We present a new algorithm for amortized inference in sparse probabilistic graphical models (PGMs), which we call $\Delta$-amortized inference ($\Delta$-AI). Our approach is based on the observation that when the sampling of variables in a PGM is seen as a sequence of actions taken by an agent, sparsity of the PGM enables local credit assignment in the agent's policy learning objective. This yields a local constraint that can be turned into a local loss in the style of generative flow networks (GFlowNets) that enables off-policy training but avoids the need to instantiate all the random variables for each parameter update, thus speeding up training considerably. The $\Delta$-AI objective matches the conditional distribution of a variable given its Markov blanket in a tractable learned sampler, which has the structure of a Bayesian network, with the same conditional distribution under the target PGM. As such, the trained sampler recovers marginals and conditional distributions of interest and enables inference of partial subsets of variables. We illustrate $\Delta$-AI's effectiveness for sampling from synthetic PGMs and training latent variable models with sparse factor structure.

翻译：我们提出了一种新的用于稀疏概率图模型（PGM）摊销推理的算法，称为Δ-摊销推理（Δ-AI）。该方法基于以下观察：当PGM中的变量采样被视为智能体采取的一系列动作时，PGM的稀疏性使得智能体策略学习目标能够实现局部信用分配。这产生了一个局部约束，可转化为生成流网络（GFlowNet）风格的局部损失，从而支持离策略训练，但无需为每次参数更新实例化所有随机变量，从而显著加速训练过程。Δ-AI目标使变量在其马尔可夫毯条件下的条件分布（在具有贝叶斯网络结构的可学习采样器中）与目标PGM下的同一条件分布相匹配。由此训练得到的采样器能够恢复目标边缘分布和条件分布，并支持对变量子集的推理。我们通过合成PGM采样和训练具有稀疏因子结构的潜变量模型，展示了Δ-AI的有效性。