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摘要翻译：
我们考虑了估计一个高斯或二元分布的参数的问题，这样得到的无向图形模型是稀疏的。我们的方法是求解一个带有L_1范数惩罚项的极大似然问题。该问题是凸问题，但对于节点数超过数十个的问题，现有内点方法的内存需求和复杂性是令人望而却步的。在高斯情形下，我们提出了两个解决至少有一千个节点的问题的新算法。我们的第一个算法使用块坐标下降，可以解释为递归L_1范数惩罚回归。我们的第二种算法基于Nesterov的一阶方法，比现有的内点方法产生了更好的复杂度估计。利用对数配分函数的对数行列式松弛(Wainwright&Jordan(2006))，我们证明了这些算法可以用来求解二元情形下的近似稀疏极大似然问题。我们在合成数据、基因表达和参议院投票记录数据上测试我们的算法。
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英文标题：
《Model Selection Through Sparse Maximum Likelihood Estimation》
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作者：
Onureena Banerjee, Laurent El Ghaoui, Alexandre d'Aspremont
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最新提交年份：
2007
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分类信息：
一级分类：Computer Science 计算机科学
二级分类：Artificial Intelligence 人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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一级分类：Computer Science 计算机科学
二级分类：Machine Learning 机器学习
分类描述：Papers on all aspects of machine learning research (supervised, unsupervised, reinforcement learning, bandit problems, and so on) including also robustness, explanation, fairness, and methodology. cs.LG is also an appropriate primary category for applications of machine learning methods.
关于机器学习研究的所有方面的论文（有监督的，无监督的，强化学习，强盗问题，等等），包括健壮性，解释性，公平性和方法论。对于机器学习方法的应用，CS.LG也是一个合适的主要类别。
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英文摘要：
We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm penalty term. The problem as formulated is convex but the memory requirements and complexity of existing interior point methods are prohibitive for problems with more than tens of nodes. We present two new algorithms for solving problems with at least a thousand nodes in the Gaussian case. Our first algorithm uses block coordinate descent, and can be interpreted as recursive l_1-norm penalized regression. Our second algorithm, based on Nesterov's first order method, yields a complexity estimate with a better dependence on problem size than existing interior point methods. Using a log determinant relaxation of the log partition function (Wainwright & Jordan (2006)), we show that these same algorithms can be used to solve an approximate sparse maximum likelihood problem for the binary case. We test our algorithms on synthetic data, as well as on gene expression and senate voting records data.
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PDF链接：
https://arxiv.org/pdf/0707.0704
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