Learning and Testing Junta Distributions
Bibliographic record
Abstract
We consider the problem of learning distributions in the presence of irrelevant features. This problem is formalized by introducing a new notion of k-junta distributions. Informally, a distribution D over the domain X is a k-junta distribution with respect to another distribution U over the same domain if there is a set J ⊆ [n] of size |J | ≤ k that captures the difference between D and U . We show that it is possible to learn k-junta distributions with respect to the uniform distribution over the Boolean hypercube {0, 1} in time poly(n, 1/ ). This result is obtained via a new Fourier-based learning algorithm inspired by the Low-Degree Algorithm of Linial, Mansour, and Nisan (1993). We also consider the problem of testing whether an unknown distribution is a k-junta distribution with respect to the uniform distribution. We give a nearly-optimal algorithm for this task. Both the analysis of the algorithm and the lower bound showing its optimality are obtained by establishing connections between the problem of testing junta distributions and testing uniformity of weighted collections of distributions.
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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 | 0.109 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.003 | 0.012 |
| Open science | 0.005 | 0.005 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.002 | 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".