Some Estimation Methods for Overdetermined Integer Linear Models
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Bibliographic record
Abstract
Estimating the integer parameter vector in a linear model with additive Gaussian noise arises from many applications, including communications, control, and global navigation satellite systems.For an overdetermined integer linear model, the optimal method is to solve an integer least squares (ILS) problem, which is unfortunately NP-hard; and a suboptimal method often used in applications which needs a fast solution is Babai's method.Unfortunately the performance of the Babai estimator can be much worse than that of the ILS estimator.This thesis proposes two new estimation methods and analyzes the performance of the two estimators.The two proposed methods are between the ILS method and Babai's method in terms of time complexity and estimation quality.Simulation results show that these two methods can be much more efficient than the ILS method, while the quality of the two estimators can be much better than that of the Babai estimator.In addition, the thesis analyzes the performance of the randomized Babai estimator and some interesting and useful theoretical results are obtained.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.003 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it