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Our approach provides an alternative to the now-standard conformal prediction for uncertainty quantification, with novel theoretical insights and computational advantages. The data-adaptive prediction band is universally applicable with minimal distributional assumptions, has strong non-asymptotic coverage properties, and is easy to implement using standard convex programs. Our approach can be viewed as a novel variance interpolation with confidence and further leverages techniques from semi-definite programming and sum-of-squares optimization. Theoretical and numerical performances for the proposed approach for uncertainty quantification are analysed.<\/jats:p>","DOI":"10.1111\/rssb.12542","type":"journal-article","created":{"date-parts":[[2022,8,19]],"date-time":"2022-08-19T22:54:30Z","timestamp":1660949670000},"page":"1558-1580","source":"Crossref","is-referenced-by-count":0,"title":["Universal Prediction Band via Semi-Definite Programming"],"prefix":"10.1093","volume":"84","author":[{"given":"Tengyuan","family":"Liang","sequence":"first","affiliation":[{"name":"Booth School of Business , Chicago , Illinois , USA"},{"name":"University of Chicago , Chicago , Illinois , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2022,8,19]]},"reference":[{"key":"2023030906300832900_","volume-title":"Learning positive functions in a Hilbert 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