Learning to Discover Probabilistic Graphical Model Structures
Bibliographic record
Abstract
In this work we consider structure discovery of undirected graphical models from observational data. Inferring likely structures from few examples is a complex task often requiring formulating priors and sophisticated inference procedures. In the setting of Gaussian Graphical Models (GGMs) a popular approach to formulating an estimator is with a penalized maximum likelihood objective on the precision matrix. This objective is often difficult to design to specifically fit ones priors and the graph structure recovery is often not explicitly possible to embed in the objective, moreover incorporating any additional assumptions often requires a great deal of research effort. By contrast, it may be easier to generate samples of data that are arise from graphs with the desired properties. We propose here to leverage this latter source of information in order to learn a function that maps from empirical covariance matrices to estimated graph structures. This learned function brings two benefits: it implicitly models the desired structure or sparsity properties to form suitable priors, and it can more directly be tailored to the specific problem of edge structure discovery. We apply this framework to several critical real world problems in structure discovery and show that it can be competitive to standard approaches such as graphical lasso, at a fraction of the execution speed. We use deep neural networks to parametrize our estimators. Experimentally, our learn able graph discovery method trained on synthetic data generalizes well to different data: identifying relevant edges in real data, completely unknown at training time. We find that on genetics, brain imaging, and simulation data we obtain competitive (and often superior) performance, compared with analytical methods.
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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 | 0.007 | 0.037 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.004 | 0.006 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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".