论文标题
高斯先验中的自由能屏障和高维单峰分布的冷启动MCMC失败
On free energy barriers in Gaussian priors and failure of cold start MCMC for high-dimensional unimodal distributions
论文作者
论文摘要
我们展示了具有高斯工艺先验的非线性回归模型中产生的高维单模态后分布的示例，MCMC方法可以花费指数运行时进入大部分后量度浓度的区域。我们的结果适用于最差的初始化（“冷启动”）算法，这些算法是局部的，从某种意义上说，它们的阶梯尺寸平均不能太大。基于梯度或随机步行步骤的一般MCMC方案的反示例符合，该理论用于大都市 - 危机调整后的PCN和MALA等方法。
We exhibit examples of high-dimensional unimodal posterior distributions arising in non-linear regression models with Gaussian process priors for which MCMC methods can take an exponential run-time to enter the regions where the bulk of the posterior measure concentrates. Our results apply to worst-case initialised (`cold start') algorithms that are local in the sense that their step-sizes cannot be too large on average. The counter-examples hold for general MCMC schemes based on gradient or random walk steps, and the theory is illustrated for Metropolis-Hastings adjusted methods such as pCN and MALA.
