Variational Inference based on Robust Divergences
Variational Inference based on Robust Divergences
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发表时间：
2017-10
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通讯作者：
Futoshi Futami;Issei Sato;Masashi Sugiyama
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作者：
Futoshi Futami;Issei Sato;Masashi Sugiyama
对离群值的鲁棒性是现实世界机器学习应用中的一个核心问题。当将模型替换为重尾模型时（例如，从高斯到Student-t）是鲁棒化的标准方法，但它只能应用于简单模型。在本文中，基于Zellner的优化和变分公式的贝叶斯推理，我们提出了一个离群鲁棒的伪贝叶斯变分方法取代Kullback-Leibler分歧用于数据拟合的一个强大的分歧，如beta和gamma-divergences。我们的方法的一个优点是，也可以处理上级但复杂的模型，如深度网络。我们从理论上证明了，对于具有ReLU激活函数的深度网络，我们提出的方法中的影响函数是有界的，而在普通变分推理中是无界的。这意味着，我们提出的方法是鲁棒的输入和输出离群值，而普通的变分方法不是。我们通过实验证明，我们的稳健变分方法在深度网络的回归和分类中优于普通变分推理。
Robustness to outliers is a central issue in real-world machine learning applications. While replacing a model to a heavy-tailed one (e.g., from Gaussian to Student-t) is a standard approach for robustification, it can only be applied to simple models. In this paper, based on Zellner's optimization and variational formulation of Bayesian inference, we propose an outlier-robust pseudo-Bayesian variational method by replacing the Kullback-Leibler divergence used for data fitting to a robust divergence such as the beta- and gamma-divergences. An advantage of our approach is that superior but complex models such as deep networks can also be handled. We theoretically prove that, for deep networks with ReLU activation functions, the \emph{influence function} in our proposed method is bounded, while it is unbounded in the ordinary variational inference. This implies that our proposed method is robust to both of input and output outliers, while the ordinary variational method is not. We experimentally demonstrate that our robust variational method outperforms ordinary variational inference in regression and classification with deep networks.