ssmd_train.m

function model = ssmd_train(X,Y,model)
% SSMD_TRAIN Selective Sampling Mistake Driven
%
%    MODEL = SSMD_TRAIN(X,Y,MODEL) trains an classifier according to the
%    Selective Sampling Mistake Driven algorithm. The algorithm will query
%    a label only on certain rounds.
%
%    Additional parameters:
%    - model.K is the parameter to tune the query rate.
%      Default value is 1.
%
%   References:
%     - Cavallanti, G., Cesa-Bianchi, N., & Gentile, C. (2011)
%       Learning noisy linear classifiers via adaptive and selective sampling
%       Machine Learning, 83, (pp. 71-102).

%    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.w=zeros(1,size(X,1));
    model.w2=zeros(1,size(X,1));
    model.errTot=0;
    model.numSV=zeros(numel(Y),1);
    model.aer=zeros(numel(Y),1);
    model.pred=zeros(numel(Y),1);

    model.KbInv=eye(size(X,1))/model.a;
    model.numAskedLabels=zeros(numel(Y),1);
    model.numQueries=0;
    model.N=0;
end

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

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

    val_f=model.w*X(:,i);

    Yi=Y(i);
    
    KbInv_x=model.KbInv*X(:,i);
    r=X(:,i)'*KbInv_x;
    
    % Include the current sample to predict
    val_f=val_f/(r+1);

    model.errTot=model.errTot+(sign(val_f)~=Yi);
    model.aer(model.iter)=model.errTot/model.iter;
    model.pred(model.iter)=val_f;

    Kii=norm(X(:,i))^2;
    
    if val_f^2<=Kii*model.K*log(model.iter)/model.N
        model.numQueries=model.numQueries+1;
        if val_f*Yi<=0
            model.S(end+1)=model.iter;
            model.w=model.w+(Yi-val_f)/(1+r)*KbInv_x';
            model.KbInv=model.KbInv-KbInv_x*KbInv_x'/(1+r);
            model.N=model.N+1;
        end
    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