An Iterative Algebraic Geometric Approach for Identification of Switched ARX Models with Noise
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Bibliographic record
Abstract
Abstract The algebraic geometric (AG) approach has been used to identify switched auto regressive exogenous (SARX) models in hybrid systems, and it has several advantages over other SARX identification methods. This paper is focused on improving the estimation accuracy of the AG approach for systems corrupted with indispensable noises. A stochastic hybrid decoupling polynomial (SHDP) is constructed by reformulating the hybrid decoupling polynomial (HDP) used in the original AG method. An iterative scheme is developed to estimate parameters of the SHDP, which are used to calculate the SARX model parameters. This estimation involves linear regression with multiplicative noises, therefore a novel approach is proposed to solve this regression problem. Then, the parameters are recovered from the SHDP. Finally, all these steps for SARX model identification are summarized in an algorithm called the iterative algebraic geometric (IAG) approach. Simulations and experimental validation results are shown to demonstrate the effectiveness of and the improvement made by the proposed IAG method.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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