Learning Latent Variable Gaussian Graphical Models

Zhaoshi Meng; Brian Eriksson; Alfred O. Hero III

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arXiv · 1406.2721

Learning Latent Variable Gaussian Graphical Models

Zhaoshi Meng·Brian Eriksson·Alfred O. Hero III

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Abstract

Gaussian graphical models (GGM) have been widely used in many high-dimensional applications ranging from biological and financial data to recommender systems. Sparsity in GGM plays a central role both statistically and computationally. Unfortunately, real-world data often does not fit well to sparse graphical models. In this paper, we focus on a family of latent variable Gaussian graphical models (LVGGM), where the model is conditionally sparse given latent variables, but marginally non-sparse. In LVGGM, the inverse covariance matrix has a low-rank plus sparse structure, and can be learned in a regularized maximum likelihood framework. We derive novel parameter estimation error bounds for LVGGM under mild conditions in the high-dimensional setting. These results complement the existing theory on the structural learning, and open up new possibilities of using LVGGM for statistical inference.

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BibTeX RIS

Zhaoshi Meng, Brian Eriksson, Alfred O. Hero III. 2014-06-10. Learning Latent Variable Gaussian Graphical Models. https://arxiv.org/abs/1406.2721

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