Bayesian inference for doubly-intractable probabilistic 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 an 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：针对双重难解概率图模型的贝叶斯推断通常采用交换算法的变体或近似马尔可夫链蒙特卡罗（MCMC）采样器。然而，现有两类算法均需依赖完美采样器或适用于复杂模型的序列采样器，这些采样器往往难以获得，或在处理高维问题时存在混合效果不佳的缺陷。本文提出一种无需完美采样或序列采样的方法，可同时适用于精确与近似两类MCMC算法。本方法的核心在于利用难解概率图模型底层可处理的独立模型，构建Metropolis-Hastings比值的有限样本无偏蒙特卡罗（非MCMC）估计量。这一创新被证明是实现高维可扩展性的关键。研究以伊辛模型为例验证了方法的有效性。基于梯度的提案构造方法（如朗之万与哈密顿蒙特卡罗方法）亦作为本通用流程的自然推论得以实现，并在实验中进行了展示。