Learning Probabilistic Filters with Strictly Proper Scoring Rules

arXiv:2606.26497 · cs.LG, math.DS, stat.ML · Submitted 2026-06-25 · Read on arXiv

cs.LG, math.DS, stat.ML

Submitted: 2026-06-25

Updated: 2026-10-05

Comments: 87 pages, 17 figures

Code: https://github.com/wispcarey/Proper-Scoring-Ensemble-Filter

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Data Assimilation — 43× in this paper · explained in 2 episodes
• Benchmark — 34× in this paper · explained in 2 episodes
• Transformer — 29× in this paper · explained in 2 episodes
• Fine-Tuning — 24× in this paper · explained in 5 episodes
• Calibration — 22× in this paper · explained in 7 episodes
• Abundance — 9× in this paper · explained in 1 episode
• Verification — 9× in this paper · explained in 2 episodes
• Accuracy — 8× in this paper · explained in 1 episode
• Consistency — 8× in this paper · explained in 3 episodes
• Loss Function — 8× in this paper · explained in 2 episodes
• Degeneracy — 6× in this paper · explained in 3 episodes
• Generalization — 6× in this paper · explained in 13 episodes
• Lyapunov function — 6× in this paper · explained in 2 episodes
• Multi-Head Attention — 6× in this paper
• Objective Function — 6× in this paper · explained in 2 episodes
• Inverse Problem — 5× in this paper · explained in 2 episodes
• Attention Mechanism — 4× in this paper · explained in 3 episodes
• Optimal Transport — 4× in this paper · explained in 5 episodes
• Stochastic Dynamics — 4× in this paper · explained in 2 episodes
• Bayesian Inference — 3× in this paper · explained in 5 episodes
• Probabilistic Forecasting — 3× in this paper · explained in 3 episodes
• Transformer Architecture — 3× in this paper · explained in 2 episodes
• Uncertainty Quantification — 3× in this paper · explained in 8 episodes
• Wasserstein Distance — 3× in this paper · explained in 4 episodes
• Abstraction — 2× in this paper · explained in 1 episode
• Core — 2× in this paper · explained in 2 episodes
• Exchangeability — 2× in this paper · explained in 2 episodes
• Latent Representation — 2× in this paper · explained in 2 episodes
• Latent Representations — 2× in this paper · explained in 3 episodes
• Regularization — 2× in this paper · explained in 3 episodes
• Signal-to-noise ratio (SNR) — 2× in this paper · explained in 2 episodes
• Activation Function — 1× in this paper · explained in 1 episode
• Adam — 1× in this paper · explained in 2 episodes
• Adaptive Algorithm — 1× in this paper · explained in 1 episode
• Adaptive Sampling — 1× in this paper · explained in 1 episode
• Aggregation — 1× in this paper · explained in 1 episode
• Deep Reinforcement Learning — 1× in this paper · explained in 2 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Generative AI — 1× in this paper · explained in 2 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Normalizing Flow — 1× in this paper · explained in 3 episodes
• Principal Component Analysis (PCA) — 1× in this paper · explained in 4 episodes
• Reinforcement Learning — 1× in this paper · explained in 4 episodes
• Sample Complexity — 1× in this paper · explained in 15 episodes
• Score Function — 1× in this paper · explained in 4 episodes
• Trace — 1× in this paper · explained in 2 episodes
• Transferability — 1× in this paper · explained in 4 episodes

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