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:考虑了从非线性回归问题产生的高维和非逻辑后部措施中有效随机生成随机样本的问题,从ArXiv:2009.05298中扩展调查范围,确定了模型的当地和全球稳定性特性,根据这些特性,可通过适当的日志组合措施在瓦塞尔斯坦距离上近似这种后端分布,从而可以使用快速梯度基取样算法,为此确定了在所有相关数量上(假设“暖度”初始化)的多元规模(假设“温度”初始化)的趋同保证。