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Robust Bayesian inference of networks using Dirichlet t-distributions

机译:使用Dirichlet t分布的鲁棒贝叶斯网络推理

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摘要

Bayesian graphical modeling provides an appealing way to obtain uncertaintyestimates when inferring network structures, and much recent progress has beenmade for Gaussian models. These models have been used extensively inapplications to gene expression data, even in cases where there appears to besignificant deviations from the Gaussian model. For more robust inferences, itis natural to consider extensions to t-distribution models. We argue that theclassical multivariate t-distribution, defined using a single latent Gammarandom variable to rescale a Gaussian random vector, is of little use in highlymultivariate settings, and propose other, more flexible t-distributions. Usingan independent Gamma-divisor for each component of the random vector defineswhat we term the alternative t-distribution. The associated model allows one toextract information from highly multivariate data even when most experimentscontain outliers for some of their measurements. However, the use of thisalternative model comes at increased computational cost and imposes constraintson the achievable correlation structures, raising the need for a compromisebetween the classical and alternative models. To this end we propose the use ofDirichlet processes for adaptive clustering of the latent Gamma-scalars, eachof which may then divide a group of latent Gaussian variables. Dirichletprocesses are commonly used to cluster independent observations; here they areused instead to cluster the dependent components of a single observation. Theresulting Dirichlet t-distribution interpolates naturally between the twoextreme cases of the classical and alternative t-distributions and combinesmore appealing modeling of the multivariate dependence structure with favorablecomputational properties.
机译:在推断网络结构时,贝叶斯图形建模提供了一种吸引人的方法来获得不确定性估计,并且高斯模型已经取得了许多最新进展。这些模型已广泛用于基因表达数据的应用中,即使在与高斯模型有明显偏差的情况下也是如此。为了获得更可靠的推论,我们自然会考虑扩展t分布模型。我们认为,使用单个潜在Gammarandom变量重新定标高斯随机向量的经典多元t分布在高度多元设置中几乎没有用,并提出了其他更灵活的t分布。对随机向量的每个分量使用独立的Gamma除数定义了我们所谓的替代t分布。即使大多数实验包含某些测量值的异常值,相关模型也可以从高度多元的数据中提取信息。然而,使用该替代模型会增加计算成本,并且对可实现的相关结构施加了约束,从而增加了在经典模型与替代模型之间进行折衷的需求。为此,我们建议使用Dirichlet过程对潜在的Gamma标量进行自适应聚类,然后每个分类都可以划分一组潜在的高斯变量。 Dirichlet过程通常用于对独立的观测进行聚类。在这里,它们被用来聚类单个观察的相关成分。结果Dirichlet t分布自然地在经典t分布和替代t分布的两种极端情况之间进行插值,并将多元吸引结构的更吸引人的建模与良好的计算特性结合在一起。

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  • 年度 2012
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