论文标题
无限维贝叶斯逆问题的无梯度子空调的集合采样器
A gradient-free subspace-adjusting ensemble sampler for infinite-dimensional Bayesian inverse problems
论文作者
论文摘要
在高维度中对尖锐的后验进行采样是一个具有挑战性的问题，尤其是当可能性的梯度不可用时。在低至中度的维度中，仿射不变方法（一类无梯度的方法）在采样浓缩后代的成功中已经成功。但是，合奏成员的数量必须超过未知状态的维度，以便将正确的分布定为目标。相反，预处理的曲柄 - 尼科尔森（PCN）算法成功地在高维度中取样，但是当后验与先前的后验显着不同时，样品变得高度相关。在本文中，我们以两种不同的方式将上述方法结合起来，以寻找妥协。第一种方法涉及将PCN中的提案协方差与当前合奏的相互变化膨胀，而第二种方法在不断适应低维子空间的同时，在其正交补体上使用PCN进行了近似仿射不变的步骤。
Sampling of sharp posteriors in high dimensions is a challenging problem, especially when gradients of the likelihood are unavailable. In low to moderate dimensions, affine-invariant methods, a class of ensemble-based gradient-free methods, have found success in sampling concentrated posteriors. However, the number of ensemble members must exceed the dimension of the unknown state in order for the correct distribution to be targeted. Conversely, the preconditioned Crank-Nicolson (pCN) algorithm succeeds at sampling in high dimensions, but samples become highly correlated when the posterior differs significantly from the prior. In this article we combine the above methods in two different ways as an attempt to find a compromise. The first method involves inflating the proposal covariance in pCN with that of the current ensemble, whilst the second performs approximately affine-invariant steps on a continually adapting low-dimensional subspace, while using pCN on its orthogonal complement.
