论文标题
在高维广义线性模型中基于采样的后推断的多项式时间保证
Polynomial time guarantees for sampling based posterior inference in high-dimensional generalised linear models
论文作者
论文摘要
考虑了一般高维统计模型中计算后验功能的问题。基于Nickl和Wang的证明策略（2022），但仅使用局部可能性条件，并且在不依赖M估计理论的情况下，为基于梯度的MCMC算法提供了非扰动统计和计算保证。鉴于合适的初始分散器，这些保证在关键算法数量中多项式缩放。抽象结果应用于几个具体统计模型，包括密度估计，具有广义线性模型的非参数回归以及PDES的规范统计非线性逆问题。
The problem of computing posterior functionals in general high-dimensional statistical models with possibly non-log-concave likelihood functions is considered. Based on the proof strategy of Nickl and Wang (2022), but using only local likelihood conditions and without relying on M-estimation theory, nonasymptotic statistical and computational guarantees are provided for a gradient based MCMC algorithm. Given a suitable initialiser, these guarantees scale polynomially in key algorithmic quantities. The abstract results are applied to several concrete statistical models, including density estimation, nonparametric regression with generalised linear models and a canonical statistical non-linear inverse problem from PDEs.
