Moment-Sum-Of-Squares Approach For Fast Risk Estimation In Uncertain\n Environments
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Bibliographic record
Abstract
In this paper, we address the risk estimation problem where one aims at\nestimating the probability of violation of safety constraints for a robot in\nthe presence of bounded uncertainties with arbitrary probability distributions.\nIn this problem, an unsafe set is described by level sets of polynomials that\nis, in general, a non-convex set. Uncertainty arises due to the probabilistic\nparameters of the unsafe set and probabilistic states of the robot. To solve\nthis problem, we use a moment-based representation of probability\ndistributions. We describe upper and lower bounds of the risk in terms of a\nlinear weighted sum of the moments. Weights are coefficients of a univariate\nChebyshev polynomial obtained by solving a sum-of-squares optimization problem\nin the offline step. Hence, given a finite number of moments of probability\ndistributions, risk can be estimated in real-time. We demonstrate the\nperformance of the provided approach by solving probabilistic collision\nchecking problems where we aim to find the probability of collision of a robot\nwith a non-convex obstacle in the presence of probabilistic uncertainties in\nthe location of the robot and size, location, and geometry of the obstacle.\n
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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