Universal Prediction Band via Semi-Definite Programming
Universal Prediction Band via Semi-Definite Programming
复制标题
通过半定规划的通用预测带
DOI：
10.1111/rssb.12542
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Liang, Tengyuan
中科院分区：
文献类型：
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作者：
Liang, Tengyuan
我们提出了一种计算效率高的方法来构建非参数，异方差预测带的不确定性量化，有或没有任何用户指定的预测模型。我们的方法提供了一种替代现在标准的共形预测的不确定性量化，具有新的理论见解和计算优势。数据自适应预测带是普遍适用的最小分布假设，具有很强的非渐近覆盖特性，并且很容易使用标准凸规划实现。我们的方法可以被视为一种新的方差插值的信心，并进一步利用半定规划和平方和优化技术。理论和数值性能的不确定性量化所提出的方法进行了分析。
We propose a computationally efficient method to construct nonparametric, heteroscedastic prediction bands for uncertainty quantification, with or without any user-specified predictive model. 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.