[go: up one dir, main page]

Archive for SMC

OWABI⁷, 26 February 2026: Prequential posteriors (11am UK time)

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , , on February 25, 2026 by xi'an

Speaker:  Shreya Sinha Roy (University of Warwick)

Title: Prequential posteriors
Abstract: Data assimilation is a fundamental task in updating forecasting models upon observing new data, with applications ranging from weather prediction to online reinforcement learning. Deep generative forecasting models (DGFMs) have shown excellent performance in these areas, but assimilating data into such models is challenging due to their intractable likelihood functions. This limitation restricts the use of standard Bayesian data assimilation methodologies for DGFMs. To overcome this, we introduce prequential posteriors, based upon a predictive-sequential (prequential) loss function; an approach naturally suited for temporally dependent data which is the focus of forecasting tasks. Since the true data-generating process often lies outside the assumed model class, we adopt an alternative notion of consistency and prove that, under mild conditions, both the prequential loss minimizer and the prequential posterior concentrate around parameters with optimal predictive performance. For scalable inference, we employ easily parallelizable wastefree sequential Monte Carlo (SMC) samplers with preconditioned gradient-based kernels, enabling efficient exploration of high-dimensional parameter spaces such as those in DGFMs. We validate our method on both a synthetic multi-dimensional time series and a real-world meteorological dataset; highlighting its practical utility for data assimilation for complex dynamical systems.
Keywords: diffusion models, simulation based inference, sequential methods.
Reference: S. S. Roy, R. Everitt, C. P Robert, R. Dutta. Prequential posteriors. Preprint at ArXiv:2511.17721, 202

prequential posteriors

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , on December 15, 2025 by xi'an

Data assimilation is a fundamental task in updating forecasting models upon observing new data, with applications ranging from weather prediction to online reinforcement learning. Deep generative forecasting models (DGFMs) have shown excellent performance in these areas, but assimilating data into such models is challenging due to their intractable likelihood functions. This limitation restricts the use of standard Bayesian data assimilation methodologies for DGFMs. To overcome this, we introduce prequential posteriors, based upon a predictive-sequential (prequential) loss function; an approach naturally suited for temporally dependent data which is the focus of forecasting tasks. Since the true data-generating process often lies outside the assumed model class, we adopt an alternative notion of consistency and prove that, under mild conditions, both the prequential loss minimizer and the prequential posterior concentrate around parameters with optimal predictive performance. For scalable inference, we employ easily parallelizable wastefree sequential Monte Carlo (SMC) samplers with preconditioned gradient-based kernels, enabling efficient exploration of high-dimensional parameter spaces such as those in DGFMs. We validate our method on both a synthetic multi-dimensional time series and a real-world meteorological dataset; highlighting its practical utility for data assimilation for complex dynamical systems.

gradient flow for projected Langevin dynamics

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , , on April 7, 2025 by xi'an

Daniel Lacker (Columbia U) gave a talk at the probability seminar of Paris Dauphine this week which I happened to attend by happenstance, on a recent paper, Projected Langevin dynamics and a gradient flow for entropic optimal transport, written with Giovanni Conforti and, Soumik Pal. The talk was quite progressive and I hence could follow most of it. The core idea is in studying Langevin-type diffusion dynamics that sample from an entropy-regularized optimal transport, i.e. looking for an optimal distribution (in the sense of achieving entropy minimisation problem within a Wasserstein space, with regularisation) obtained via a gradient flow equation (as eg in variational inference) that couples two SDEs that are recentred by conditional expectation terms. Expectations in the equations are estimated by a Nadaraya-Watson estimate in optimal transport problem (reminding me of SMC), with no theoretical derivation of an optimal bandwidth, and they achieve quantitive bounds on the convergence, namely for exponential convergence, energy decay and new logarithmic Sobolev inequalities. From the talk and a quick glance at the paper, it is unclear to me there are direct algorithmic consequences, since the SDEs need be discretised, while the expectation approximations are costly, being repeated at each iteration of the discretised SDE.

Congrats, Dr. Marival!

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , , , on March 26, 2025 by xi'an