Renyi's divergence and entropy rates for finite alphabet Markov sources
Bibliographic record
Abstract
In this work, we examine the existence and the computation of the Renyi divergence rate, lim/sub n/spl rarr//spl infin// 1/n D/sub /spl alpha//(p/sup (n)//spl par/q/sup (n)/), between two time-invariant finite-alphabet Markov sources of arbitrary order and arbitrary initial distributions described by the probability distributions p/sup (n)/ and q/sup (n)/, respectively. This yields a generalization of a result of Nemetz (1974) where he assumed that the initial probabilities under p/sup (n)/ and q/sup (n)/ are strictly positive. The main tools used to obtain the Renyi divergence rate are the theory of nonnegative matrices and Perron-Frobenius theory. We also provide numerical examples and investigate the limits of the Renyi divergence rate as /spl alpha//spl rarr/1 and as /spl alpha//spl darr/0. Similarly, we provide a formula for the Renyi entropy rate lim/sub n/spl rarr//spl infin// 1/n H/sub /spl alpha//(p/sup (n)/) of Markov sources and examine its limits as /spl alpha//spl rarr/1 and as /spl alpha//spl darr/0. Finally, we briefly provide an application to source coding.
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.
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 | 0.004 | 0.030 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".