Robust changepoint detection in the variability of multivariate functional data
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
We consider the problem of robustly detecting changepoints in the variability of a sequence of independent multivariate functions. We develop a novel changepoint procedure, called the functional Kruskal–Wallis for covariance changepoint procedure, based on rank statistics and multivariate functional data depth. The functional Kruskal–Wallis for covariance changepoint procedure allows the user to test for at most one changepoint or an epidemic period, or to estimate the number and locations of an unknown number of changepoints in the data. We show that when the ‘signal-to-noise’ ratio is bounded below, the changepoint estimates produced by the functional Kruskal–Wallis for covariance changepoint procedure attain the minimax localisation rate for detecting general changes in distribution in the univariate setting. We also provide the behaviour of the proposed test statistics for the at-most-one-change and epidemic settings under the null hypothesis and, as a simple consequence of our main result, these tests are consistent. In simulation, we show that our method is particularly robust when compared to similar changepoint methods. We present an application of the functional Kruskal–Wallis for covariance changepoint procedure to intraday asset returns and functional magnetic resonance imaging scans. As a by-product of our main result, we provide a concentration result for integrated functional depth functions, which may be of general interest.
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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 | 0.005 | 0.040 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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