Distance Computation in the Space of Phylogenetic Trees
Bibliographic record
Abstract
A phylogenetic tree represents the evolutionary history of a set of organisms. There are many different methods to construct phylogenetic trees from biological data. To either compare one such algorithm with another, or to find the likelihood that a certain tree is generated from the data, researchers need to be able to compute the distance between trees. In 2001, Billera, Holmes, and Vogtmann introduced a space of phylogenetic trees, and defined the distance between two trees to be the length of the shortest path between them in that space. We use the combinatorial and geometric properties of the tree space to develop two algorithms for computing this geodesic distance. In doing so, we show that the possible shortest paths between two trees can be compactly represented by a partially ordered set. We calculate the shortest distance between the start and target trees for each potential path by converting the problem into one of finding the shortest path through a certain subspace of Euclidean space. In particular, we show there is a linear time algorithm for finding the shortest path between a point in the all positive orthant and a point in the all negative orthant of R^k contained in the subspace of R^k consisting of all orthants with the first i coordinates non- positive and the remaining coordinates non-negative for 0 <= i <= k. This case is of interest, because the general problem of finding a shortest path through higher dimensional Euclidean space with obstacles is NP-hard. The resulting algorithms for computing the geodesic distance appear to be the best available to date.
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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 | 0.001 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.003 | 0.005 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| 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".