Towards Certainty: Exploiting Monotonicity with Fast Marching Methods to Reduce Predictive Uncertainty
Abstract: In recent years, neural networks have achieved impressive performance on a wide range of tasks. However, neural networks tend to make overly optimistic predictions about out-of-distribution data. When managing model risks, it is important to know what we do not know. Although there have been many successes in detecting out-of-distribution data, it is unclear how we can extract further information from these uncertain predictions. To address this problem, we propose to use three types of monotonicity to extract further information by solving a mean-variance optimization problem. The fast marching method is proposed as an efficient solution. We demonstrate, using empirical examples, that it is possible to provide confident bounds for a large portion of uncertain predictions by monotonicity.
Submission Length: Regular submission (no more than 12 pages of main content)
Previous TMLR Submission Url: https://openreview.net/forum?id=SFa93igP8G&referrer=%5BAuthor%20Console%5D(%2Fgroup%3Fid%3DTMLR%2FAuthors%23your-submissions)
Changes Since Last Submission: A number of changes have been made.
1. The manuscript has been clarified further. In addition, the details of the methods have been added and some technical information has been moved to the appendix.
2. The empirical examples have been rerun with a more careful setting of baselines.
3. We have added more discussion regarding the related work, in particular Chen (2022).
Assigned Action Editor: ~Stefan_Magureanu1
Submission Number: 3453
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