Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning
A N Gorban1, E M Mirkes1, A Zinovyev2
1Department of Mathematics, University of Leicester, Leicester, LE1 7RH, UK.
Abstract:
Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including high sensitivity to contaminating factors and dimensionality curse. Therefore, a lot of recent applications in machine learning exploited properties of non-quadratic error functionals based on L1 norm or even sub-linear potentials corresponding to quasinorms Lp (0
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