Probabilistic inference is a fundamental task in modern machine learning. Recent advances in tensor network (TN) contraction algorithms have enabled the development of better exact inference methods. However, many common inference tasks in probabilistic graphical models (PGMs) still lack corresponding TN-based adaptations. In this work, we advance the connection between PGMs and TNs by formulating and implementing tensor-based solutions for the following inference tasks: (i) computing the partition function, (ii) computing the marginal probability of sets of variables in the model, (iii) determining the most likely assignment to a set of variables, and (iv) the same as (iii) but after having marginalized a different set of variables. We also present a generalized method for generating samples from a learned probability distribution. Our work is motivated by recent technical advances in the fields of quantum circuit simulation, quantum many-body physics, and statistical physics. Through an experimental evaluation, we demonstrate that the integration of these quantum technologies with a series of algorithms introduced in this study significantly improves the effectiveness of existing methods for solving probabilistic inference tasks.

提出了基于张量网络的概率图模型推理任务解决方法，包括计算配分函数、计算模型中变量集的边缘概率、确定变量集的最可能赋值以及根据不同变量集边缘化后确定最可能赋值，并通过与量子技术的集成得到了明显的改进。

张量网络与微分编程时代的概率推理