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| − | [[Basic RBM]] | + | [[MLreview2013]] |
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| − | ==Basic restricted Boltzmann machine to learn letter patterns==
| + | * [[MLreview2013#RBM|Basic Restricted Boltzman Machine (RBM)]] |
| | + | * [[MLreview2013#MLP|Multi-Layer Perceptron (MLP)]] |
| | + | * [[MLreview2013#SVM|Support Vector Machine (SVM)]] |
| | + | * [[MLreview2013#MDP|Policy Iteration]] |
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| − | clear; nh=100; nepochs=150; lrate=0.01;
| + | [[Fundamentals of Computational Neuroscience (2nd Edition): Programs]] |
| − | %load data from text file and rearrange into matrix
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| − | load pattern1.txt;
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| − | letters = permute( reshape( pattern1, [12 26 13]), [1 3 2]);
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| − |
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| − | %%train rbm for nepochs presentations of the 26 letters
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| − | input = reshape(letters,[12*13 26])
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| − | vb =zeros(12*13,1); hb =zeros(nh,1); w =.1*randn(nh,12*13);
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| − |
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| − | figure; hold on;
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| − | xlabel 'epoch'; ylabel 'error'; xlim([0 nepochs]);
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| − | for epoch=1:nepochs;
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| − | err=0;
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| − | for i=1:26
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| − | %Sample hidden units given input, then reconstruct.
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| − | v = input(:,i);
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| − | h = 1./(1 + exp(-(w *v + hb))); %sigmoidal activation
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| − | hs= h > rand(nh,1); %probabilistic sampling
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| − | vr= 1./(1 + exp(-(w'*hs+ vb))); %input reconstruction
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| − | hr= 1./(1 + exp(-(w *vr+ hb))); %hidden reconstruction
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| − |
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| − | %Contrastive Divergence rule: dw ~ h*v - hr*vr
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| − | dw = lrate*(h*v'-hr*vr'); w = w +dw;
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| − | dvb = lrate*( v - vr ); vb= vb+dvb;
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| − | dhb = lrate*( h - hr ); hb= hb+dhb;
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| − | err = err + sum( (v-vr).^2 ); %reconstruction error
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| − | end
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| − | plot( epoch, err/(12*13*26), '.'); drawnow;%figure output
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| − | end
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| − |
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| − | %%plot reconstructions of noisy letters
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| − | r = randomFlipMatrix(round(.2*12*13)); %(20% of bits flipped)
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| − | noisy_letters = abs(letters - reshape(r,[12 13 26]));
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| − | recon = reshape(noisy_letters, 12*13, 26); %put data in matrix
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| − | recon=recon(:,1:5); %only plot first 10
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| − | figure; set(gcf,'Position',get(0,'screensize'));
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| − |
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| − | for i=0:3
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| − | for j=1:5
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| − | subplot(3+1, 5, i*5 + j);
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| − | imagesc( reshape(recon(:,j),[12 13]) ); %plot
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| − | colormap gray; axis off; axis image;
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| − |
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| − | h = 1./(1 + exp(-(w *recon(:,j) + hb))); %compute hidden
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| − | hs= h > rand(nh,1); %sample hidden
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| − | recon(:,j) = 1./(1 + exp(-(w'*hs + vb)));%compute visible
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| − | recon(:,j) = recon(:,j) > rand(12*13,1); %sample visible
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| − | end
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| − | end
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| − |
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| − | function r=randomFlipMatrix(n);
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| − | % returns matrix with components 1 at n random positions
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| − | r=zeros(156,26);
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| − | for i=1:26
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| − | x=randperm(156);
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| − | r(x(1:n),i)=1;
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| − | end
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| − | | |
| − | | |
| − | ==An MLP with backpropagation for solving the XOR problem==
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| − | clear; clf;
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| − | N_i=2; N_h=2; N_o=1;
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| − | w_h=rand(N_h,N_i)-0.5; w_o=rand(N_o,N_h)-0.5;
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| − |
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| − | % training vectors (XOR)
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| − | r_i=[0 1 0 1 ; 0 0 1 1];
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| − | r_d=[0 1 1 0];
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| − |
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| − | % Updating and training network with sigmoid activation function
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| − | for trial=1:10000;
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| − | % training randomly on one pattern
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| − | i=ceil(4*rand);
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| − | r_h=1./(1+exp(-w_h*r_i(:,i)));
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| − | r_o=1./(1+exp(-w_o*r_h));
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| − | d_o=(r_o.*(1-r_o)).*(r_d(:,i)-r_o);
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| − | d_h=(r_h.*(1-r_h)).*(w_o'*d_o);
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| − | w_o=w_o+0.7*(r_h*d_o')';
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| − | w_h=w_h+0.7*(r_i(:,i)*d_h')';
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| − | % test all pattern
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| − | r_o_test=1./(1+exp(-w_o*(1./(1+exp(-w_h*r_i)))));
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| − | d(trial)=0.5*sum((r_o_test-r_d).^2);
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| − | end
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| − | plot(d)
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| − | | |
| − | ==Using libsvm for classification==
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| − | | |
| − | clear; close all; figure; hold on; axis square
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| − |
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| − | %% training data and training SVM
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| − | r1=2+rand(300,1); a1=2*pi*rand(300,1); polar(a1,r1,'bo');
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| − | r2=randn(300,1); a2=.5*pi*rand(300,1); polar(a2,r2,'rx');
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| − |
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| − | x=[r1.*cos(a1),r1.*sin(a1);r2.*cos(a2),r2.*sin(a2)];
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| − | y=[zeros(300,1);ones(300,1)];
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| − | model=svmtrain(y,x);
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| − |
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| − | %% test data and SVM predicition
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| − | r1=2+rand(300,1); a1=2*pi*rand(300,1);
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| − | r2=randn(300,1); a2=.5*pi*rand(300,1);
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| − | x=[r1.*cos(a1),r1.*sin(a1);r2.*cos(a2),r2.*sin(a2)];
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| − | yp=svmpredict(y,x,model);
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| − |
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| − | figure; hold on; axis square
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| − | [tmp,I]=sort(yp);
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| − | plot(x(1:600-sum(yp),1),x(1:600-sum(yp),2),'bo');
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| − | plot(x(600-sum(yp)+1:600,1),x(600-sum(yp)+1:600,2),'rx');
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| − | | |
| − | | |
| − | ==Program for the chain example using policy iteration==
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| − | | |
| − | % Chain example: Policy iteration
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| − |
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| − | % Parameters
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| − | clear; N=10; P=0.8; gamma=0.9;
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| − |
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| − | % Reward function
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| − | r = zeros(1,N) - 0.1; r(1)=-1; r(N)=1;
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| − |
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| − | % Initiality random start policy and value function
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| − | policy = ceil(2*rand(1,N)); policy(1)=2; policy(N)=1;
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| − | Vpi = rand(1,N); Vpi(1)=r(1); Vpi(N)=r(N);
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| − |
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| − | for iter=1:3
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| − | % Estimate V for this policy
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| − | for i=1:10
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| − | for s=2:N-1
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| − | snext = s-1+2*(policy(s)-1);
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| − | sother = s+1-2*(policy(s)-1);
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| − | Vpi(s) = r(s)+gamma*(P*Vpi(snext)+(1-P)*Vpi(sother));
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| − | end
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| − | end
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| − | %Updating policy
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| − | for s=2:N-1
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| − | [tmp, policy(s)] = max([Vpi(s-1),Vpi(s+1)]);
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| − | end
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| − | end
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| − | plot(Vpi);
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