Learning with aggregation and correlation in the presence of large fluctuations
Bibliographic record
Abstract
Consider a scenario where one aims to learn models from dynamic and evolving data being characterized by very large fluctuations that are neither attributable to noise nor outliers. This may be the case, for instance, when predicting the potential future damages of earthquakes or oil spills, or when conducting financial data analysis. If follows that, in such a situation, the standard central limit theorem does not apply, since the associated Gaussian distribution exponentially suppresses large fluctuations. In this paper, we present an analysis of data aggregation and correlation in such scenarios. To this end, we introduce the Lévy, or stable, distribution which is a generalization of the Gaussian distribution. Our theoretical conclusions are illustrated with various simulations, as well as against a benchmarking financial database. We show which specific strategies should be adopted for aggregation, depending on the stability exponent of the Lévy distribution. Our results firstly show scenarios where it may be impossible to determine the mean and the standard deviation of an aggregate. Secondly, we discuss the case where an aggregate may have to be characterized with its largest fluctuations. Thirdly, we illustrate that the correlation in between two attributes may be underestimated if a Gaussian distribution is erroneously assumed.
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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 | 0.010 | 0.035 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| 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 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".