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.

本文介绍了一种条件稀疏的潜变量高斯图模型（LVGGM），利用正则化的极大似然方法来学习具有低秩加稀疏结构的逆协方差矩阵，并在高维情况下得到了新的参数估计误差界限。

学习潜变量高斯图模型

Learning Latent Variable Gaussian Graphical Models

Rejoinder to "Latent variable graphical model selection via convex
optimization" by Venkat Chandrasekaran, Pablo A. Parrilo and Alan S. Willsky
[arXiv:1008.1290].

对 Venkat Chandrasekaran、Pablo A. Parrilo 和 Alan S. Willsky 的文章 “通过凸优化进行潜变量图模型选择” 的回应。

潜变量图模型选择的凸优化方法

Rejoinder: Latent variable graphical model selection via convex  optimization

Suppose we want to build a system that answers a natural language question by
representing its semantics as a logical form and computing the answer given a
structured database of facts. The core part of such a system is the semantic
parser that maps questions to logical forms. Semantic parsers are typically
trained from examples of questions annotated with their target logical forms,
but this type of annotation is expensive.
Our goal is to learn a semantic parser from question-answer pairs instead,
where the logical form is modeled as a latent variable. Motivated by this
challenging learning problem, we develop a new semantic formalism,
dependency-based compositional semantics (DCS), which has favorable linguistic,
statistical, and computational properties. We define a log-linear distribution
over DCS logical forms and estimate the parameters using a simple procedure
that alternates between beam search and numerical optimization. On two standard
semantic parsing benchmarks, our system outperforms all existing
state-of-the-art systems, despite using no annotated logical forms.

研究使用问题 - 回答对来学习语义解析器，其中逻辑形式被建模为潜变量，并提出了一种新的语义形式 —— 基于依赖的组成语义学。该方法具有有利的语言学、统计和计算性质，并在两个标准语义解析基准测试中优于所有现有的最先进系统。