Near-Optimality of the Minimum Average Redundancy Code for Almost All Monotone Sources
Bibliographic record
Abstract
Consider the source coding problem of finding the optimal code, in the sense of average redundancy, for the class of monotone sources with n symbols. The solution of this problem, known as the M code, is the Huffman code for the average distribution of the monotone sources. In this paper, we evaluate the average redundancy of the M code (on the class of monotone sources), and compare it with that of the Huffman code. It is demonstrated that for large n, although the M code is a fixed code (i.e., the codewords are independent of the symbol probabilities) for all monotone sources, its average redundancy is very close to that of the Huffman code. Moreover, it is shown that when n is large, the M code is a near-optimal code not only in the sense of average redundancy, but also the redundancy of almost all monotone sources. In particular, the redundancy of the M code converges in probability to its average value (≅0.029). As a result, the maximum redundancy of the M code, which can be as large as log n - log ln n, rarely occurs.
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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 | 0.002 | 0.022 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 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) | 0.001 | 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 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".