Chapter

Empirical Inference

pp 245-259

Date:

Kernels, Pre-images and Optimization

  • John C. SnyderAffiliated withDepartment of Chemistry, Department of Physics, University of California Email author 
  • , Sebastian MikaAffiliated withidalab GmbH
  • , Kieron BurkeAffiliated withDepartment of Chemistry, Department of Physics, University of California
  • , Klaus-Robert MüllerAffiliated withMachine Learning Group, Technical University of BerlinDepartment of Brain and Cognitive Engineering, Korea University Email author 

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Abstract

In the last decade, kernel-based learning has become a state-of-the-art technology in Machine Learning. We briefly review kernel PCAKernel principal component analysis (kPCA) (kPCA) and the pre-image problem that occurs in kPCA. Subsequently, we discuss a novel direction where kernel-based models are used for property optimization. For this purpose, a stable estimation of the model’s gradient is essential and non-trivial to achieve. The appropriate use of pre-image projections is key to successful gradient-based optimization—as will be shown for toy and real-world problems from quantum chemistry and physics.