Decomposing Gaussians with unknown covariance
Why this work is in the frame
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Bibliographic record
Abstract
Abstract Common workflows in machine learning and statistics rely on the ability to partition the information in a dataset into independent portions. Recent work has shown that this may be possible even when conventional sample splitting is not, such as when the number of samples, $ n $, is one or when observations are not independent and identically distributed. In the case of multivariate Gaussian data, these alternatives to sample splitting require knowledge of the covariance matrix. In many important problems, such as in spatial or longitudinal data analysis and in graphical modelling, the covariance matrix may be unknown and even of primary interest. Therefore, in this work we develop new approaches for decomposing multivariate Gaussians with unknown covariance. First, we present a general algorithm that encompasses all previous decomposition methods for Gaussian data as special cases and which can further handle the case of unknown covariance. It yields a new and more flexible alternative to sample splitting when $ n \,{\gt}\, 1 $. When $ n=1 $, we prove that it is impossible to partition the information in a multivariate Gaussian into independent portions without knowing the covariance matrix. Hence, we use the general algorithm to decompose a single multivariate Gaussian with unknown covariance into dependent parts with tractable conditional distributions and demonstrate their use for inference and validation. The proposed decomposition strategy extends naturally to Gaussian processes. In simulations and for electroencephalography data, we apply these decompositions to the tasks of model selection and post-selection inference in settings where alternative strategies are unavailable.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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