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Record W4286611073 · doi:10.1145/3528223.3530095

Regression-based Monte Carlo integration

2022· article· en· W4286611073 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

VenueACM Transactions on Graphics · 2022
Typearticle
Languageen
FieldMathematics
TopicMathematical Approximation and Integration
Canadian institutionsUniversity of WaterlooÉcole de Technologie SupérieureMcGill University
Fundersnot available
KeywordsMonte Carlo methodMonte Carlo integrationEstimatorApplied mathematicsMathematicsQuasi-Monte Carlo methodHybrid Monte CarloComputer scienceMathematical optimizationCalculus (dental)AlgorithmMarkov chain Monte CarloStatistics

Abstract

fetched live from OpenAlex

Monte Carlo integration is typically interpreted as an estimator of the expected value using stochastic samples. There exists an alternative interpretation in calculus where Monte Carlo integration can be seen as estimating a constant function---from the stochastic evaluations of the integrand---that integrates to the original integral. The integral mean value theorem states that this constant function should be the mean (or expectation) of the integrand. Since both interpretations result in the same estimator, little attention has been devoted to the calculus-oriented interpretation. We show that the calculus-oriented interpretation actually implies the possibility of using a more complex function than a constant one to construct a more efficient estimator for Monte Carlo integration. We build a new estimator based on this interpretation and relate our estimator to control variates with least-squares regression on the stochastic samples of the integrand. Unlike prior work, our resulting estimator is provably better than or equal to the conventional Monte Carlo estimator. To demonstrate the strength of our approach, we introduce a practical estimator that can act as a simple drop-in replacement for conventional Monte Carlo integration. We experimentally validate our framework on various light transport integrals. The code is available at https://github.com/iribis/regressionmc.

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 categoriesInsufficient payload (model declined to judge)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Methods · Consensus signal: none
Teacher disagreement score0.901
Threshold uncertainty score0.999

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.001
Science and technology studies0.0010.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0020.000

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 head0.069
GPT teacher head0.323
Teacher spread0.253 · 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