Transformation Invariant Control ofVoxel-Wise False Discovery Rate
Bibliographic record
Abstract
Multiple testing for statistical maps remains a critical and challenging problem in brain mapping. Since the false discovery rate (FDR) criterion was introduced to the neuroimaging community a decade ago, many variations have been proposed, mainly to enhance detection power. However, a fundamental geometrical property known as transformation invariance has not been adequately addressed, especially for the voxel-wise FDR. Correction of multiple testing applied after spatial transformation is not necessarily equivalent to transformation applied after correction in the original space. Without the invariance property, assigning different testing spaces will yield different results. We find that normalized residuals of linear models with Gaussian noises are uniformly distributed on a unit high-dimensional sphere, independent of t-statistics and F-statistics. By defining volumetric measure in the hyper-spherical space mapped by normalized residuals, instead of the image's Euclidean space, we can achieve invariant control of the FDR under diffeomorphic transformation. This hyper-spherical measure also reflects intrinsic "volume of randomness" in signals. Experiments with synthetic, semi-synthetic and real images demonstrate that our method significantly reduces FDR inconsistency introduced by the choice of testing spaces.
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How this classification was reachedexpand
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 | 0.004 | 0.012 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".