On Undirected Representations of Bayesian Networks
Bibliographic record
Abstract
Empirical studies clearly demonstrate the effectiveness of the nested jointree (NJT) representation in probabilistic inference. A NJT is a traditional Markov network (MN) together with a possible local MN nested in each clique. These nested MNs can themselves contain other nested MNs in a recursivemanner. However, the NJT representation is not necessarily a faithful representation of a given Bayesian network (BN). This means that the effectiveness of a NJT has been demonstrated while only exploiting some of the independency information available in the given BN. In this paper, weintroduce a new kind of probabilistic network, called a hierarchical Markov network (HMN). A HMN is a hierarchy of MNs. We give an algorithm to transform a BN into a canonical HMN. The main result of this paper is that the constructed HMN is unique and equivalent to the input BN. Since HMNs are a faithful representation of BNs, a query may be optimized using independencies in a HMN that otherwise would have gone unrepresentedinaNJTapproach. 1
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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 | 0.004 | 0.025 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.005 | 0.010 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.007 | 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".