A new reproducing kernel‐based nonlinear dimension reduction method for survival data
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Bibliographic record
Abstract
Abstract Based on the theories of sliced inverse regression (SIR) and reproducing kernel Hilbert space (RKHS), a new approach RDSIR (RKHS‐based Double SIR) to nonlinear dimension reduction for survival data is proposed. An isometric isomorphism is constructed based on the RKHS property, then the nonlinear function in the RKHS can be represented by the inner product of two elements that reside in the isomorphic feature space. Due to the censorship of survival data, double slicing is used to estimate the weight function to adjust for the censoring bias. The nonlinear sufficient dimension reduction (SDR) subspace is estimated by a generalized eigen‐decomposition problem. The asymptotic property of the estimator is established based on the perturbation theory. Finally, the performance of RDSIR is illustrated on simulated and real data. The numerical results show that RDSIR is comparable with the linear SDR method. Most importantly, RDSIR can also effectively extract nonlinearity from survival 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 | 0.004 | 0.013 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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