论文标题
概率的甲骨文不平等和量化统计反向问题的不确定性的量化
A Probabilistic Oracle Inequality and Quantification of Uncertainty of a modified Discrepancy Principle for Statistical Inverse Problems
论文作者
论文摘要
在本说明中，我们考虑光谱截止估计器在任意白噪声下解决统计线性反问题。截断水平由基于经典差异原理的最近引入的自适应方法确定。我们提供概率的甲骨文不平等，并量化一般线性问题的不确定性。此外，我们将新方法与现有方法进行比较，即早期停止顺序差异原理和平衡原理，无论是从理论上还是数值上。
In this note we consider spectral cut-off estimators to solve a statistical linear inverse problem under arbitrary white noise. The truncation level is determined with a recently introduced adaptive method based on the classical discrepancy principle. We provide probabilistic oracle inequalities together with quantification of uncertainty for general linear problems. Moreover, we compare the new method to existing ones, namely early stopping sequential discrepancy principle and the balancing principle, both theoretically and numerically.
