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Kalman Filter for Online Classification of Non-Stationary Data
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Proposes a Kalman filter based online Bayesian classifier with a parameter-drift state space model whose forgetting coefficient gamma is learned online by SGD, optionally fine-tuning the backbone and a calibration parameter, evaluated on CIFAR-100 and CLOC.
Problem
Online continual learning on non-stationary data streams requires automatic adaptation to the drift structure and well-calibrated predictive uncertainty, while evaluating next-step prediction (prequential log-loss).
Approach
Model the linear readout weights as a Gaussian Markov process with a variance-preserving drift parameterized by a forgetting coefficient gamma; run exact Kalman recursions for the weight posterior (with a Gaussian approximation to softmax for classification), and learn gamma and a calibration scale alpha online by SGD on the predictive log-likelihood, optionally fine-tuning the backbone.
Key results
- On non-stationary CIFAR-100 with backbone finetuning, the learned-gamma Kalman filter reaches 51.2% average online accuracy versus 44.5% for the stationary Kalman filter (gamma=1).
- On stationary CIFAR-100, the replay-free Kalman filter with learned gamma reaches 16.9% with backbone finetuning, and with replay 19.0%, exceeding ER (13.62%) and ACE (14.42%) and approaching ER++ (18.45%).
- On CLOC learning from scratch, replay-free Kalman filter matches online SGD with replay, and with a pretrained backbone it learns more efficiently than all baselines.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| learn γ instead of fixing it at 0.999 (ablation) | Kalman Filter with no backbone finetuning · Stationary CIFAR-100 | Average Online Accuracy: 9.2 % -> 11.4 % | Helped |
| learn γ instead of fixing it at 0.999 (ablation) | Kalman Filter with no backbone finetuning · Non-stationary CIFAR-100 | Average Online Accuracy: 31.9 % -> 32.7 % | Helped |
| learn γ instead of fixing it at 1.0 (ablation) | Kalman Filter with no backbone finetuning · Stationary CIFAR-100 | Average Online Accuracy: 10.9 % -> 11.4 % | Helped |
| learn γ instead of fixing it at 1.0 (ablation) | Kalman Filter with no backbone finetuning · Non-stationary CIFAR-100 | Average Online Accuracy: 12.1 % -> 32.7 % | Helped |
| learn γ instead of fixing it at 0.999 (ablation) | Kalman Filter with backbone finetuning · Stationary CIFAR-100 | Average Online Accuracy: 15.9 % -> 16.9 % | Helped |
| learn γ instead of fixing it at 0.999 (ablation) | Kalman Filter with backbone finetuning · Non-stationary CIFAR-100 | Average Online Accuracy: 50.5 % -> 51.2 % | Helped |
| learn γ instead of fixing it at 1.0 (ablation) | Kalman Filter with backbone finetuning · Stationary CIFAR-100 | Average Online Accuracy: 16.4 % -> 16.9 % | Helped |
| learn γ instead of fixing it at 1.0 (ablation) | Kalman Filter with backbone finetuning · Non-stationary CIFAR-100 | Average Online Accuracy: 44.5 % -> 51.2 % | Helped |
| learn γ instead of fixing it at 0.999 (ablation) | Kalman Filter with backbone finetuning and replay · Stationary CIFAR-100 | Average Online Accuracy: 18.9 % -> 19.0 % | Helped |
| learn γ instead of fixing it at 0.999 (ablation) | Kalman Filter with backbone finetuning and replay · Non-stationary CIFAR-100 | Average Online Accuracy: 55.5 % -> 55.5 % | No clear effect |
| learn γ instead of fixing it at 1.0 (ablation) | Kalman Filter with backbone finetuning and replay · Stationary CIFAR-100 | Average Online Accuracy: 18.5 % -> 19.0 % | Helped |
| learn γ instead of fixing it at 1.0 (ablation) | Kalman Filter with backbone finetuning and replay · Non-stationary CIFAR-100 | Average Online Accuracy: 51.6 % -> 55.5 % | Helped |
Surprising findings
- A purely linear Kalman filter on a fixed random backbone outperforms online SGD on CLOC, even without replay.
- On stationary CIFAR-100, the fixed-gamma=0.999 variant underperforms the stationary gamma=1 filter, showing forgetting can hurt when no drift exists.
Limitations
- Softmax likelihood is approximated by a Gaussian likelihood per class, so classification predictions rely on an approximate posterior.
- Dealing with catastrophic forgetting is explicitly out of scope; only online accuracy is measured.
- Hyperparameters are selected via an MDL-based criterion with per-benchmark choices, which adds tuning complexity.
Experimental setup
Datasets: CIFAR-100 CLOC
Benchmarks: CIFAR-100 (stationary) CIFAR-100 (non-stationary, task-agnostic Split-CIFAR100) CLOC
Metrics: average online accuracy cumulative log predictive probability
Baselines: ER ER++ ACE Online SGD
Builds on: online Bayesian linear regression experience replay prequential MDL
Closest papers by meaning
- Forgetting, Ignorance or Myopia: Revisiting Key Challenges in Online Continual Learning (NeurIPS 2024 · similarity 0.88)
- Predictively-Oriented Kalman Filtering (NeurIPS 2026 · similarity 0.87)
- Online Learning via Learned Latent Bayesian Tracking (NeurIPS 2026 · similarity 0.86)
- Enhancing Online Continual Learning with Plug-and-Play State Space Model and Class-Conditional Mixture of Discretization (CVPR 2025 · similarity 0.86)
- KAC: Kolmogorov-Arnold Classifier for Continual Learning (CVPR 2025 · similarity 0.86)
- Learning to Continually Learn with the Bayesian Principle (ICML 2024 · similarity 0.86)
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