Bayesian inference for nonnegative matrix factorisation models.
Bayesian inference for nonnegative matrix factorisation models.
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DOI：
10.1155/2009/785152
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发表时间：
2009
影响因子：
--
通讯作者：
Cemgil AT
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文献类型：
--
作者：
Cemgil AT
我们描述了非负矩阵分解（NMF）与Kullback-Leibler（KL）误差测量的统计框架，与层次生成模型组成的观察和先验分量。省略先验导致标准KL-NMF算法作为特殊情况，其中最大似然参数估计通过期望最大化（EM）算法进行。从这个角度出发，我们通过变分贝叶斯或蒙特卡罗开发了完整的贝叶斯推理。我们的构造保留了共轭性，使我们能够开发更强大的模型，同时保留标准NMF的吸引力，如单调收敛和易于实现。我们说明了我们的方法模型阶数的选择和图像重建。
We describe nonnegative matrix factorisation (NMF) with a Kullback-Leibler (KL) error measure in a statistical framework, with a hierarchical generative model consisting of an observation and a prior component. Omitting the prior leads to the standard KL-NMF algorithms as special cases, where maximum likelihood parameter estimation is carried out via the Expectation-Maximisation (EM) algorithm. Starting from this view, we develop full Bayesian inference via variational Bayes or Monte Carlo. Our construction retains conjugacy and enables us to develop more powerful models while retaining attractive features of standard NMF such as monotonic convergence and easy implementation. We illustrate our approach on model order selection and image reconstruction.