k_dgs_mod_train.m

function model = k_dgs_mod_train(X,Y,model)
% K_DGS_MOD_TRAIN Kernel Modified Dekel-Gentile-Sridharan selective sampler algorithm
%
%    MODEL = K_DGS_MOD_TRAIN(X,Y,MODEL) trains an classifier according to
%    the modified Dekel-Gentile-Sridharan selective sampler algorithm,
%    using kernels. The algorithm will query a label only on certain
%    rounds.
%
%    Additional parameters:
%    - model.delta is probability coefficient.
%      Default value is 0.1.
%    - model.originalQueryRule if set to 1 it will the original query rule
%      proposed by Dekel et al.
%      Default value is 0.
%    - model.alpha is the constant used in the modified query rule.
%      Default value is 1.
%
%   References:
%     - Orabona, F., Cesa-Bianchi, N. (2011).
%       Better Selective Sampling Algorithms.
%       Proceedings of the 26th International Conference on Machine Learning.
%
%     - Dekel, O., Gentile, C., & Sridharan, K. (2010).
%       Robust Selective Sampling from Single and Multiple Teachers.
%       Proceedings of the 23rd Annual Conference on Learning Theory.

%    This file is part of the DOGMA library for Matlab.
%    Copyright (C) 2009-2011, Francesco Orabona
%
%    This program is free software: you can redistribute it and/or modify
%    it under the terms of the GNU General Public License as published by
%    the Free Software Foundation, either version 3 of the License, or
%    (at your option) any later version.
%
%    This program is distributed in the hope that it will be useful,
%    but WITHOUT ANY WARRANTY; without even the implied warranty of
%    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
%    GNU General Public License for more details.
%
%    You should have received a copy of the GNU General Public License
%    along with this program.  If not, see <http://www.gnu.org/licenses/>.
%
%    Contact the author: francesco [at] orabona.com

n = length(Y);   % number of training samples

model.a=1;

if isfield(model,'iter')==0
    model.iter=0;
    model.beta=[];
    model.beta2=[];
    model.errTot=0;
    model.numSV=zeros(numel(Y),1);
    model.aer=zeros(numel(Y),1);
    model.pred=zeros(numel(Y),1);

    model.KbInv=[];
    model.sum_rt=0;
    model.numAskedLabels=zeros(numel(Y),1);
    model.numQueries=0;
    model.th=zeros(numel(Y),1);
    model.Y_S=[];
    model.obsErr=0;
end

if isfield(model,'delta')==0
    model.delta=.1;
end

if isfield(model,'originalQueryRule')==0
    model.originalQueryRule=0;
end

if isfield(model,'alpha')==0
    model.alpha=1;
end


for i=1:n
    model.iter=model.iter+1;

    Kii=feval(model.ker,X(:,i),X(:,i),model.kerparam);
    
    if numel(model.S)>0
        if isempty(model.ker)
            K_f=X(model.S,i);
        else
            K_f=feval(model.ker,model.SV,X(:,i),model.kerparam);
        end
        val_f=model.beta*K_f;
        coeff=model.KbInv*K_f;
        r=Kii-K_f'*coeff;
    else
        val_f=0;
        r=Kii;
    end

    Yi=Y(i);
        
    %rt=delta/(delta+1);

    model.errTot=model.errTot+(sign(val_f)~=Yi);
    model.aer(model.iter)=model.errTot/model.iter;
    model.pred(model.iter)=val_f;
    if model.originalQueryRule==0
       th=model.alpha*r*(4*model.sum_rt+36*log(model.iter/model.delta))*log(model.iter);
    else
       th=r*(1+4*model.sum_rt+36*log(model.iter/model.delta));
    end
    model.th(model.iter)=model.sum_rt;
                
    if val_f^2<=th
        model.numQueries=model.numQueries+1;
        
        dimS=numel(model.S);
        model.SV(:,end+1)=X(:,i);

        if dimS>0
            % incremental update of the inverse matrix
            model.KbInv=[model.KbInv, zeros(dimS,1);zeros(1,dimS+1)];
            model.KbInv=model.KbInv+[coeff; -1]*[coeff; -1]'/(r+model.a);
        else    
            model.KbInv=full(1/(Kii+model.a));
        end
        
        model.S(end+1)=model.iter;
        model.Y_S(end+1)=Yi;
        
        % Projection step
        model.Y_S(end)=model.Y_S(end)-sign(val_f)*max(abs(val_f)-1,0)/r;

        model.beta=model.Y_S*model.KbInv;
        
        model.sum_rt=model.sum_rt+r/(r+1);
    end
    
    model.numAskedLabels(model.iter)=model.numQueries;
    model.numSV(model.iter)=numel(model.S);
    
    if mod(i,model.step)==0
      fprintf('#%.0f SV:%5.2f(%d)\tAER:%5.2f\tAskedLabels:%5.2f(%d)\n', ...
            ceil(i/1000),numel(model.S)/model.iter*100,numel(model.S),...
            model.aer(model.iter)*100,model.numQueries/model.iter*100,...
            model.numQueries);
    end
end