Probabilistic models over weighted orderings: fixed-parameter tractable variable elimination
Bibliographic record
Abstract
Probabilistic models with weighted formulas, known as Markov models or log-linear models, are used in many domains. Recent models of weighted orderings between elements that have been proposed as flexible tools to express preferences under uncertainty, are also potentially useful in applications like planning, temporal reasoning, and user modeling. Their computational properties are very different from those of conventional Markov models; because of the transitivity of the less than relation, standard methods that exploit structure of the models, such as variable elimination, are not directly applicable, as there are no conditional independencies between the orderings within connected components. The best known algorithms for general inference in these models are exponential in the number of statements. Here, we present the first algorithms that exploit the available structure. We begin with the special case of models in the form of chains; we present an exact O(n3) algorithm, where n is the total number of elements. Next, we generalize this technique to models in which the set of statements are comprised of arbitrary sets of atomic weighted preference formulas (while the query and evidence are conjunctions of atomic preference formulas), and the resulting exact algorithm runs in time O(m * n2 * nc), where m is the number of preference formulas, n is the number of elements, and c is the maximum number of elements in a linear cut (which depends both on the structure of the model and the order in which the elements are processed)—therefore, this algorithm is tractable for cases in which c can be bounded to a low value. Finally, we report on the results of an empirical evaluation of both algorithms, showing how they scale with reasonably-sized models.
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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 | 0.003 | 0.019 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.004 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.007 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.002 | 0.006 |
| Insufficient payload (model declined to judge) | 0.008 | 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".