When performing inference on probabilistic models, target densities often become intractable, necessitating the use of Monte Carlo samplers. We develop a methodology for unbiased differentiation of the Metropolis-Hastings sampler, allowing us to differentiate through probabilistic inference. By fusing recent advances in stochastic differentiation with Markov chain coupling schemes, the procedure can be made unbiased, low-variance, and automatic. This allows us to apply gradient-based optimization to objectives expressed as expectations over intractable target densities. We demonstrate our approach by finding an ambiguous observation in a Gaussian mixture model and by maximizing the specific heat in an Ising model.

本文提出了一种用于无偏区别Metropolis-Hastings采样器的方法，使得我们能够通过概率推理进行不可行目标密度的优化，该方法通过融合随机区分的最新进展和马尔可夫链耦合方案，可以使该过程无偏、低方差和自动化，然后将其应用于期望为不可行目标密度的优化中。在文中所提出的方法中，分别应用到高斯混合模型中找到不明显的观察和Ising模型中的特定热容的最大化。

Metropolis-Hastings微分优化难以计算的密度函数