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arXiv 1901.09712cs.LGstat.ML
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具有潜在条件高斯变量的Ising模型

Ising Models with Latent Conditional Gaussian Variables

Friedrich-Schiller-Universität Jena(耶拿弗里德里希·席勒大学)

Frank Nussbaum, Joachim Giesen

摘要:

伊辛模型描述了二元特征变量向量的联合概率分布。通常情况下,并非所有的变量都相互作用,人们对学习相互作用变量的稀疏网络结构感兴趣。然而,在潜在变量的存在下,学习稀疏模型的传统方法可能会失败。这是因为潜变量引起了观测变量的间接相互作用。在只有几个潜在的条件高斯变量的情况下,这些虚假的相互作用有助于一个额外的低秩分量的观察到的伊辛模型的相互作用参数。因此,我们建议使用凸正则化似然问题来学习伊辛模型参数的稀疏+低秩分解。我们表明,同样的问题可以得到一个最大熵的问题与一种新类型的放松,其中样本的手段共同需要匹配的预期值只有一个给定的公差的对偶。凸优化问题的解决方案在高维环境中具有一致性,其中允许观察到的二进制变量的数量和潜在条件高斯变量的数量随着训练样本的数量而增长。

英文摘要:

Ising models describe the joint probability distribution of a vector of binary feature variables. Typically, not all the variables interact with each other and one is interested in learning the presumably sparse network structure of the interacting variables. However, in the presence of latent variables, the conventional method of learning a sparse model might fail. This is because the latent variables induce indirect interactions of the observed variables. In the case of only a few latent conditional Gaussian variables these spurious interactions contribute an additional low-rank component to the interaction parameters of the observed Ising model. Therefore, we propose to learn a sparse + low-rank decomposition of the parameters of an Ising model using a convex regularized likelihood problem. We show that the same problem can be obtained as the dual of a maximum-entropy problem with a new type of relaxation, where the sample means collectively need to match the expected values only up to a given tolerance. The solution to the convex optimization problem has consistency properties in the high-dimensional setting, where the number of observed binary variables and the number of latent conditional Gaussian variables are allowed to grow with the number of training samples.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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