Incorporating Linear Dependencies into Graph Gaussian Processes
Bibliographic record
Abstract
Graph Gaussian processes are an important technique for learning unknown functions on graphs while quantifying uncertainty. \nThese processes encode prior information by using kernels that reflect the structure of the graph, allowing function values at nearby nodes to be correlated. However, there are limited choices for kernels on graphs, and most existing graph kernels can be shown to rely on the graph Laplacian and behave in a manner that resembles Euclidean radial basis functions. In many applications, additional prior information which goes beyond the graph structure encoded in Laplacian is available: in this work, we study the case where the dependencies between nodes in the target function are known as linear, possibly up to some noise. We propose a type of kernel for graph Gaussian processes that incorporate linear dependencies between nodes, based on an inter-domain-type construction. We show that this construction results in kernels that can encode directed information, and are robust under misspecified linear dependencies. We also show that the graph Matérn kernel, one of the commonly used Laplacian-based kernels, can be obtained as a special case of this construction. We illustrate the properties of these kernels on a set of synthetic examples. We then evaluate these kernels in a real-world traffic speed prediction task, and show that they easily out-perform the baseline kernels. We also use these kernels to learn offline reinforcement learning policies in maze environments. We show that they are significantly more stable and data-efficient than strong baselines, and they can incorporate prior information to generalize to unseen tasks.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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 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".