Discussion : Latent Variable Graphical Model Selection via Convex Optimization
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چکیده
1. Introduction. We would like to congratulate the authors for their refreshing contribution to this high-dimensional latent variables graphical model selection problem. The problem of covariance and concentration matrices is fundamentally important in several classical statistical methodolo-gies and many applications. Recently, sparse concentration matrices estimation had received considerable attention, partly due to its connection to sparse structure learning for Gaussian graphical models. See, for example, Meinshausen and Bühlmann (2006) and Ravikumar et al. (2008). Cai, Liu & Zhou (2012) considered rate-optimal estimation. The authors extended the current scope to include latent variables. They assume that the fully observed Gaussian graphical model has a naturally sparse dependence graph. However, there are only partial observations available for which the graph is usually no longer sparse. Let X be (p + r) −variate Gaussian with a sparse concentration matrix S * (O,H). We only observe X O , p out of the whole p + r variables, and denote its covariance matrix by Σ * O. In this case, usually the p × p concentration matrix (Σ * O) −1 are not sparse. Let
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Rejoinder: Latent Variable Graphical Model Selection via Convex Optimization by Venkat Chandrasekaran,
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Discussion of “Latent Variable Graphical Model Selection via Convex Optimization”
We wish to congratulate the authors for their innovative contribution, which is bound to inspire much further research. We find latent variable model selection to be a fantastic application of matrix decomposition methods, namely, the superposition of low-rank and sparse elements. Clearly, the methodology introduced in this paper is of potential interest across many disciplines. In the followin...
متن کاملDiscussion: Latent Variable Graphical Model Selection via Convex Optimization by Steffen Lauritzen
We want to congratulate the authors for a thought-provoking and very interesting paper. Sparse modeling of the concentration matrix has enjoyed popularity in recent years. It has been framed as a computationally convenient convex 1constrained estimation problem in Yuan and Lin (2007) and can be applied readily to higher-dimensional problems. The authors argue—we think correctly—that the sparsit...
متن کاملDiscussion: Latent variable graphical model selection via convex optimization
We want to congratulate the authors for a thought-provoking and very interesting paper. Sparse modeling of the concentration matrix has enjoyed popularity in recent years. It has been framed as a computationally convenient convex l1-constrained estimation problem in Yuan and Lin (2007) and can be applied readily to higher-dimensional problems. The authors argue— we think correctly—that the spar...
متن کاملDiscussion: Latent variable graphical model selection via convex optimization
We wish to congratulate the authors for their innovative contribution, which is bound to inspire much further research. We find latent variable model selection to be a fantastic application of matrix decomposition methods , namely, the superposition of low-rank and sparse elements. Clearly, the methodology introduced in this paper is of potential interest across many disciplines. In the followi...
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تاریخ انتشار 2012