The Gaussian Process Density Sampler
Bibliographic record
Abstract
The Gaussian process is a useful prior on functions for Bayesian regression and classification. Density estimation with a Gaussian process prior has been difficult, however, due to the requirements that densities be nonnegative and integrate to unity. The statistics community has explored the use of a logistic Gaussian process for density estimation, relying on various methods of approximating the normalization constant (e.g. [1, 4]). We propose the Gaussian Process Density Sampler (GPDS), a nonparametric, practical and consistent method of constructing a Markov chain on the properties of a posterior distribution on an unknown density, without approximation. The GPDS is composed of four parts. The first part is a GP-based prior on density functions. We develop an exchangeable procedure for generating exact samples in data space from a common density drawn from this prior. Second, we show that this prior allows practical inference of specific values of the unnormalized density, using the recently-developed technique of exchange sampling [3]. Third, we extend this MCMC algorithm to draw samples from the predictive distribution on data space that arises when the posterior on density functions is integrated out. This is our primary result. Finally, we demonstrate a sampling procedure for inference of the Gaussian process hyperparameters.
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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 | 0.006 | 0.030 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.010 | 0.003 |
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".