Bounds on the Excess Minimum Risk via Generalized Information Divergence Measures
Bibliographic record
Abstract
Given finite-dimensional random vectors Y, X, and Z that form a Markov chain in that order (Y→X→Z), we derive the upper bounds on the excess minimum risk using generalized information divergence measures. Here, Y is a target vector to be estimated from an observed feature vector X or its stochastically degraded version Z. The excess minimum risk is defined as the difference between the minimum expected loss in estimating Y from X and from Z. We present a family of bounds that generalize a prior bound based on mutual information, using the Rényi and α-Jensen–Shannon divergences, as well as Sibson’s mutual information. Our bounds are similar to recently developed bounds for the generalization error of learning algorithms. However, unlike these works, our bounds do not require the sub-Gaussian parameter to be constant, and therefore, apply to a broader class of joint distributions over Y, X, and Z. We also provide numerical examples under both constant and non-constant sub-Gaussianity assumptions, illustrating that our generalized divergence-based bounds can be tighter than the ones based on mutual information for certain regimes of the parameter α.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.012 | 0.070 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.003 | 0.009 |
| Open science | 0.003 | 0.006 |
| Research integrity | 0.002 | 0.006 |
| Insufficient payload (model declined to judge) | 0.003 | 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 source (direct Gemma or distilled Codex), 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".