Mutual information is critically dependent on prior assumptions: would the <i>correct</i> estimate of mutual information please identify itself?
Bibliographic record
Abstract
MOTIVATION: Mutual information (MI) is a quantity that measures the dependence between two arbitrary random variables and has been repeatedly used to solve a wide variety of bioinformatic problems. Recently, when attempting to quantify the effects of sampling variance on computed values of MI in proteins, we encountered striking differences among various novel estimates of MI. These differences revealed that estimating the 'true' value of MI is not a straightforward procedure, and minor variations of assumptions yielded remarkably different estimates. RESULTS: We describe four formally equivalent estimates of MI, three of which explicitly account for sampling variance, that yield non-equal values of MI given exact frequencies. These MI estimates are essentially non-predictive of each other, converging only in the limit of implausibly large datasets. Lastly, we show that all four estimates are biologically reasonable estimates of MI, despite their disparity, since each is actually the Kullback-Leibler divergence between random variables conditioned on equally plausible hypotheses. CONCLUSIONS: For sparse contingency tables of the type universally observed in protein coevolution studies, our results show that estimates of MI, and hence inferences about physical phenomena such as coevolution, are critically dependent on at least three prior assumptions. These assumptions are: (i) how observation counts relate to expected frequencies; (ii) the relationship between joint and marginal frequencies; and (iii) how non-observed categories are interpreted. In any biologically relevant data, these assumptions will affect the MI estimate as much or more-so than observed data, and are independent of uncertainty in frequency parameters.
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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 | 0.001 | 0.001 |
| 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 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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".