Robust functional principal component regression
Bibliographic record
Abstract
This diploma thesis is about robust functional principal component regression. It is based on functional data where we observe underlying stochastic processes. In a regression setting we want to regress a scalar response onto such stochastic process. As in a multivariate setting this regression is sensitive to outliers in both response and explaining variable. That means we want to robustify this regression. A common technique for such model is to use functional principal components of the corresponding process. In this thesis we give a short overview of functional data analysis including functional principal componentsas well as a brief introduction to robust statistics. We compare two different types of estimators. One is made for regular, densely observed data whereas a new approach for irregular, longitudinal data is proposed. In a simulation study all estimators are applied to 2 models in various settings. These cover regular and irregular as well as dense or sparse data. The data is used in both clean and contaminated fashion. The results of this simulation study are partly satisfying, especially in regular settings. However, in very sparse, irregular settings the estimators are not as good. Finally, the estimators are applied to a real world example. In the Canadian Weather data we regress the annual precipitationonto temperature curves in various locations. All methods perform comparably while the newly proposed methods seem to work the best.
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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 | 0.004 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.010 | 0.005 |
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".