Hierarchical tucker tensor regression: Application to brain imaging data analysis
Why this work is in the frame
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Bibliographic record
Abstract
We present a novel generalized linear tensor regression model, which takes tensor-variate inputs as covariates and finds low-rank (almost) best approximation of regression coefficient arrays using hierarchical Tucker decomposition. With limited sample size, our model is highly compact and extremely efficient as it requires only O(dr <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> + dpr) parameters for order d tensors of mode size p and rank r, which avoids the exponential growth in d, in contrast to O(r <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sup> + dpr) parameters of Tucker regression modeling. Our model also maintains the flexibility like classical Tucker regression by allowing distinct ranks on different modes according to a dimension tree structure. We evaluate our new model on both synthetic data and real-life MRI images to show its effectiveness.
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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 | 0.000 | 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