Exploiting Contextual Independence In Probabilistic Inference
Bibliographic record
Abstract
Bayesian belief networks have grown to prominence because they provide compact representations for many problems for which probabilistic inference is appropriate, and there are algorithms to exploit this compactness. The next step is to allow compact representations of the conditional probabilities of a variable given its parents. In this paper we present such a representation that exploits contextual independence in terms of parent contexts; which variables act as parents may depend on the value of other variables. The internal representation is in terms of contextual factors (confactors) that is simply a pair of a context and a table. The algorithm, contextual variable elimination, is based on the standard variable elimination algorithm that eliminates the non-query variables in turn, but when eliminating a variable, the tables that need to be multiplied can depend on the context. This algorithm reduces to standard variable elimination when there is no contextual independence structure to exploit. We show how this can be much more efficient than variable elimination when there is structure to exploit. We explain why this new method can exploit more structure than previous methods for structured belief network inference and an analogous algorithm that uses trees.
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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 | 0.006 | 0.036 |
| Meta-epidemiology (narrow) | 0.001 | 0.002 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.008 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.001 | 0.003 |
| 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".