Active Stratified Sampling with Clustering-Based Type Systems for Predicting the Search Tree Size of Problems with Real-Valued Heuristics
Bibliographic record
Abstract
In this paper we advance the line of research launched by Knuth which was later improved by Chen for predicting the size of the search tree expanded by heuristic search algorithms such as IDA*. Chen's Stratified Sampling (SS) uses a partition of the nodes in the search tree called type system to guide its sampling. Recent work has shown that SS using type systems based on integer-valued heuristic functions can be quite effective. However, type systems based on real-valued heuristic functions are often too large to be practical. We use the k-means clustering algorithm for creating effective type systems for domains with real-valued heuristics. Orthogonal to the type systems, another contribution of this paper is the introduction of an algorithm called Active SS. SS allocates the same number of samples for each type. Active SS is the application of the idea of active sampling to search trees. Active SS allocates more samples to the types with higher uncertainty. Our empirical results show that (i) SS using clustering-based type systems tends to produce better predictions than competing schemes that do not use a type system, and that (ii) Active SS can produce better predictions than the regular version of SS.
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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 | 0.009 | 0.042 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".