Modeling strongly correlated random variables is a critical task in the context of latent variable models. A new probabilistic model, called Gaussian Pairwise Markov Field, is presented to generalize existing Markov Fields latent variables models, and to introduce more correlations between variables. This is done by considering the correlations within Gaussian Markov Random Fields models which are much richer than in the classical Markov Field models. The assets of the Gaussian Pairwise Markov Field model are explained. In particular, it offers a generalization of the classical Markov Field modelization that is highlighted. The new model is also considered in the practical case of unsupervised segmentation of images corrupted by long-range spatially-correlated noise, producing interesting new results.

在潜在变量模型的背景下，建模高度相关的随机变量是一项关键任务。提出了一个新的概率模型，称为高斯成对马尔可夫场，以概括现有的马尔可夫场潜变量模型，并引入变量之间的更多相关性。这是通过考虑高斯马尔可夫随机场模型中的相关性来完成的，该相关性比经典马尔可夫场模型中的相关性要丰富得多。解释了高斯成对马尔可夫场模型的资产。特别是，它提供了突出显示的经典Markov Field建模的概括。在无监督分割的图像的实际情况下，还考虑了新模型，该图像被远程空间相关的噪声破坏，产生了有趣的新结果。