Exactly Sparse Gaussian Variational Inference with Application to\n Derivative-Free Batch Nonlinear State Estimation
Bibliographic record
Abstract
We present a Gaussian Variational Inference (GVI) technique that can be\napplied to large-scale nonlinear batch state estimation problems. The main\ncontribution is to show how to fit both the mean and (inverse) covariance of a\nGaussian to the posterior efficiently, by exploiting factorization of the joint\nlikelihood of the state and data, as is common in practical problems. This is\ndifferent than Maximum A Posteriori (MAP) estimation, which seeks the point\nestimate for the state that maximizes the posterior (i.e., the mode). The\nproposed Exactly Sparse Gaussian Variational Inference (ESGVI) technique stores\nthe inverse covariance matrix, which is typically very sparse (e.g.,\nblock-tridiagonal for classic state estimation). We show that the only blocks\nof the (dense) covariance matrix that are required during the calculations\ncorrespond to the non-zero blocks of the inverse covariance matrix, and further\nshow how to calculate these blocks efficiently in the general GVI problem.\nESGVI operates iteratively, and while we can use analytical derivatives at each\niteration, Gaussian cubature can be substituted, thereby producing an efficient\nderivative-free batch formulation. ESGVI simplifies to precisely the\nRauch-Tung-Striebel (RTS) smoother in the batch linear estimation case, but\ngoes beyond the 'extended' RTS smoother in the nonlinear case since it finds\nthe best-fit Gaussian (mean and covariance), not the MAP point estimate. We\ndemonstrate the technique on controlled simulation problems and a batch\nnonlinear Simultaneous Localization and Mapping (SLAM) problem with an\nexperimental dataset.\n
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".