Centrality and shape-related comparisons in a tree-structured Markov random field
Bibliographic record
Abstract
Understanding the effects of the choice of the tree on the joint distribution of a tree-structured Markov random field (MRF) is crucial for fully exploiting the intelligibility of such probabilistic graphical models. Tools must be developed in this regard: this is the overarching objective of this paper. Our discussion is two-fold. First, we examine concepts specific to network centrality theory. We put forth a new conception of centrality for MRFs that not only accounts for the tree topology, but also the underlying stochastic dynamics. In this vein, we compare synecdochic pairs, random vectors comprising a MRF's component and its sum, using stochastic orders. The resulting orderings are transferred to risk-allocation quantities, which therefore serve as new centrality indices tailored to our stochastic framework. Second, we shed light on the influence of the tree's shapes, by establishing convex orderings for MRFs encrypted on trees of different shapes. This results in the design of a new partial order on tree shapes. This analysis is done within the framework of a propagation-based family of tree-structured MRFs with the uncommon property of having fixed Poisson marginal distributions unaffected by the dependence scheme. This work is a first step into the analysis of MRFs' trees' shapes and a stepping stone to extending this analysis to a broader framework.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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 teacher head, 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".