Bibliographic record
Abstract
Abstract In this article we lay out some basic structures, technical machineries, and key applications, of Linear Operator‐Based Statistical Analysis, and organize them toward a unified paradigm. This paradigm can play an important role in analyzing big data due to the nature of linear operators: they process large number of functions in batches. The system accommodates at least four statistical settings: multivariate data analysis, functional data analysis, nonlinear multivariate data analysis via kernel learning, and nonlinear functional data analysis via kernel learning. We develop five linear operators within each statistical setting: the covariance operator, the correlation operator, the conditional covariance operator, the regression operator, and the partial correlation operator, which provide us with a powerful means to study the interconnections between random variables or random functions in a nonparametric and comprehensive way. We present a case study tracing the development of sufficient dimension reduction, and describe in detail how these linear operators play increasingly critical roles in its recent development. We also present a coordinate mapping method which can be systematically applied to implement these operators at the sample level. The Canadian Journal of Statistics 46: 79–103; 2018 © 2017 Statistical Society of Canada
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How this classification was reachedexpand
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 | 0.000 | 0.001 |
| 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 | 0.001 | 0.000 |
| Open science | 0.002 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".