The paper considers the problem of learning uncertainty regions for parameter estimation problems. The regions are ellipsoids that minimize the average volumes subject to a prescribed coverage probability.
In the simplistic Gaussian setting, the authors prove that the optimal ellipsoid is centered around the conditional mean and shaped as the conditional covariance matrix. For more practical cases, they propose a differentiable optimization approach using a neural network called LMVE to approximately compute the optimal ellipsoids.
LMVE combines nearest-neighbor approaches, covariance estimation, and conformal prediction to generate ellipsoids with minimal average volume and prescribed coverage probability. It significantly reduces memory and computation resources compared to existing methods, while improving accuracy. The authors demonstrate the advantages of LMVE on four real-world localization datasets.
The key steps of LMVE are:
The experiments show that LMVE outperforms existing methods in terms of average ellipsoid volume while maintaining the required coverage levels. It also has lower computational complexity and memory requirements.
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by Itai Alon,Da... kl. arxiv.org 05-07-2024
https://arxiv.org/pdf/2405.02441.pdfDybere Forespørgsler