MLreview2013

Basic restricted Boltzmann machine to learn letter patterns

clear; nh=100;  nepochs=150;  lrate=0.01; 
%load data from text file and rearrange into matrix
load pattern1.txt; 
letters = permute( reshape( pattern1, [12 26 13]), [1 3 2]);

%%train rbm for nepochs presentations of the 26 letters
input = reshape(letters,[12*13 26])
vb =zeros(12*13,1);  hb =zeros(nh,1);  w =.1*randn(nh,12*13);

figure; hold on; 
xlabel 'epoch'; ylabel 'error'; xlim([0 nepochs]);
for epoch=1:nepochs;
  err=0;  
  for i=1:26
    %Sample hidden units given input, then reconstruct.
    v = input(:,i);
    h = 1./(1 + exp(-(w *v + hb))); %sigmoidal activation
    hs= h > rand(nh,1);             %probabilistic sampling 
    vr= 1./(1 + exp(-(w'*hs+ vb))); %input reconstruction
    hr= 1./(1 + exp(-(w *vr+ hb))); %hidden reconstruction

    %Contrastive Divergence rule: dw ~ h*v - hr*vr
    dw  = lrate*(h*v'-hr*vr');  w = w +dw;
    dvb = lrate*( v  -  vr  );  vb= vb+dvb;
    dhb = lrate*( h  -  hr  );  hb= hb+dhb;
    err = err   + sum( (v-vr).^2 );   %reconstruction error
  end
  plot( epoch, err/(12*13*26), '.');  drawnow;%figure output
end

%%plot reconstructions of noisy letters 
r = randomFlipMatrix(round(.2*12*13)); %(20% of bits flipped)
noisy_letters = abs(letters - reshape(r,[12 13 26]));
recon = reshape(noisy_letters, 12*13, 26); %put data in matrix
recon=recon(:,1:5);                        %only plot first 10
figure; set(gcf,'Position',get(0,'screensize')); 

for i=0:3
  for j=1:5
    subplot(3+1, 5, i*5 + j);
    imagesc( reshape(recon(:,j),[12 13]) );  %plot 
    colormap gray; axis off; axis image;
    
    h = 1./(1 + exp(-(w *recon(:,j) + hb))); %compute hidden
    hs= h > rand(nh,1);                      %sample hidden
    recon(:,j) = 1./(1 + exp(-(w'*hs + vb)));%compute visible
    recon(:,j) = recon(:,j) > rand(12*13,1); %sample visible
  end
end
 
function r=randomFlipMatrix(n);
% returns matrix with components 1 at n random positions  
r=zeros(156,26);
for i=1:26
    x=randperm(156);
    r(x(1:n),i)=1;
end

An MLP with backpropagation for solving the XOR problem

clear; 
N_i=2; N_h=2; N_o=1;
w_h=randn(N_h,N_i); w_o=randn(N_o,N_h);

% training vectors (XOR)
r_i=[0 1 0 1 ; 0 0 1 1];
r_d=[0 1 1 0];

% Updating and training network with sigmoid activation function
for trial=1:5000;
    r_h=1./(1+exp(-w_h*r_i));
    r_o=1./(1+exp(-w_o*r_h));
  % error over all pattern
    d(trial)=0.5*sum((r_o-r_d).^2);
  % training  
    d_o=(r_o.*(1-r_o)).*(r_d-r_o);
    d_h=(r_h.*(1-r_h)).*(w_o'*d_o);
    w_o=w_o+0.7*(r_h*d_o')';
    w_h=w_h+0.7*(r_i*d_h')';
end
plot(d)  

Using libsvm for classification

clear; close all; figure; hold on; axis square

%% training data and training SVM
r1=2+rand(300,1); a1=2*pi*rand(300,1); polar(a1,r1,'bo');
r2=randn(300,1); a2=.5*pi*rand(300,1); polar(a2,r2,'rx');

x=[r1.*cos(a1),r1.*sin(a1);r2.*cos(a2),r2.*sin(a2)];
y=[zeros(300,1);ones(300,1)];
model=svmtrain(y,x);

%% test data and SVM predicition
r1=2+rand(300,1); a1=2*pi*rand(300,1); 
r2=randn(300,1); a2=.5*pi*rand(300,1); 
x=[r1.*cos(a1),r1.*sin(a1);r2.*cos(a2),r2.*sin(a2)];
yp=svmpredict(y,x,model);

figure; hold on; axis square
[tmp,I]=sort(yp);
plot(x(1:600-sum(yp),1),x(1:600-sum(yp),2),'bo');
plot(x(600-sum(yp)+1:600,1),x(600-sum(yp)+1:600,2),'rx');

Program for the chain example using policy iteration

% Chain example: Policy iteration 

 % Parameters
 clear; N=10; P=0.8; gamma=0.9; 

 % Reward function
 r = zeros(1,N) - 0.1; r(1)=-1;  r(N)=1;

 % Initiality random start policy and value function
 policy = ceil(2*rand(1,N)); policy(1)=2; policy(N)=1;
 Vpi = rand(1,N); Vpi(1)=r(1); Vpi(N)=r(N);

 for iter=1:3
    % Estimate V for this policy
    for i=1:10
        for s=2:N-1
            snext  = s-1+2*(policy(s)-1);
            sother = s+1-2*(policy(s)-1);
            Vpi(s) = r(s)+gamma*(P*Vpi(snext)+(1-P)*Vpi(sother));
        end
    end
    %Updating policy
    for s=2:N-1
        [tmp, policy(s)] = max([Vpi(s-1),Vpi(s+1)]);
    end
 end
 plot(Vpi);