On Approximation of System Behavior From Large Noisy Data Using Statistical Properties of Measurement Noise
Bibliographic record
Abstract
This paper develops a method to determine an approximate behavior of a given linear time-invariant dynamical system from noise-corrupted data, which can be used for both data-driven simulation and predictive control using the behavioral systems theory. The system input and output are assumed to be measured subject to additive zero-mean white noise with known covariance. From the measured big data set, an approximated representation of the true behavior of the system is constructed using the statistical properties of measurement noise. The proposed construction method has no structural constraint on the representation. When the size of the measured data set is large, the proposed approximate representation converges in probability to one that represents the true behavior of the system. This allows data-driven simulation and control to be performed using simple convex quadratic programming algorithms. Furthermore, a Kalman filter-like algorithm is developed for better prediction of future output. A numerical example is presented to illustrate the proposed method and its efficacy under high measurement noise levels.
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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 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".