Optimizing Erlangization-based approximations for finite discrete distributions and discrete phase-type distributions
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
In He et al.[Citation8], continuous phase-type (PH) distributions are constructed to approximate finite discrete probability distributions and discrete PH-distributions. The approximations are based on Erlangization with a fixed number of phases. In this article, we first introduce continuous PH approximations with Erlang distributions of different orders. Then we develop an algorithm to find the continuous PH approximation with the minimum variance, among all such PH approximations with the same total number of phases. Thus, the proposed continuous PH approximations lead to a smaller gap between the variances of the Erlangization-based approximations and the original discrete random variables, which is achieved without adding more phases. The new approximations are useful to mitigate the burden in computation caused by the large number of phases needed in Erlangization approximation. Stochastic dominance is shown between the original (discrete) distributions and the approximations, which leads to bounds on the quantities of original distributions and/or stochastic models (e.g., reliability models). The approximation method is applied to analyze reliability models and a COVID-19 isolation program.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.002 | 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 it