SPIDER The Spider Objects

Structure Output Learning using Joint Kernel Method

   A=reg_jkm(H) returns a reg_jkm object initialized with hyperparameters H.   
   Requires input of the form (x_i,z_i) -> y_i where y_i is a scalar
   and one is interested in learning the map y=f(x,z) in order to find
   pre-images z*=g(x)=argmax_z* f(x,z*). 
   Expects the data object to be of the form
   d.X{1}=x_: d.X{2}=z_: d.Y=y_: 
   and x_ and z_ should be normalized so ||x_i||=||z_i||=1
   Hyperparameters, and their defaults   
    ridge=1e-5           -- regularization on input kernel  
    child=kernel         -- the kernel for inputs stored as member "child"  
    ok=kernel            -- the kernel for outputs  
    output_preimage=0    -- output index from training sample of  preimage   
                            instead of actual label  
                                     =1    -- output f(x,y), i.e. the score assigned to these
     training_method =0 (default) --Perform ridge regression to learn the
                                         =1 -- Perform kernel matching pursuit
                                         to learn the mapping
     max_Xsv             = 100 -- maximal number of Support Vectors. This
                                     parameter is only taken into account
                                     when training_method is set to 1
     optimizer             = 'full_inversion' -- Optimization method for
                                         kernel matching pursuit
    alpha                -- the weights   
    Xsv                  -- the Support Vectors  
    train, test 
    a.child = joint_kernel;
    m=100;n=2;   example of identity map in 2 dimensions, 10 examples
    X=[I; randn(m,n)]; 
    Z=[I; I];
    Y=[ones(m,1) ; zeros(m,1)];
      data gives 20 examples of correct map (top) and 10 false maps (bottom)
      now.. normalize data to have length 1 (required)
    for i=1:length(X)
      setup data
    d=data(X); d2 = data(Z);
    dj = joint_data({d,d2},Y);
    [r a]=train(a,dj);