Structure detection of NARMAX models using bootstrap methods
Bibliographic record
Abstract
Systems described by nonlinear difference equations, linear-in-the-parameters, which expand the current output in terms of present and past inputs and past outputs are considered NARMAX (Nonlinear AutoRegressive, Moving Average eXogenous) models. Many systems are described by NARMAX models using only a few terms. However, depending on the order of the system, the number of candidate terms can be very large. Selection of a subset of these candidate terms is necessary for an efficient system description. This remains an unresolved issue in system identification for over-parameterized models. A bootstrap based structure detection algorithm is proposed as a means of determining the structure of highly over-parameterized models. The performance of our bootstrap structure detection technique was evaluated by using it to estimate the structure of two NARMAX models, with colored input and white, zero-mean, output additive noise, and comparing the results to those of the t-test and stepwise regression. The proposed method is simple to use and is robust in the presence of noise.
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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 | 0.020 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".