Bayesian inference for doubly-intractable pairwise exponential graphical models typically involves variations of the exchange algorithm or approximate Markov chain Monte Carlo (MCMC) samplers. However, existing methods for both classes of algorithms require either perfect samplers or sequential samplers for complex models, which are often either not available, or suffer from poor mixing, especially in high dimensions. We develop a method that does not require perfect or sequential sampling, and can be applied to both classes of methods: exact and approximate MCMC. The key to our approach is to utilize the tractable independence model underlying the intractable probabilistic graphical model for the purpose of constructing a finite sample unbiased Monte Carlo (and not MCMC) estimate of the Metropolis--Hastings ratio. This innovation turns out to be crucial for scalability in high dimensions. The method is demonstrated on the Ising model. Gradient-based alternatives to construct a proposal, such as Langevin and Hamiltonian Monte Carlo approaches, also arise as a natural corollary to our general procedure, and are demonstrated as well.

翻译：针对双重难处理成对指数图模型的贝叶斯推断通常涉及交换算法或近似马尔可夫链蒙特卡洛（MCMC）采样器的变体。然而，现有两类算法的方法要么需要复杂模型的完美采样器，要么需要顺序采样器——这些工具通常不可用，或在高维情形下存在混合不良的问题。我们开发了一种无需完美采样或顺序采样的方法，可同时适用于精确和近似MCMC两类算法。其关键在于利用难处理概率图模型底层的可处理独立模型，构建Metropolis-Hastings比率的有限样本无偏蒙特卡洛（而非MCMC）估计。这一创新对高维场景的可扩展性至关重要。该方法在伊辛模型上进行了验证。作为我们通用程序的自然推论，基于梯度的提议构造方法（如朗之万和哈密顿蒙特卡洛方法）同样得到实现与验证。