# Recurrent Neural Filters: Learning Independent Bayesian Filtering Steps for Time Series Prediction

arXiv: https://arxiv.org/abs/1901.08096 · HTML: https://mlsanity.com/paper/1901.08096/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2019.

## Built on by (most cited first, 14 of 14)

- [Time Series Anomaly Detection for Cyber-Physical Systems via Neural System Identification and Bayesian Filtering](https://mlsanity.com/paper/2106.07992/) (2021)
- [Robust Multivariate Time-Series Forecasting: Adversarial Attacks and Defense Mechanisms](https://mlsanity.com/paper/2207.09572/) (2022)
- [A Two-Block RNN-based Trajectory Prediction from Incomplete Trajectory](https://mlsanity.com/paper/2203.07098/) (2022)
- [S4M: S4 for multivariate time series forecasting with Missing values](https://mlsanity.com/paper/2503.00900/) (2025)
- [Infomaxformer: Maximum Entropy Transformer for Long Time-Series Forecasting Problem](https://mlsanity.com/paper/2301.01772/) (2023)
- [Masked Multi-Step Probabilistic Forecasting for Short-to-Mid-Term Electricity Demand](https://mlsanity.com/paper/2302.06818/) (2023)
- [Multi-task Envisioning Transformer-based Autoencoder for Corporate Credit Rating Migration Early Prediction](https://mlsanity.com/paper/2207.04539/) (2022)
- [TimeTuner: Diagnosing Time Representations for Time-Series Forecasting with Counterfactual Explanations](https://mlsanity.com/paper/2307.09916/) (2023)
- [Masked Multi-Step Multivariate Time Series Forecasting with Future Information](https://mlsanity.com/paper/2209.14413/) (2022)
- [Neural Bayesian Filtering](https://mlsanity.com/paper/2510.03614/) (2025)
- [Vision-Guided Forecasting -- Visual Context for Multi-Horizon Time Series Forecasting](https://mlsanity.com/paper/2107.12674/) (2021)
- [Forecast-Then-Optimize Deep Learning Methods](https://mlsanity.com/paper/2506.13036/) (2025)
- [Predictive Coding Enhances Meta-RL To Achieve Interpretable Bayes-Optimal Belief Representation Under Partial Observability](https://mlsanity.com/paper/2510.22039/) (2025)
- [Model-Free Neural Filtering: A Comparison with Classical Filters in Nonlinear Systems](https://mlsanity.com/paper/2601.21266/) (2026)

## Abstract (arXiv)

Despite the recent popularity of deep generative state space models, few comparisons have been made between network architectures and the inference steps of the Bayesian filtering framework -- with most models simultaneously approximating both state transition and update steps with a single recurrent neural network (RNN). In this paper, we introduce the Recurrent Neural Filter (RNF), a novel recurrent autoencoder architecture that learns distinct representations for each Bayesian filtering step, captured by a series of encoders and decoders. Testing this on three real-world time series datasets, we demonstrate that the decoupled representations learnt not only improve the accuracy of one-step-ahead forecasts while providing realistic uncertainty estimates, but also facilitate multistep prediction through the separation of encoder stages.