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Generalized Stratified Sampling Using the Hilbert Curve

2003· article· en· W2010306732 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueJournal of Graphics Tools · 2003
Typearticle
Languageen
FieldEngineering
TopicManufacturing Process and Optimization
Canadian institutionsUniversity of Waterloo
Fundersnot available
KeywordsStratification (seeds)Hilbert spaceStratified samplingSampling (signal processing)MathematicsCurse of dimensionalityMonte Carlo methodApplied mathematicsConvergence (economics)Coherence (philosophical gambling strategy)AlgorithmStatisticsComputer scienceMathematical analysisTelecommunications

Abstract

fetched live from OpenAlex

Abstract Stratified sampling is a widely used strategy to improve convergence in Monte Carlo techniques. The efficiency of a stratification technique mainly depends on the coherence of the strata. This paper presents an approach to generate an arbitrary number of coherent strata, independently of the dimensionality of the domain, using the Hilbert space-filling curve. Using this approach, it is possible to draw an arbitrary number of stratified samples from higher dimensional spaces using only one-dimensional stratification. This technique can also be used to generalize nonuniform stratified sampling. Source code is available online.

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.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Simulation or modeling · Consensus signal: Simulation or modeling
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.372
Threshold uncertainty score0.274

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.054
GPT teacher head0.270
Teacher spread0.215 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it