Optimal depth-first strategies for and-or trees
Bibliographic record
Abstract
A probabilistic boolean expression (PBE) consists of a boolean expression over a set of boolean variables, each with a corresponding cost and probability value that indicates respectively the cost of determining a variable's value and the probability that the value is true. Given a PBE, a resolution strategy is a sequential testing algorithm that determines the value of the expression, where each test is a query of the value of one variable. A strategy is optimal if its expected cost is minimum, over all possible strategies. The minimum cost resolution strategy problem (MRSP) is to find an optimal strategy of a given PBE. As MRSP is NP-hard in general, we consider the restricted case in which each variable occurs exactly once; the corresponding expressions are sometimes called and-or trees, since they have a tree representation in which internal nodes correspond to (boolean) operators and leaf nodes correspond to variables. We further assume that variables are independent, and focus on a depth-first algorithm, dfa, that orders subexpressions within subtrees based on probability/cost ratios. Our main results are that dfa produces optimal strategies for and-or trees with depth 1 or 2, but can be very bad for and-or trees with depth 3 or more.
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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 | 0.002 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".