Robust Gradient Learning With Applications

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Abstract
This paper addresses the robust gradient learning (RGL) problem. Gradient learning models aim at learning the gradient vector of some target functions in supervised learning problems, which can be further used to applications, such as variable selection, coordinate covariance estimation, and supervised dimension reduction. However, existing GL models are not robust to outliers or heavy-tailed noise. This paper provides an RGL framework to address this problem in both regression and classification. This is achieved by introducing a robust regression loss function and proposing a robust classification loss. Moreover, our RGL algorithm works in an instance-based kernelized dictionary instead of some fixed reproducing kernel Hilbert space, which may provide more flexibility. To solve the proposed nonconvex model, a simple computational algorithm based on gradient descent is provided and the convergence of the proposed method is also analyzed. We then apply the proposed RGL model to applications, such as nonlinear variable selection and coordinate covariance estimation. The efficiency of our proposed model is verified on both synthetic and real data sets.
Funding Information
  • IWT: Ph.D. Post-Doctoral Grants through the SBO POM Project (100031)
  • iMinds Medical Information Technologies (SBO 2014)
  • European Research Council within the European Union Seventh Framework Programme FP7 2007-2013 through the ERC AdG ADATADRIVE-B Project (290923)
  • Research Council KUL through the MaNet Project (GOA/10/09)
  • OPTEC Project (CoE PFV/10/002, BIL12/11T)
  • Ph.D. Post-Doctoral Grants
  • Flemish Government: FWO: Ph.D. Post-Doctoral Grants through the Structured Systems Project (G.0377.12)
  • Tensor Based Data Similarity Project (G.088114N)
  • Belgian Federal Science Policy Office: IUAP P7 19 through the Dynamical Systems Control and Optimization 2012-2017

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