Locally Sparse Estimator for Functional Linear Regression Models
Bibliographic record
Abstract
Zhenhua Lina, Jiguo Caob*, Liangliang Wangb & Haonan Wangca Department of Statistical Sciences, University of Toronto, Toronto, ON, Canadab Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, BC, Canadac Department of Statistics, Colorado State University, Fort Collins, ColoradoCONTACT Jiguo Cao jiguo_cao@sfu.ca Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, BC V5A 1S6, CanadaColor versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/JCGS.Supplementary materials for this article are available online. Please go to www.tandfonline.com/r/JCGS.ABSTRACTA new locally sparse (i.e., zero on some subregions) estimator for coefficient functions in functional linear regression models is developed based on a novel functional regularization technique called “fSCAD.” The nice shrinkage property of fSCAD allows the proposed estimator to locate null subregions of coefficient functions without over shrinking nonzero values of coefficient functions. Additionally, a roughness penalty is incorporated to control the roughness of the locally sparse estimator. Our method is theoretically sounder and computationally simpler than existing methods. Asymptotic analysis reveals that the proposed estimator is consistent and can identify null subregions with probability tending to one. Extensive simulations confirm the theoretical analysis and show excellent numerical performance of the proposed method. Practical merit of locally sparse modeling is demonstrated by two real applications. Supplemental materials for the article are available online.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".