Approximate Gaussian variance inference for state‐space models
Bibliographic record
Abstract
Summary State‐space models require an accurate knowledge of the process error () and measurement error () covariance matrices for exact state estimation. Even though the matrix can be, in many situations, considered to be known from the measuring instrument specifications, it is still a challenge to infer the matrix online while providing reliable estimates along with a low computational cost. In this article, we propose an analytically tractable online Bayesian inference method for inferring the matrix in state‐space models. We refer to this method as approximate Gaussian variance inference (AGVI) using which we are able to treat the error variance and covariance terms in the full matrix as Gaussian hidden states and infer them simultaneously with the other hidden states in a closed‐form manner. The two case studies show that the method is able to provide statistically consistent estimates for the mean and uncertainties of the error variance terms for univariate and multivariate cases. The method also exceeds the performance of the existing adaptive Kalman filter methods both in terms of accuracy and computational efficiency.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.017 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".