Prequential posteriors

TL;DR

This paper introduces prequential posteriors for data assimilation in deep generative forecasting models, enabling efficient Bayesian updating with intractable likelihoods, and demonstrates their effectiveness on synthetic and real-world datasets.

Contribution

It proposes a novel prequential posterior framework tailored for temporally dependent data and scalable inference methods for complex models like DGFMs.

Findings

Prequential posteriors concentrate around optimal predictive parameters.

The method performs well on synthetic multi-dimensional time series.

Effective on real-world meteorological data.

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.