Dropout training for SVMs with data augmentation

Abstract

Dropout and other feature noising schemes have shown promise in controlling over-fitting by artificially corrupting the training data. Though extensive studies have been performed for generalized linear models, little has been done for support vector machines (SVMs), one of the most successful approaches for supervised learning. This paper presents dropout training for both linear SVMs and the nonlinear extension with latent representation learning. For linear SVMs, to deal with the intractable expectation of the non-smooth hinge loss under corrupting distributions, we develop an iteratively re-weighted least square (IRLS) algorithm by exploring data augmentation techniques. Our algorithm iteratively minimizes the expectation of a reweighted least square problem, where the re-weights are analytically updated. For nonlinear latent SVMs, we consider learning one layer of latent representations in SVMs and extend the data augmentation technique in conjunction with first-order Taylor-expansion to deal with the intractable expected hinge loss and the nonlinearity of latent representations. Finally, we apply the similar data augmentation ideas to develop a new IRLS algorithm for the expected logistic loss under corrupting distributions, and we further develop a non-linear extension of logistic regression by incorporating one layer of latent representations. Our algorithms offer insights on the connection and difference between the hinge loss and logistic loss in dropout training. Empirical results on several real datasets demonstrate the effectiveness of dropout training on significantly boosting the classification accuracy of both linear and nonlinear SVMs.

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Correspondence to Ning Chen.

Additional information

Ning Chen received her PhD degree in the Department of Computer Science and Technology at Tsinghua University, China, where she is currently an assistant researcher. She was a visiting researcher in the Machine Learning Department of Carnegie Mellon University, USA. Her research interests are primarily in machine learning, especially probabilistic graphical models with applications on data mining and bioinformatics.

Jun Zhu received his BS, MS and PhD degrees all from the Department of Computer Science and Technology at Tsinghua University, China, where he is currently an associate professor. He was a project scientist and postdoctoral fellow in the Machine Learning Department, Carnegie Mellon University, USA. His research interests focus on developing machine learning methods to understand scientific/ engineering data arising from various fields. He is a member of the IEEE.

Jianfei Chen received his BS degree from Department of Computer Science and Technology, Tsinghua University, China, where he is currently a PhD student. His research interests are primarily in machine learning, especially on probabilistic graphical models, Bayesian nonparametrics and data mining problems such as social networks.

Ting Chen received his BS degree in computer science from Tsinghua University, China in 1993 and PhD degree from SUNY Stony Brook, USA in 1997. He is currently a professor in Tsinghua National Lab for Information Science and Technology. He was a professor of biological sciences, computer science, and mathematics at University of Southern California, USA. His research interests are in applying machine learning and computer algorithms to answer questions in biology and medicine.

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Chen, N., Zhu, J., Chen, J. et al. Dropout training for SVMs with data augmentation. Front. Comput. Sci. 12, 694–713 (2018). https://doi.org/10.1007/s11704-018-7314-7

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Keywords

  • dropout
  • SVMs
  • logistic regression
  • data augmentation
  • iteratively reweighted least square