Efficient Symbolic Integration for Probabilistic Inference
Bibliographic record
Abstract
Weighted model integration (WMI) extends weighted model counting (WMC) to the integration of functions over mixed discrete-continuous probability spaces. It has shown tremendous promise for solving inference problems in graphical models and probabilistic programs. Yet, state-of-the-art tools for WMI are generally limited either by the range of amenable theories, or in terms of performance. To address both limitations, we propose the use of extended algebraic decision diagrams (XADDs) as a compilation language for WMI. Aside from tackling typical WMI problems, XADDs also enable partial WMI yielding parametrized solutions. To overcome the main roadblock of XADDs -- the computational cost of integration -- we formulate a novel and powerful exact symbolic dynamic programming (SDP) algorithm that seamlessly handles Boolean, integer-valued and real variables, and is able to effectively cache partial computations, unlike its predecessor. Our empirical results demonstrate that these contributions can lead to a significant computational reduction over existing probabilistic inference algorithms.
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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 | 0.002 | 0.016 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.009 | 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".