Lower Bounds for Computing Statistical Depth
Bibliographic record
Abstract
Given a nite set of points S, two measures of the depth of a query point with respect to S are the Simplicial depth of Liu and the Halfspace depth of Tukey (also known as Location depth). We show that computing these depths requires n log n) time, which matches the upper bound complexities of the algorithms of Rousseeuw and Ruts. Our lower bound proofs may also be applied to two bivariate sign tests: that of Hodges, and that of Oja and Nyblom. 1 Introduction The notion of depth for a point with respect to a data set has been studied extensively by statisticians and computer scientists. Applications include robust estimation, hypothesis testing, graphical display [MRR + 01], data description, multivariate condence regions, p-values, quality indices, control charts [RR96], and even voting theory [RR99]. In general, the depth of a point quanties the degree to which is centrally located in a data set. An introduction to several denitions of depth, as well as their prop...
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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 | 0.012 | 0.095 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.006 | 0.007 |
| Science and technology studies | 0.002 | 0.007 |
| Scholarly communication | 0.007 | 0.023 |
| Open science | 0.005 | 0.013 |
| Research integrity | 0.003 | 0.011 |
| Insufficient payload (model declined to judge) | 0.011 | 0.003 |
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".