Accelerating Bayesian Structure Learning in Sparse Gaussian Graphical Models
Bibliographic record
Abstract
Bayesian structure learning in Gaussian graphical models is often done by search algorithms over the graph space.The conjugate prior for the precision matrix satisfying graphical constraints is the well-known G-Wishart.With this prior, the transition probabilities in the search algorithms necessitate evaluating the ratios of the prior normalizing constants of G-Wishart.In moderate to high-dimensions, this ratio is often approximated by using sampling-based methods as computationally expensive updates in the search algorithm.Calculating this ratio so far has been a major computational bottleneck.We overcome this issue by representing a search algorithm in which the ratio of normalizing constants is carried out by an explicit closed-form approximation.Using this approximation within our search algorithm yields significant improvement in the scalability of structure learning without sacrificing structure learning accuracy.We study the conditions under which the approximation is valid.We also evaluate the efficacy of our method with simulation studies.We show that the new search algorithm with our approximation outperforms state-of-the-art methods in both computational efficiency and accuracy.The implementation of our work is available in the R package BDgraph.
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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 | 0.016 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| 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".