A simple sketching algorithm for entropy estimation over streaming data.
Bibliographic record
Abstract
We consider the problem of approximating the empirical Shannon entropy of a highfrequency data stream under the relaxed strict-turnstile model, when space limitations make exact computation infeasible. An equivalent measure of entropy is the Renyi entropy that depends on a constant α. This quantity can be estimated efficiently and unbiasedly from a low-dimensional synopsis called an α-stable data sketch via the method of compressed counting. An approximation to the Shannon entropy can be obtained from the Renyi entropy by taking α sufficiently close to 1. However, practical guidelines for parameter calibration with respect to α are lacking. We avoid this problem by showing that the random variables used in estimating the Renyi entropy can be transformed to have a proper distributional limit as α approaches 1: the maximally skewed, strictly stable distribution with α = 1 defined on the entire real line. We propose a family of asymptotically unbiased log-mean estimators of the Shannon entropy, indexed by a constant ζ > 0, that can be computed in a single-pass algorithm to provide an additive approximation. We recommend the log-mean estimator with ζ = 1 that has exponentially decreasing tail bounds on the error probability, asymptotic relative efficiency of 0.932, and near-optimal computational complexity. Appearing in Proceedings of the 16 International Conference on Artificial Intelligence and Statistics (AISTATS) 2013, Scottsdale, AZ, USA. Volume 31 of JMLR: W&CP 31. Copyright 2013 by the authors.
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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 | 0.018 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".