Alternating weighted least squares parameter estimation for biological S-systems
Bibliographic record
Abstract
The S-system, which is a set of nonlinear ordinary differential equations and derived from the generalized mass action law, is a consistent model to describe various biological systems. Parameters in S-systems contain important biological information and yet can not be obtained directly from experiments. Therefore, the parameter estimation methods are a choice to estimate parameters in S-systems. However, the parameter estimation for this model turns out to be a complex nonlinear optimization problem. A novel method, alternating weighted least squares (AWLS), is proposed in this paper to estimate the parameters in S-systems. The fast deterministic AWLS method takes advantage of the special structure of the S-system model and reduces solving the nonlinear optimization problem into alternately solving weighed least squares problems which have analytical solutions. The effectiveness of AWLS is demonstrated by the simulation studies and the results show that the AWLS outperforms the existing alternating regression method.
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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".