scrambling, and where the Halton sequence is based on Owen (2017). (No pure QMC was harmed in the process!) The flows are constructed using the package FlowMC. As expected the QMC version brings a significant improvement in the quality of the Monte Carlo approximations, for equivalent computing times, with however a rapid decrease in the efficiency as the dimension of the targetted distribution increases. On the other hand, the architecture of the flow demonstrates little relevance. And the type of RQMC sequence makes a difference, the advantage apparently going to a scrambled Sobol’ sequence.
mostly MC[nuary]
Posted in Books, Kids, Statistics, University life with tags Monte Carlo methods, Monte Carlo Statistical Methods, mostly Monte Carlo seminar, normalising flow, overdamped Langevin algorithm, Paris, PariSanté campus, quasi-Monte Carlo methods, seminar, The Prairie Chair on January 6, 2024 by xi'an
