Fast Approximate Multioutput Gaussian Processes
Why this work is in the frame
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Bibliographic record
Abstract
Gaussian processes regression models are an appealing machine learning method as they learn expressive nonlinear models from exemplar data with minimal parameter tuning and estimate both the mean and covariance of unseen points. However, cubic computational complexity growth with the number of samples has been a long standing challenge. Training requires the inversion of $N \times N$N×N kernel at every iteration, whereas regression needs computation of an $m \times N$m×N kernel, where $N$N and $m$m are the number of training and test points, respectively. This work demonstrates how approximating the covariance kernel using eigenvalues and functions leads to an approximate Gaussian process with significant reduction in training and regression complexity. Training now requires computing only an $N \times n$N×n eigenfunction matrix and an $n \times n$n×n inverse, where $n$n is a selected number of eigenvalues. Furthermore, regression now only requires an $m \times n$m×n matrix. Finally, in a special case, the hyperparameter optimization is completely independent from the number of training samples. The proposed method can regress over multiple outputs, learn the correlations between them, and estimate their derivatives to any order. The computational complexity reduction, regression capabilities, multioutput correlation learning, and comparison to the state of the art are demonstrated in simulation examples. Finally we show how the proposed approach can be utilized to model real human 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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 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 it