论文标题
错误引导的无可能的MCMC
Error-guided likelihood-free MCMC
论文作者
论文摘要
这项工作为具有棘手的证据和可能性功能的模型提供了一种新颖的后推理方法。简单地为科学应用开发了错误引导的无可能的MCMC或EG-LF-MCMC,研究人员有兴趣在模型参数上获得近似的后验密度,同时避免需要对完整观察数据的组件估算器进行昂贵的培训或相关方法的表达性摘要统计数据的繁琐设计,以及相关方法。我们的技术基于两个阶段。在第一阶段,我们从先验中绘制样本,模拟各自的观察结果,并记录其与真实观察相关的错误$ε$。我们训练分类器,以区分相应的$(ε,\boldsymbolθ)$ - 元组。在第二阶段,上述分类器以训练集的最小记录的$ε$值来调节,并用于计算马尔可夫链蒙特卡洛采样程序中的过渡概率。通过根据特定的$ε$值调节MCMC,我们的方法也可以以摊销方式使用,以推断观测值的后验密度,该观测值位于距离观察到的数据的给定距离。我们评估了针对基准问题的方法,具有语义和结构不同的数据,并将其性能与最先进的近似贝叶斯计算(ABC)进行比较。
This work presents a novel posterior inference method for models with intractable evidence and likelihood functions. Error-guided likelihood-free MCMC, or EG-LF-MCMC in short, has been developed for scientific applications, where a researcher is interested in obtaining approximate posterior densities over model parameters, while avoiding the need for expensive training of component estimators on full observational data or the tedious design of expressive summary statistics, as in related approaches. Our technique is based on two phases. In the first phase, we draw samples from the prior, simulate respective observations and record their errors $ε$ in relation to the true observation. We train a classifier to distinguish between corresponding and non-corresponding $(ε, \boldsymbolθ)$-tuples. In the second stage the said classifier is conditioned on the smallest recorded $ε$ value from the training set and employed for the calculation of transition probabilities in a Markov Chain Monte Carlo sampling procedure. By conditioning the MCMC on specific $ε$ values, our method may also be used in an amortized fashion to infer posterior densities for observations, which are located a given distance away from the observed data. We evaluate the proposed method on benchmark problems with semantically and structurally different data and compare its performance against the state of the art approximate Bayesian computation (ABC).