EM algorithm on the approximation of arbitrary PDFs by Gaussian, gamma and lognormal mixture distributions
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Bibliographic record
Abstract
In wireless communication systems, finding a model to describe shadow fading that is easy-to-work and has a good fidelity with the observed phenomena is a topic that is receiving the attention of several studies. This is because the well-known lognormal model, discussed in the literature, does not describe accurately what is experienced in the real world. Because gamma distribution has closed form expressions a few authors have proposed the use of the gamma PDF in order to model shadowing effect, since it facilitates the mathematical analysis of the system being designed. Other authors have proposed the use of lognormal mixture model to approximate the probability distribution of the local mean received power. This last approach yielded good results when compared to the distribution of actual measurements. Motivated by these facts, we present in this paper a study on the approximation of arbitrary PDFs by Gaussian, gamma, and lognormal mixture models using Expectation Maximization (EM) algorithm to estimate the necessary parameters. We show the results of our implementation of the algorithms and discuss important insights about them.
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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 | 0.000 |
| 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 | 0.001 | 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