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.

翻译：在对概率模型进行推断时，目标密度往往变得难解，从而需要使用蒙特卡洛采样器。我们开发了一种对Metropolis-Hastings采样器进行无偏微分的方法，使得我们能够对概率推断过程进行微分。通过将随机微分的最新进展与马尔可夫链耦合方案相结合，该过程可以实现无偏、低方差且自动化。这使我们能够将基于梯度的优化应用于表示为关于难解目标密度的期望的目标函数。我们通过在高斯混合模型中寻找模糊观测值以及最大化伊辛模型中的比热来展示我们的方法。