# Kalman Filter for Online Classification of Non-Stationary Data

arXiv: https://arxiv.org/abs/2306.08448 · HTML: https://mlsanity.com/paper/2306.08448/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 60 references that are in the map.
- First posted on arXiv 14 Jun 2023.

## Builds on (most cited first, 30 of 33)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Continual Learning with Deep Generative Replay](https://mlsanity.com/paper/1705.08690/) (2017)
- [Memory Aware Synapses: Learning what (not) to forget](https://mlsanity.com/paper/1711.09601/) (2017)
- [Learning to Prompt for Continual Learning](https://mlsanity.com/paper/2112.08654/) (2021)
- [Dark Experience for General Continual Learning: a Strong, Simple Baseline](https://mlsanity.com/paper/2004.07211/) (2020)
- [PackNet: Adding Multiple Tasks to a Single Network by Iterative Pruning](https://mlsanity.com/paper/1711.05769/) (2017)
- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Gradient based sample selection for online continual learning](https://mlsanity.com/paper/1903.08671/) (2019)
- [Online Continual Learning with Maximally Interfered Retrieval](https://mlsanity.com/paper/1908.04742/) (2019)
- [Gradient Projection Memory for Continual Learning](https://mlsanity.com/paper/2103.09762/) (2021)
- [On Tiny Episodic Memories in Continual Learning](https://mlsanity.com/paper/1902.10486/) (2019)
- [Online Continual Learning in Image Classification: An Empirical Survey](https://mlsanity.com/paper/2101.10423/) (2021)
- [New Insights on Reducing Abrupt Representation Change in Online Continual Learning](https://mlsanity.com/paper/2104.05025/) (2021)
- [Class-incremental Learning via Deep Model Consolidation](https://mlsanity.com/paper/1903.07864/) (2019)
- [A Neural Dirichlet Process Mixture Model for Task-Free Continual Learning](https://mlsanity.com/paper/2001.00689/) (2020)
- [The CLEAR Benchmark: Continual LEArning on Real-World Imagery](https://mlsanity.com/paper/2201.06289/) (2022)
- [The Description Length of Deep Learning Models](https://mlsanity.com/paper/1802.07044/) (2018)
- [Online Continual Learning with Natural Distribution Shifts: An Empirical Study with Visual Data](https://mlsanity.com/paper/2108.09020/) (2021)
- [Online Continual Learning for Embedded Devices](https://mlsanity.com/paper/2203.10681/) (2022)
- [Information-theoretic Online Memory Selection for Continual Learning](https://mlsanity.com/paper/2204.04763/) (2022)
- [Low-rank extended Kalman filtering for online learning of neural networks from streaming data](https://mlsanity.com/paper/2305.19535/) (2023)
- [Online Learning of the Kalman Filter with Logarithmic Regret](https://mlsanity.com/paper/2002.05141/) (2020)
- [Detecting and Adapting to Irregular Distribution Shifts in Bayesian Online Learning](https://mlsanity.com/paper/2012.08101/) (2020)
- [NEVIS'22: A Stream of 100 Tasks Sampled from 30 Years of Computer Vision Research](https://mlsanity.com/paper/2211.11747/) (2022)
- [On-Line Learning of Linear Dynamical Systems: Exponential Forgetting in Kalman Filters](https://mlsanity.com/paper/1809.05870/) (2018)

## Built on by (most cited first, 15 of 15)

- [Non-Stationary Learning of Neural Networks with Automatic Soft Parameter Reset](https://mlsanity.com/paper/2411.04034/) (2024)
- [Bayesian Online Natural Gradient (BONG)](https://mlsanity.com/paper/2405.19681/) (2024)
- [Temporal Test-Time Adaptation with State-Space Models](https://mlsanity.com/paper/2407.12492/) (2024)
- [Transformers for Supervised Online Continual Learning](https://mlsanity.com/paper/2403.01554/) (2024)
- [A unifying framework for generalised Bayesian online learning in non-stationary environments](https://mlsanity.com/paper/2411.10153/) (2024)
- [Closed-Form Last Layer Optimization](https://mlsanity.com/paper/2510.04606/) (2025)
- [Topic-Level Bayesian Surprise and Serendipity for Recommender Systems](https://mlsanity.com/paper/2308.06368/) (2023)
- [LoKO: Low-Rank Kalman Optimizer for Online Fine-Tuning of Large Models](https://mlsanity.com/paper/2410.11551/) (2024)
- [Likelihood approximations via Gaussian approximate inference](https://mlsanity.com/paper/2410.20754/) (2024)
- [Bayesian Natural Gradient Fine-Tuning of CLIP Models via Kalman Filtering](https://mlsanity.com/paper/2511.01694/) (2025)
- [Low-Rank Filtering and Smoothing for Sequential Deep Learning](https://mlsanity.com/paper/2410.06800/) (2024)
- [Mathematics of Continual Learning](https://mlsanity.com/paper/2504.17963/) (2025)
- [Online Learning via Learned Latent Bayesian Tracking](https://mlsanity.com/paper/2609.31559/) (2026)
- [Formalizing Forgetting: Theory of Forgetting for Online Continual Learning](https://mlsanity.com/paper/2610.14787/) (2026)
- [Variational Filtering for Bayesian Last Layers with an Independent Binary Probit Surrogate](https://mlsanity.com/paper/2610.16578/) (2026)

## Abstract (arXiv)

In Online Continual Learning (OCL) a learning system receives a stream of data and sequentially performs prediction and training steps. Important challenges in OCL are concerned with automatic adaptation to the particular non-stationary structure of the data, and with quantification of predictive uncertainty. Motivated by these challenges we introduce a probabilistic Bayesian online learning model by using a (possibly pretrained) neural representation and a state space model over the linear predictor weights. Non-stationarity over the linear predictor weights is modelled using a parameter drift transition density, parametrized by a coefficient that quantifies forgetting. Inference in the model is implemented with efficient Kalman filter recursions which track the posterior distribution over the linear weights, while online SGD updates over the transition dynamics coefficient allows to adapt to the non-stationarity seen in data. While the framework is developed assuming a linear Gaussian model, we also extend it to deal with classification problems and for fine-tuning the deep learning representation. In a set of experiments in multi-class classification using data sets such as CIFAR-100 and CLOC we demonstrate the predictive ability of the model and its flexibility to capture non-stationarity.