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Record W4408757431 · doi:10.1002/wics.70013

Nuclear Norm Regularization

2025· review· en· W4408757431 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.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueWiley Interdisciplinary Reviews Computational Statistics · 2025
Typereview
Languageen
FieldEngineering
TopicSparse and Compressive Sensing Techniques
Canadian institutionsUniversity of Toronto
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsMathematicsRegularization (linguistics)Norm (philosophy)Computer scienceApplied mathematicsEconometricsArtificial intelligencePhilosophyEpistemology

Abstract

fetched live from OpenAlex

ABSTRACT Nuclear norm, also known as trace norm, has been widely used in statistical machine learning. Nuclear norm regularization has emerged as an important tool for addressing various statistical problems involving the estimation of low‐rank matrices, particularly in tasks such as matrix completion and reduced rank regression. This review delves into the foundational models, practical implementations, and recent advancements in nuclear norm regularization. We discuss key implementation techniques, including semidefinite programming and singular value thresholding, which enable efficient solutions to low‐rank matrix estimation problems. Additionally, we examine the application of nuclear norm regularization in matrix covariate and matrix response regression, as well as its extension to tensor regression problems. Our study highlights the versatility and efficacy of nuclear norm regularization in providing both theoretical guarantees and scalable computational methods. Future research directions include improving computational efficiency, refining conditions for theoretical guarantees and extending applications to higher‐order tensors.

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 categoriesMeta-epidemiology (narrow)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: none
GenreCandidate signal: Review · Consensus signal: Review
Teacher disagreement score0.787
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0020.000
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 head0.031
GPT teacher head0.332
Teacher spread0.300 · 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