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Record W2603865942

Exact L 2 -Norm Plane Separation

2007· article· fr· W2603865942 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

VenuePolyPublie (École Polytechnique de Montréal) · 2007
Typearticle
Languagefr
FieldMathematics
TopicAdvanced Optimization Algorithms Research
Canadian institutionsHEC MontréalPolytechnique MontréalGroup for Research in Decision Analysis
Fundersnot available
KeywordsNorm (philosophy)Quadratic equationExact solutions in general relativityRegular polygonMathematicsComputationHeuristicMathematical optimizationApplied mathematicsComputer scienceAlgorithmMathematical analysisGeometry
DOInot available

Abstract

fetched live from OpenAlex

We consider the problem of separating two sets of points in an n-dimensional real space with a (hyper)plane that minimizes the sum of Lp-norm distances to the plane of points lying on the wrong side of it. Despite recent progress, practical techniques for the exact solution of cases other than the L1 and L∞-norm were unavailable. We propose and implement a new approach, based on non-convex quadratic programming, for the exact solution of the L2-norm case. We solve in reasonable computing times artificial problems of up to 20000 points (in 6 dimensions) and 13 dimensions (with 2000 points). We also observe that, for difficult real-life instances from the UCI Repository, computation times are substantially reduced by incorporating heuristic results in the exact solution process. Finally, we compare the classification performance of the planes obtained for the L1, L2 and L∞ formulations. It appears that, despite the fact that L2 formulation is computationally more expensive, it does not give significantly better results than the L1 and L∞ formulations.

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)0.003
metaresearch head score (Gemma)0.002
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Insufficient payload (model declined to judge)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Simulation or modeling · Consensus signal: none
GenreCandidate signal: Methods · Consensus signal: Methods
Teacher disagreement score0.677
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0030.002
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0010.002
Science and technology studies0.0010.000
Scholarly communication0.0000.001
Open science0.0010.000
Research integrity0.0010.001
Insufficient payload (model declined to judge)0.0010.000

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 head0.022
GPT teacher head0.320
Teacher spread0.298 · 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