Bayesian Structure Learning for Graphical Models With Symmetry Constraints
Bibliographic record
Abstract
PAM50 gene expression profiling, a popular and widely used tool, is employed to identify and assess the functional relationships and pathways among genes in patients with breast cancer. Motivated by a study aimed at concurrently recovering dependency and symmetric networks for the PAM50 gene data set, we consider the graphical Gaussian model with symmetry constraints on edges and vertices. The symmetry constraints in the model are represented by imposing equality constraints on the concentration matrix. This model allows us to simultaneously explore the dependency relationships and symmetrical structure among the variables. The symmetrical structure of PAM50 gene expression can deepen our understanding of their functional similarities and the inherent symmetrical properties of gene regulatory behavior. Prioritizing candidate genes with high functional similarity will help elucidate the underlying biological mechanisms for the disease progression. To effectively capture the network's structure, we utilize a birth-death Markov Chain Monte Carlo method. This method is a continuous-time and transdimensional search algorithm that is particularly effective in this context. To further improve the efficiency of the algorithm, we propose a stepwise model learning strategy combined with an approximation method for the posterior distribution. To validate the effectiveness of our approach, we finally apply it in various simulation studies as well as in a practical application involving the PAM50 gene expression data set.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.004 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".