High‐Dimensional Multiresponse Partially Functional Linear Regression
Why this work is in the frame
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Bibliographic record
Abstract
We propose a new class of high-dimensional multiresponse partially functional linear regressions (MR-PFLRs) to investigate the relationship between scalar responses and a set of explanatory variables, which include both functional and scalar types. In this framework, both the dimensionality of the responses and the number of scalar covariates can diverge to infinity. To account for within-subject correlation, we develop a functional principal component analysis (FPCA)-based penalized weighted least squares estimation procedure. In this approach, the precision matrix is estimated using penalized likelihoods, and the regression coefficients are then estimated through the penalized weighted least squares method, with the precision matrix serving as the weight. This method allows for the simultaneous estimation of both functional and scalar regression coefficients, as well as the precision matrix, while identifying significant features. Under mild conditions, we establish the consistency, rates of convergence, and oracle properties of the proposed estimators. Simulation studies demonstrate the finite-sample performance of our estimation method. Additionally, the practical utility of the MR-PFLR model is showcased through an application to Alzheimer's disease neuroimaging initiative (ADNI) data.
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Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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 it