Robust L1 principal component analysis and its Bayesian variational inference
Robust L1 principal component analysis and its Bayesian variational inference
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DOI：
10.1162/neco.2007.11-06-397
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发表时间：
2008-02-01
影响因子：
2.9
通讯作者：
Gao, Junbin
中科院分区：
文献类型：
--
作者：
Gao, Junbin
我们引入了一种稳健的概率L1-PCA模型，将观测数据中噪声的传统高斯分布替换为拉普拉斯分布(或L1分布)。由于L1分布的重尾特性，所提出的模型对数据异常值具有更强的鲁棒性。在这封信中，我们演示了变分近似方案如何能够有效地推断概率L1-PCA模型中的关键参数。由于L1密度可以展开为无穷多个高斯密度的叠加，因此我们将L1-PCA模型表示为叠加上的边缘模型。通过这样做，可以基于变分期望最大化类型的算法来实现易于处理的贝叶斯推理。
We introduce a robust probabilistic L1-PCA model in which the conventional gaussian distribution for the noise in the observed data was replaced by the Laplacian distribution (or L1 distribution). Due to the heavy tail characteristics of the L1 distribution, the proposed model is supposed to be more robust against data outliers. In this letter, we demonstrate how a variational approximation scheme enables effective inference of key parameters in the probabilistic L1-PCA model. As the L1 density can be expanded as a superposition of infinite number of gaussian densities, we express the L1-PCA model as a marginalized model over the superpositions. By doing so, a tractable Bayesian inference can be achieved based on the variational expectation-maximization-type algorithm.