Non-asymptotic equipartition properties for independent and identically distributed sources
Bibliographic record
Abstract
Given an independent and identically distributed source X = {Xi}i=1∞with finite Shannon entropy or differential entropy (as the case may be) H(X), the non-asymptotic equipartition property (NEP) with respect to H(X) is established, which characterizes, for any finite block length n, how close -1/n ln p(X1X2...Xn) is to H(X) by determining the information spectrum of X1X2...Xn, i.e., the distribution of -1/n ln p(X1X2...Xn). Non-asymptotic equipartition properties (with respect to conditional entropy, mutual information, and relative entropy) in a similar nature can also be established [3]. These non-asymptotic equipartition properties are instrumental to the development of non-asymptotic coding (including both source and channel coding) results in information theory in the same way as the asymptotic equipartition property to all asymptotic coding theorems established so far in information theory. As an example, the NEP with respect to H(X) is used to establish a non-asymptotic fixed rate source coding theorem, which reveals, for any finite block length n, a complete picture about the tradeoff between the minimum rate of fixed rate coding of X1...Xnand error probability when the error probability is a constant, or goes to 0 with block length n at a sub-polynomial n-α, 0-α, α ≥ 1, or sub-exponential e-nα, 01X2...Xnwith error probability Θ(n-α/(√in n)) is H(X) + √(σH2(X)(2α)) √(ln n/n) + O(ln n/n), where α >; 0 and σH2(X) = E[-lnp(X1)]2- H2(X) is the information variance of X. With the help of the NEP with respect to other information quantities, non-asymptotic channel coding theorems of similar nature will be established in a separate paper.
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 | 0.012 | 0.085 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".