A fast convergence two-step procedure for AR modeling of power spectral densities
Bibliographic record
Abstract
A new technique for the minimization of customary cost functions for all-pole modeling of power spectral densities is presented. In the literature, optimizations are usually based on unnormalized autoregressive (AR) coefficients. In contrast, the proposed method is centered on a two-step descent using normalized AR coefficients on the one hand and the residual power on the other hand. For each cost function, efficient ways to obtain gradients are derived and a descent-based optimization is formulated. The resulting procedure converges significantly faster than the corresponding gradient descents on un-normalized coefficients, while still being computationally efficient. In addition to the traditional Yule-Walker distance, the Itakura-Saito distance, the COSH distance, the RMS log-spectral ratio distance, and a mean-squared error cost function are treated. Convergence results and curves are presented accordingly for different situations.
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How this classification was reachedexpand
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 | 0.000 | 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 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".