Mutual information spectra for comparing categorical maps
Bibliographic record
Abstract
The continual accumulation of categorical data sets, presented as nominal categories mapped onto regular grids, provides for the increased desire to compare the patterns observed between these maps. We present a measurement scheme for the comparison of categorical maps that decomposes the differences in multidimensional nested coincidence tables according to variables that record occurrence frequencies of categories (Z), at levels of spatial aggregation (Y), on specific maps (X). Sequences of conditional entropies computed according to the specific questions asked (e.g. is there coincidence between colours and locations), characterize the correspondence between the three types of variables in common units (bits) measured by mutual information. The form of these sequences, as a variable runs from coarse to fine detail, referred to as spectra, provide meaningful characterizations of the similarities/differences between categorical maps, including their spatial configuration. We introduce the information theory‐based conceptual framework and illustrate its beneficial application by comparing a series of demonstration maps.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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 | 0.000 |
| 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 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".