中文摘要：

高斯Markov随机场是具有Markov性质、符合多元高斯分布的概率模型.高斯均值场是高斯Markov随机场模型上一种基本的变分推理方法,该方法通过引入基于变量簇分解的自由分布进行变分转换,计算出目标函数的下界.自由分布结构选择是变分推理的重要步骤,也是折中变分精度与计算复杂性的关键.提出了一个新的结构选择标准,并设计了一个结构选择算法.首先,在高斯Markov随机场上定义了耦合度和类耦合度概念来度量变量簇间的依赖关系,证明了高斯均值场的耦合度-精度定理,并进一步给出了类耦合度结构选择指标;然后,结合类耦合度指标和变量簇归一化技术,设计了一个高斯均值场结构选择算法;通过对比实验验证了算法的有效性.

英文摘要：

Gaussian Markov random field is a probabilistic model with multivariate Gaussian distribution and conditional independence assumptions. Gaussian mean field is a basic variational inference method on the Gaussian Markov random field, which computes the lower bound of the objective function through variational transformation with free distribution of the variables factorized into clusters. The structure selection of free distribution plays an important role in variational inference, and it is critical to the tradeoff between the variational accuracy and the computational complexity. This paper deals with the structure selection criterion and algorithm issues for the Gaussian mean field, and then provides a new structure selection criterion and an efficient structure selection algorithm. First, the concepts of coupling and quasi-coupling are proposed to measure the dependence among variable clusters of the Gaussian Markov random field model, and the coupling-accuracy theorem is proved for the Gaussian mean field, which provides the quasi-coupling as the new structure selection criterion. Then a normalized structure selection algorithm is designed based on the quasi-coupling criterion and the normalization technique for Gaussian mean field, which avoids unbalanced computational complexity among clusters through cluster normalization. Finally, numerical comparison experiments are presented to demonstrate the validity and efficiency of the normalized structure selection algorithm.