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Record W2056592727 · doi:10.1198/016214508000000751

Functional Additive Models

2008· article· en· W2056592727 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 the American Statistical Association · 2008
Typearticle
Languageen
FieldMathematics
TopicStatistical Methods and Inference
Canadian institutionsNatural Sciences and Engineering Research Council of Canada
Fundersnot available
KeywordsFunctional principal component analysisFunctional data analysisAdditive modelMathematicsLinear formLinear modelPrincipal component regressionRegression analysisPrincipal component analysisRegressionProper linear modelGeneralized additive modelLinear regressionCovarianceComputer scienceBayesian multivariate linear regressionEconometricsStatistics

Abstract

fetched live from OpenAlex

In commonly used functional regression models, the regression of a scalar or functional response on the functional predictor is assumed to be linear. This means that the response is a linear function of the functional principal component scores of the predictor process. We relax the linearity assumption and propose to replace it by an additive structure, leading to a more widely applicable and much more flexible framework for functional regression models. The proposed functional additive regression models are suitable for both scalar and functional responses. The regularization needed for effective estimation of the regression parameter function is implemented through a projection on the eigenbasis of the covariance operator of the functional components in the model. The use of functional principal components in an additive rather than linear way leads to substantial broadening of the scope of functional regression models and emerges as a natural approach, because the uncorrelatedness of the functional principal components is shown to lead to a straightforward implementation of the functional additive model, based solely on a sequence of one-dimensional smoothing steps and without the need for backfitting. This facilitates the theoretical analysis, and we establish the asymptotic consistency of the estimates of the components of the functional additive model. We illustrate the empirical performance of the proposed modeling framework and estimation methods through simulation studies and in applications to gene expression time course data.

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)0.012
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMetaresearch
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 score0.614
Threshold uncertainty score0.997

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.012
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 head0.087
GPT teacher head0.346
Teacher spread0.259 · 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