The problem of efficiently generating random samples from high-dimensional and non-log-concave posterior measures arising from nonlinear regression problems is considered. Extending investigations from arXiv:2009.05298, local and global stability properties of the model are identified under which such posterior distributions can be approximated in Wasserstein distance by suitable log-concave measures. This allows the use of fast gradient based sampling algorithms, for which convergence guarantees are established that scale polynomially in all relevant quantities (assuming `warm' initialisation). The scope of the general theory is illustrated in a non-linear inverse problem from integral geometry for which new stability results are derived.
翻译:本文考虑了高维且非对数凸后验分布的随机样本快速生成问题,这种问题源于非线性回归问题。拓展arXiv:2009.05298的研究,本文找到了模型的局部和全局稳定性特性,从而可以通过适当的对数凸测度在Wasserstein距离下逼近这些后验分布。这允许使用快速基于梯度的采样算法,对于这些算法的收敛性保证也得到了证明,这些保证在所有相关数量(假设"运行热"初始)的多项式尺度下缩放。本文以积分几何中的非线性反问题为例说明了这个通用理论的应用,并推导了新的稳定性结果。