Algebra of inference in graphical models revisited
Bibliographic record
Abstract
Graphical Models use the intuitive and well-studied methods of graph theory to implicitly represent dependencies between variables in large systems and model the global behaviour of a complex system by specifying only local factors. The variational perspective poses inference as optimization and provides a rich framework to study inference when the object of interest is a (log) probability. However, graphical models can operate on a much wider set of algebraic structures. This paper builds on the work of Aji and McEliece (2000), to formally and broadly express what constitutes an inference problem in a graphical model. We then study the computational complexity of inference and show that inference in any commutative semiring is NP-hard under randomized reduction. By confining inference to four basic operations of min, max, sum and product, we introduce the inference hierarchy with an eye on computational complexity and establish the limits of message passing using distributive law in solving the problems in this hierarchy.
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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 | 0.014 | 0.032 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.004 |
| Bibliometrics | 0.003 | 0.005 |
| Science and technology studies | 0.003 | 0.013 |
| Scholarly communication | 0.009 | 0.022 |
| Open science | 0.004 | 0.006 |
| Research integrity | 0.003 | 0.011 |
| Insufficient payload (model declined to judge) | 0.010 | 0.002 |
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".