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Record W3046075819 · doi:10.5539/ijsp.v9n5p40

Estimating Smooth and Convex Functions

2020· article· en· W3046075819 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.

venuePublished in a venue whose home country is Canada.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenueInternational Journal of Statistics and Probability · 2020
Typearticle
Languageen
FieldDecision Sciences
TopicAdvanced Bandit Algorithms Research
Canadian institutionsnot available
Fundersnot available
KeywordsMathematicsDifferentiable functionEstimatorConvex functionRegular polygonFunction (biology)CombinatoricsApplied mathematicsConvex combinationConvex optimizationMathematical optimizationMathematical analysisStatistics

Abstract

fetched live from OpenAlex

We propose a new method for estimating an unknown regression function $f_*:[\alpha, \beta] \rightarrow \mathbb{R}$ from a dataset $(X_1, Y_1), \dots, (X_n,$ $Y_n)$ when the only information available on $f_*$ is the fact that $f_*$ is convex and twice differentiable. In the proposed method, we fit a convex function to the dataset that minimizes the sum of the roughness of the fitted function and the average squared differences between the fitted function and $f_*$. We prove that the proposed estimator can be computed by solving a convex quadratic programming problem with linear constraints. Numerical results illustrate the superior performance of the proposed estimator compared to existing methods when i) $f_*$ is the price of a stock option as a function of the strike price and ii) $f_*$ is the steady-state mean waiting time of a customer in a single server queue.

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)0.001
metaresearch head score (Gemma)0.010
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMetaresearch
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Other design · Consensus signal: none
GenreCandidate signal: Methods · Consensus signal: none
Teacher disagreement score0.926
Threshold uncertainty score0.998

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.010
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 head0.116
GPT teacher head0.424
Teacher spread0.308 · 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