Multi-Kernel Regression with Sparsity Constraint

Overview:

i)  MATLAB implementation of learning using multiple kernels with gTV regularization 

ii) Comparison with other kernel methods in a simple numerical example.

Any usage of these codes is allowed as long as the user cites the following article:

S. Aziznejad, M. Unser, "An L1 Representer Theorem for Multiple-Kernel Regression," arXiv:1811.00836 [cs.LG]

Requirements:

i) GlobalBioIm library: https://github.com/Biomedical-Imaging-Group/GlobalBioIm

ii) SimpleMKL package:  http://asi.insa-rouen.fr/enseignants/~arakoto/code/mklindex.html

Discription:

Example.m : A simple illustrative example of learning a 1D function from its noisy samples.
GT.m      : The ground-truth function in our example.
Kernel Estimators: A folder that contains our implementation of four kernel estimators:   
    i)   L2RKHS.m: RKHS with L2 regularization. 
    ii)  L1RKHS.m: RKHS with L1 regularization.
    iii) MKL.m: Multiple kernel learning using SimpleMKL algorithm.
    iv)  gTV.m: gTV-based kernel regression. Both single and multiple kernel scenarios are included.
Auxilary Functions: A folder that contains the following auxilary functions that are required in our implementations:
    i)   CrossVal.m:    A cross-validation scheme for tuning the hyper-parameters of each method
    ii)  Gram_Matrix.m: Computing the Gramian matrix for both singel and multi-kernel schemes.
    iii) Kernel_computer.m: Computing the learned kernel expansion at a given series of points.
    iv)  Kernel.m: The parametric family of Super-exponential kernels that is used in our example. 

Contact information: For more information, please send an e-mail to [email protected] or [email protected]