论文标题
$ \ ell^p $中的后验估计量对于对角线高斯先验明确定义
Maximum a posteriori estimators in $\ell^p$ are well-defined for diagonal Gaussian priors
论文作者
论文摘要
我们证明，在$ \ ell^p $上，在潜在$φ$的公共假设下，后验估计器的对角高斯先验$μ$的最大定义明确。此外，我们显示了与Onsager的连接 - 手机功能，并在Hilbert Space Case $ P = 2 $中提供了校正和强烈简化的证明，此前由Dashti等人（2013）和Kretschmann（2019）建立。 这些更正并未概括为设置$ 1 \ leq p <\ infty $，这需要用于Cameron-Martin Norm和$ p $ -NORM之间的差异的新颖凸面结果。
We prove that maximum a posteriori estimators are well-defined for diagonal Gaussian priors $μ$ on $\ell^p$ under common assumptions on the potential $Φ$. Further, we show connections to the Onsager--Machlup functional and provide a corrected and strongly simplified proof in the Hilbert space case $p=2$, previously established by Dashti et al (2013) and Kretschmann (2019). These corrections do not generalize to the setting $1 \leq p < \infty$, which requires a novel convexification result for the difference between the Cameron--Martin norm and the $p$-norm.
