TR2015-133

Learning Positive Functions in a Hilbert Space


    •  Bagnell, J.A.; Farahmand, A.-M., "Learning Positive Functions in a Hilbert Space", NIPS Workshop on Optimization for Machine Learning (OPT), December 2015.
      BibTeX Download PDF
      • @inproceedings{Bagnell2015dec,
      • author = {Bagnell, J.A. and Farahmand, A.-M.},
      • title = {Learning Positive Functions in a Hilbert Space},
      • booktitle = {NIPS Workshop on Optimization for Machine Learning (OPT)},
      • year = 2015,
      • month = dec,
      • url = {http://www.merl.com/publications/TR2015-133}
      • }
  • Research Area:

    Data Analytics


We develop a method for learning positive functions by optimizing over SoSK, a reproducing kernel Hilbert space subject to a Sum-of-Squares (SoS) constraint. This constraint ensures that only nonnegative functions are learned. We establish a new representer theorem that demonstrates that the regularized convex loss minimization subject to the SoS constraint has a unique solution and moreover, its solution lies on a finite dimensional subspace of an RKHS that is defined by data. Furthermore, we show how this optimization problem can be formulated as a semidefinite program. We conclude with an example of learning such functions.