Sparse Graphical Modeling via Stochastic Complexity
Sparse Graphical Modeling via Stochastic Complexity
复制标题
通过随机复杂性的稀疏图形建模
DOI：
10.1137/1.9781611974973.81
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Yamanishi Kenji
中科院分区：
文献类型：
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作者：
Miyaguchi Kohei;Matsushima Shin;Yamanishi Kenji
发现能够生成数据的真正稀疏模型对于理解数据源的性质是一个具有挑战性但又重要的问题。挑战的一个主要部分来自于这样一个事实，即随着模型的维度增加，可能的稀疏模型的数量呈指数级增长。在这项研究中，我们考虑了一种方法，估计真实的模型在指数大量的稀疏模型的基础上的最小描述长度原则。我们表明，一个新的标准，通过连续松弛的随机复杂性诱导选择的真实模型，通过解决的11-正则化问题的超参数被适当地选择。此外，我们提供了一个有效的优化算法，找到合适的超参数，并选择相应的稀疏模型。我们得到的稀疏图形建模问题的实验结果表明，该方法估计的真实模型有效地选择超参数来解决thel 1-正则化问题的现有方法相比。
Discovering a true sparse model capable of generating data is a challenging yet important problem for understanding the nature of the source of the data. A major part of the challenge arises from the fact that the number of possible sparse models grows exponentially as the dimensionality of the models increases. In this study, we consider a method for estimating the true model over an exponentially large number of sparse models based on the minimum description length principle. We show that a novel criterion derived bycontinuous relaxation of the stochastic complexityinduces selection of the true model by solving thel1-regularization problem for which the hyperparameters are appropriately chosen. Moreover, we provide an efficient optimization algorithm for finding the appropriate hyperparameters and select the sparse model accordingly. The experimental results we obtained for the problem of sparse graphical modeling indicate that the proposed method estimates the true model effectively in comparison to existing methods for choosing hyperparameters to solve thel1-regularization problem.