Explainable Bayesian Recurrent Neural Smoother to Capture Global State Evolutionary Correlations

TL;DR

This paper introduces an explainable Bayesian recurrent neural smoother (EBRNS) that effectively captures global state correlations for improved offline data-assisted state smoothing, combining Bayesian theory with neural networks.

Contribution

The paper presents a novel EBRNS model that integrates global state evolution into a Bayesian neural smoothing framework with a natural, explainable structure.

Findings

High smoothing accuracy demonstrated on real-world datasets

Data efficiency and lightweight model architecture achieved

Bidirectional recursion enhances global state correlation capture

Abstract

Through integrating the evolutionary correlations across global states in the bidirectional recursion, an explainable Bayesian recurrent neural smoother (EBRNS) is proposed for offline data-assisted fixed-interval state smoothing. At first, the proposed model, containing global states in the evolutionary interval, is transformed into an equivalent model with bidirectional memory. This transformation incorporates crucial global state information with support for bi-directional recursive computation. For the transformed model, the joint state-memory-trend Bayesian filtering and smoothing frameworks are derived by introducing the bidirectional memory iteration mechanism and offline data into Bayesian estimation theory. The derived frameworks are implemented using the Gaussian approximation to ensure analytical properties and computational efficiency. Finally, the neural network modules within EBRNS and its two-stage training scheme are designed. Unlike most existing approaches that artificially combine deep learning and model-based estimation, the bidirectional recursion and internal gated structures of EBRNS are naturally derived from Bayesian estimation theory, explainably integrating prior model knowledge, online measurement, and offline data. Experiments on representative real-world datasets demonstrate that the high smoothing accuracy of EBRNS is accompanied by data efficiency and a lightweight parameter scale.