Relative Entropy (RE)-Based LTI System Modeling Equipped With Simultaneous Time Delay Estimation and Online Modeling
Bibliographic record
Abstract
This paper proposes a novel and efficient method of impulse response modeling in presence of input and noisy output of a linear time-invariant (LTI) system. The approach utilizes Relative Entropy (RE) to provide the impulse response estimate of the system with an optimum length as well as the optimum time delay. Solution of the classical methods for this system modeling use two separate steps for the time delay estimation and for the system order selection. Time delay methods focus on various proposed criteria, while the existing order selection approaches choose the optimum impulse response length based on their own criteria that are different from the time delay approaches. The strength of the proposed RE based method is in using only "one" criterion, the RE based criterion, to estimate both the time delay and the impulse response length simultaneously. The desired RE is the Kullback-Leilber divergence of the estimated distribution from its unknown true distribution. A unique probabilistic validation approach estimates this unavailable desired relative entropy and minimizes this criterion to provide the impulse response estimate. In addition, estimation of the noise variance, when the Signal to Noise Ratio (SNR) is unknown, is concurrent and is based on optimizing the same RE based criterion. The method elaborates the critical role of the data length and the SNR in data based LTI system modeling. The approach is also extended for online impulse response estimation. The proposed online method reduces computational complexity of the offline model estimation upon the arrival of a new sample. The introduced efficient stopping criterion for the online approach is extremely valuable in practical applications. Simulation results depict superiority of the RE based approach as a time delay estimator or as an order selection approach compared to the conventional methods. They also illustrate precision and efficiency of the proposed method compared to the state of the art methods in simultaneous time delay estimation and order selection. Not only RE based method outperforms the competing approaches, but also is shown to be more robust to the variations of the SNR.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".