On learning the structure of sum-product networks
Bibliographic record
Abstract
LearnSPN is the standard unsupervised learning algorithm for sum-product networks (SPNs). It is based upon a “chop” operation for splitting features (columns) and a “slice” operation for clustering instances (rows). However, a number of techniques can be applied to chop and slice meaning that LearnSPN can learn a wide variety of SPNs from the same dataset. In this paper, we perform an empirical study of LearnSPN. We consider g-test and mutual information for chopping and k-means and Gaussian mixture models for slicing. Our experiments, conducted on 20 real-world datasets, suggest that the deepest SPNs tend to be learned when using mutual information for chopping and k-means for slicing. This is important, since SPNs are the only deep learning model where it is provably the case that deeper models are more expressive than shallow models. Second, our results show that the pair of g-test and Gaussian mixture models tends to yield the most accurate SPNs, especially on larger datasets. These results suggest that the particular combination of mutual information and k-means may be prone to overfitting. Lastly, we examine the sparseness of the learned SPN. Our experiments show that the pair of g-test and Gaussian mixture models regularly yields SPNs with fewer edges. This knowledge is beneficial to SPN learning algorithms that penalize networks with more edges. Our study then extends the SPN deep learning literature in both practical and theoretical directions.
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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 | 0.005 | 0.033 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.007 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.005 |
| 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".