Archive for dimension reduction
mostly [14] M[ar]C[h] seminar
Posted in Books, Statistics, University life with tags dimension reduction, GLMs, gradient algorithm, importance sampling, Issy-les-Moulineaux, log-normal distribution, MCMC, Monte Carlo methods, Mostly MC, Mostly MCMC seminar, Ocean, Paris, PariSanté campus, Porte de Versailles, PSL, seminar, Università Bocconi, Université Paris Dauphine on March 8, 2025 by xi'an
amortized Bayesian mixture model
Posted in Books, Statistics, University life with tags ABC, amortization, amortized Bayesian inference, Approximate Bayesian computation, approximate Bayesian inference, dimension reduction, doubly intractable posterior, label switching, mixtures of distributions, normalising flow, OWABI, reparameterisation, STAN, sufficiency, summary statistics, webinar on February 7, 2025 by xi'an
A few days before the January OWABI, I read through Simon Kucharsky’s and Paul Bürkner’s paper, arXived on 17 January. Which proposed an amortized Bayesian inference (ABI) method, even though the ABI is not the same as in OWABI! The motivation for their work is to start from a (standard) mixture model where the components are not analytically tractable (but still parameterised). But a generative model nonetheless. As in the earlier reviewed paper (which was arXived on the same day), by MEJ Newman, the dual representation of the joint posterior p(θ,z|x) as p(z|x,θ)p(θ|x) and p(θ|z,x)p(z|x) is (over?) emphasized (albeit unclearly why!). ABI uses neural networks and more specifically normalising flows to approximate the posterior p(θ|x) from prior predictive samples (θ,x) (as in ABC), and then directly exploit the invertibility of said flows to generate from this approximate posterior. One interesting aspect of the modelling is the derivation of summary statistics in the design of the network, albeit mixture posteriors do not allow for dimension-reduced (Bayes) sufficient statistics (and a contradictory sentence that conditioning on the summaries “does not alter the target posterior”, p7). The resulting approximate posterior generator proves much much faster than running an MCMC, obviously, and furthermore adapt to handling a sequence of datasets. A second network is constructed to approximate p(z|x,θ), using the same summaries. The network parameters are estimated through losses, rather than in a Bayesian manner, with a default Kullback-Leibler version (18). I also fail to understand why the networks are trained over unconstrained parameters when all parameters could become unconstrained when using the adequate parameterisation. And am fairly surprised at the regression towards the ill-fated step of using ordered parameters to avoid label switching… But the main quandary remains the issue of assessing the approximation effect, despite experiments aiming at pacifying such worries. And similarities with Stan and BayesFlow.
missing dimensions
Posted in Statistics with tags 12 Angry Men, data graphics, data visualisation, dimension reduction, Edward Tufte, J.R. Tolkien, Lord of the Rings, Minard, Napoléon Bonaparte, Russian campaign, Russian winter, Sidney Lumet, Star Wars, xkcd on February 14, 2021 by xi'an
data assimilation and reduced modelling for high-D problems [CIRM]
Posted in Books, Kids, Mountains, pictures, Running, Statistics, University life with tags calanques, call for contributions, CIRM, CNRS, dimension reduction, fellowships, high dimensions, Luminy, Marseille, Méditerranée, mini-courses, optimisation, Parc National des Calanques, sampling, simulation, Société Mathématique de France, Sugiton, workshop on February 8, 2021 by xi'an
Next summer, from 19 July till 27 August, there will be a six week program at CIRM on the above theme, bringing together scientists from both the academic and industrial communities. The program includes a one-week summer school followed by 5 weeks of research sessions on projects proposed by academic and industrial partners.
Confirmed speakers of the summer school (Jul 19-23) are:
- Albert Cohen (Sorbonne University)
- Masoumeh Dashti (University of Sussex)
- Eric Moulines (Ecole Polytechnique)
- Anthony Nouy (Ecole Centrale de Nantes)
- Claudia Schillings (Mannheim University)
Junior participants may apply for fellowships to cover part or the whole stay. Registration and application to fellowships will be open soon.
ABC in Clermont-Ferrand
Posted in Mountains, pictures, Statistics, Travel, University life with tags ABC, ABC-Gibbs, Approximate Bayesian computation, Auvergne, Clermont-Ferrand, conditional sufficiency, cosmostats, dimension reduction, Gibbs sampling, likelihood-free methods, PMC, volcano on September 20, 2019 by xi'an
Today I am taking part in a one-day workshop at the Université of Clermont Auvergne on ABC. With applications to cosmostatistics, along with Martin Kilbinger [with whom I worked on PMC schemes], Florent Leclerc and Grégoire Aufort. This should prove a most exciting day! (With not enough time to run up Puy de Dôme in the morning, though.)
