Posterior consistency of semi-supervised regression on graphs
Why this work is in the frame
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Bibliographic record
Abstract
Abstract Graph-based semi-supervised regression (SSR) involves estimating the value of a function on a weighted graph from its values (labels) on a small subset of the vertices; it can be formulated as a Bayesian inverse problem. This paper is concerned with the consistency of SSR in the context of classification, in the setting where the labels have small noise and the underlying graph weighting is consistent with well-clustered vertices. We present a Bayesian formulation of SSR in which the weighted graph defines a Gaussian prior, using a graph Laplacian, and the labeled data defines a likelihood. We analyze the rate of contraction of the posterior measure around the ground truth in terms of parameters that quantify the small label error and inherent clustering in the graph. We obtain bounds on the rates of contraction and illustrate their sharpness through numerical experiments. The analysis also gives insight into the choice of hyperparameters that enter the definition of the prior.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it