Scalable Bayesian Low-Rank Decomposition of Incomplete Multiway Tensors
Scalable Bayesian Low-Rank Decomposition of Incomplete Multiway Tensors
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发表时间：
2014-06
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通讯作者：
Piyush Rai;Yingjian Wang;Shengbo Guo;Gary Chen;D. Dunson;L. Carin
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作者：
Piyush Rai;Yingjian Wang;Shengbo Guo;Gary Chen;D. Dunson;L. Carin
我们提出了一个可伸缩的贝叶斯框架，用于多路张量数据的低阶分解。预先指定分解的等级的关键问题是使用乘法伽马过程事先以原则性的方式回避。连续数据和二进制数据都可以在该框架下使用完全共轭贝叶斯分析以连贯的方式进行分析。特别是，通过使用Polya-Gamma采样策略来促进非共轭二进制情况下的分析，该策略引起闭合形式的Gibbs采样更新。得到的采样器是有效的，使我们能够将我们的框架应用于大规模问题，时间复杂性与张量中观察到的条目的数量呈线性关系。这在分析非常大但很少观察到的张量和极少的已知条目时特别有吸引力。此外，我们的方法允许容易地扩展到监督设置，其中一个或多个张量模式中的实体具有标签。我们的方法在各种合成和基准真实数据集上的性能优于几种最先进的张量分解方法。
We present a scalable Bayesian framework for low-rank decomposition of multiway tensor data with missing observations. The key issue of pre-specifying the rank of the decomposition is sidestepped in a principled manner using a multiplicative gamma process prior. Both continuous and binary data can be analyzed under the framework, in a coherent way using fully conjugate Bayesian analysis. In particular, the analysis in the non-conjugate binary case is facilitated via the use of the Polya-Gamma sampling strategy which elicits closed-form Gibbs sampling updates. The resulting samplers are efficient and enable us to apply our framework to large-scale problems, with time-complexity that is linear in the number of observed entries in the tensor. This is especially attractive in analyzing very large but sparsely observed tensors with very few known entries. Moreover, our method admits easy extension to the supervised setting where entities in one or more tensor modes have labels. Our method outperforms several state-of-the-art tensor decomposition methods on various synthetic and benchmark real-world datasets.