A Bayesian Hierarchical Model for Orthogonal Tucker Decomposition with Oblivious Tensor Compression
Bibliographic record
Abstract
Low-rank representations such as the Tucker decomposition underlie many frequentist methods for tensor analysis. Bayesian analogues, in contrast, have received less attention. Notably missing in the literature is a Bayesian Tucker decomposition with orthogonal factor matrices-a standard interpretability restriction in frequentist settings. We propose a Bayesian hierarchical model for the orthogonal Tucker decomposition, which we implement via conditionally conjugate Gibbs sampler. To reduce the complexity of tensor operations in MCMC estimation, we incorporate a mechanism that uses Johnson-Lindenstrauss embeddings to compress data. Our theoretical analysis bounds change in the full-conditional posterior distributions of tensor components due to compression (with respect to Hellinger distance). We further establish posterior consistency for the decomposition's factor matrices in settings where these parameters are shared across tensor observations. Empirical results show that, for large tensor datasets, moderate compression can significantly reduce draw time (by about 50%) with only a moderate increase (up to about 15%) in median reconstruction error. Compression in the proposed model additionally enables analyses of tensor data that are too large to be held wholly in memory, thus making large-scale analyses tractable on even moderate computing resources.
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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 | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".