RKHS‐based functional nonparametric regression for sparse and irregular longitudinal data
Why this work is in the frame
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Bibliographic record
Abstract
Abstract This paper focuses on sparse and irregular longitudinal data with a scalar response. The predictor consists of sparse and irregular observations on predictor trajectories, potentially contaminated with measurement errors. For this type of data, Yao, Müller, & Wang (2005a) proposed a principal components analysis through conditional expectation (PACE) approach, which is capable of predicting each predictor trajectory based on sparse and irregular observations. Nonparametric functional data analysis provides an attractive alternative due to its high flexibility. Early work includes functional additive models as in Müller & Yao (2008) and Ferraty & Vieu (2006), which are mainly based on kernel smoothing methods. In this work, we propose a new functional nonparametric regression framework based on reproducing kernel Hilbert spaces (RKHS). The proposed method involves two steps. The first step is to estimate each predictor trajectory based on sparse and irregular observations using PACE. The second step is to conduct a RKHS‐based nonparametric regression using the estimated predictor trajectories. Our approach shows improvement over existing methods in simulation studies as well as in a real data example. The Canadian Journal of Statistics 42: 204–216; 2014 © 2014 Statistical Society of Canada
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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 | 0.014 |
| 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) | 0.000 | 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