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 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)
Changes Since Last Submission: In response to the reviewer's comments, we have made a number of changes. All changes are highlighted in purple. The following are some of the most significant changes.
1. The two-stage framework has been significantly revised from page 5 to page 7, along with detailed examples.
2. Comparisons with Chen (2022)'s baseline method are now included in Section 6.3 on page 16 and the results are presented in Table 2.
3. In Section 7, from page 17 to page 18, a brief discussion of the relationships among monotonic models, OOD detection, and FMM is presented.
Assigned Action Editor: ~Roman_Garnett1
Submission Number: 2299
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