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右奇异向量投影图：潜在混杂下的快速高维协方差估计AI 解读

Summary We consider the problem of estimating a high dimensional p × p covariance matrix Σ, given n observations of confounded data with covariance Σ+ΓΓT, where Γ is an unknown p × q matrix of latent factor loadings. We propose a simple and scalable estimator based on the projection onto the right singular vectors of the observed data matrix, which we call right singular vector projection (RSVP). Our theoretical analysis of this method reveals that, in contrast with…

存在部分隐藏变量时的稳健因果结构学习AI 解读

Summary We introduce a new method to estimate the Markov equivalence class of a directed acyclic graph (DAG) in the presence of hidden variables, in settings where the underlying DAG among the observed variables is sparse, and there are a few hidden variables that have a direct effect on many of the observed variables. Building on the so-called low rank plus sparse framework, we suggest a two-stage approach which first removes the effect of the hidden variables and then…

含潜变量的高斯条件随机场图模型选择AI 解读

We consider the problem of learning a conditional Gaussian graphical model in the presence of latent variables. Building on recent advances in this field, we suggest a method that decomposes the parameters of a conditional Markov random field into the sum of a sparse and a low-rank matrix. We derive convergence bounds for this estimator and show that it is well-behaved in the high-dimensional regime as well as "sparsistent" (i.e., capable of recovering the graph structure).…