Bayesian Learning in Sparse Graphical Factor Models via Variational Mean-Field Annealing
Bayesian Learning in Sparse Graphical Factor Models via Variational Mean-Field Annealing
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DOI：
10.5555/1756006.1859910
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发表时间：
2010-03
期刊：
影响因子：
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通讯作者：
Ryo Yoshida;M. West
中科院分区：
文献类型：
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作者：
Ryo Yoshida;M. West
我们描述了一类稀疏潜在因子模型，称为图形因子模型（GFM），和相关的稀疏学习算法后验模式估计。线性高斯GFM具有稀疏的正交因子加载矩阵，除了隐含协方差矩阵的稀疏性之外，还通过隐含精度矩阵中的零诱导条件独立结构。我们描述了稀疏潜在因子结构和数据/信号重建的鲁棒估计模型及其使用。我们开发了计算算法的模型探索和后验模式搜索，解决了硬组合优化搜索在一个巨大的空间的潜在稀疏配置。一个平均场变分技术与退火相结合，连续产生“人工”后验分布，在退火时间表中的极限温度下，定义所需的后验模式中的GFM参数空间。几个详细的实证研究和相关方法的比较进行了讨论，包括手写数字图像和癌症基因表达数据的分析。
We describe a class of sparse latent factor models, called graphical factor models (GFMs), and relevant sparse learning algorithms for posterior mode estimation. Linear, Gaussian GFMs have sparse, orthogonal factor loadings matrices, that, in addition to sparsity of the implied covariance matrices, also induce conditional independence structures via zeros in the implied precision matrices. We describe the models and their use for robust estimation of sparse latent factor structure and data/signal reconstruction. We develop computational algorithms for model exploration and posterior mode search, addressing the hard combinatorial optimization involved in the search over a huge space of potential sparse configurations. A mean-field variational technique coupled with annealing is developed to successively generate "artificial" posterior distributions that, at the limiting temperature in the annealing schedule, define required posterior modes in the GFM parameter space. Several detailed empirical studies and comparisons to related approaches are discussed, including analyses of handwritten digit image and cancer gene expression data.