Estimation of the Entropy Functional from Dependent Samples
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Bibliographic record
Abstract
Abstract The differential entropy is importantly used in many disciplines, where the estimation of entropy is often the main research objective or the first step toward it. To estimate entropy, plug-in estimators, such as histogram based entropy estimators or kernel based entropy estimators, are commonly used. Especially, though the histogram itself performs poorly in estimating density, the histogram based entropy estimator is often employed due to its computational benefit. Many efforts have been made to understand the properties of the histogram based entropy estimator theoretically, but most of such efforts are restricted to the case of independently and identically distributed (IID) samples. In this article, we show that two histogram-based entropy estimators by Gyórfi and van der Meulen (Citation1987) are almost surely consistent when samples are from a φ-mixing process. A limited simulation study is implemented to compare those two estimators and to investigate their performance for varying intensity of dependency. In addition, we discuss the extension of -consistency of the estimators in IID setting by Hall (Citation1990) to the case of dependent samples. Keywords: Dependent samplesDifferential entropyEntropy estimationHistogramφ-mixingMathematics Subject Classification: Primary 62G05Secondary 62G20 Acknowledgment We are grateful to the editor and referees for many helpful suggestions. Johan Lim was supported by Basic Science Research Fund from College of Economics at Yonsei University.
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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 | 0.002 | 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 | 0.000 | 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