Distance-preserving probabilistic embeddings with side information: variational Bayesian multidimensional scaling Gaussian process
Bibliographic record
Abstract
Embeddings or vector representations of objects have been used with remarkable success in various machine learning and AI tasks--from dimensionality reduction and data visualization, to vision and natural language processing. In this work, we seek probabilistic embeddings that faithfully represent observed relationships between objects (e.g., physical distances, preferences). We derive a novel variational Bayesian variant of multidimensional scaling that (i) provides a posterior distribution over latent points without computationally-heavy Markov chain Monte Carlo (MCMC) sampling, and (ii) can leverage existing side information using sparse Gaussian processes (GPs) to learn a nonlinear mapping to the embedding. By partitioning entities, our method naturally handles incomplete side information from multiple domains, e.g., in product recommendation where ratings are available, but not all users and items have associated profiles. Furthermore, the derived approximate bounds can be used to discover the intrinsic dimensionality of the data and limit embedding complexity. We demonstrate the effectiveness of our methods empirically on three synthetic problems and on the real-world tasks of political unfolding analysis and multi-sensor localization.
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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 | 0.016 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.002 | 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".