Comparison of Structured and Weighted Total Least-Squares Adjustment Methods for Linearly Structured Errors-in-Variables Models
Bibliographic record
Abstract
The paper focuses on a specific errors-in-variables (EIV) model named the linearly structured EIV (LSEIV) model in which all the random elements of design matrix are in a linear combination of an input vector with random errors. Two existing structured total least-squares (STLS) algorithms named constrained TLS (CTLS) and structured TLS normalization (STLN) are introduced to solve the LSEIV model by treating the input and output vectors as the noisy structure vectors. For comparison purposes, the weighted TLS (WTLS) method is also performed based on the partial EIV model. Approximated accuracy assessment methods are also presented. The plane fitting and Bursa transformation examples are illustrated to demonstrate the accuracy and computational efficiency performance of the proposed algorithms. It shows that the proposed STLS and WTLS algorithms can achieve the same accuracy if the dispersion matrix of the WTLS method is constructed based on the partial EIV model.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".