Informative Path Planning for Active Regression With Gaussian Processes via Sparse Optimization
Bibliographic record
Abstract
We study informative path planning for active regression in Gaussian Processes (GP). Here, a resource constrained robot team collects measurements of an unknown function, assumed to be a sample from a GP, with the goal of minimizing the trace of the$M$-weighted expected squared estimation error covariance (where$M$is a positive semidefinite matrix) resulting from the GP posterior mean. While greedy heuristics are a popular solution in the case of length constrained paths, it remains a challenge to computeoptimalsolutions in the discrete setting subject to routing constraints. We show that this challenge is surprisingly easy to circumvent. Using the optimality of the posterior mean for a class of functions of the squared loss yields an exact formulation as a mixed integer program. We demonstrate that this approach finds optimal solutions in a variety of settings in seconds and when terminated early, it finds sub-optimal solutions of higher quality than existing heuristics.
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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 | 0.003 | 0.011 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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".