SLI | Classes / NSC

 cd regression
 Dtrain = load('mcycleTrain.txt');
 Xtr=Dtrain(:,2); Ytr=Dtrain(:,1);
 figure;
 plot(Xtr,Ytr,'r.');

 Xtrain = [Xtr.^0 Xtr.^1];
 Ytrain = Ytr;

 th = regress( Ytrain, Xtrain )

 Xp = [0:.01:2]';
 Xp1= [Xp.^0 Xp.^1];
 rfun = Xp1 * th; 

 hold on; plot(Xp,rfun,'k-');

 % degree 5 polynomial fit
 Xtrain = [Xtr.^0 Xtr.^1 Xtr.^2 Xtr.^3 Xtr.^4 Xtr.^5];
 th = regress( Ytrain, Xtrain )

 Xp = [0:.01:2]';
 %Xp1= [Xp.^0 Xp.^1 Xp.^2 Xp.^3 Xp.^4 Xp.^5];
 Xp1= polyx( Xp , 5);
 rfun = Xp1 * th;
 hold on; plot(Xp,rfun,'b-');

 %
 X = Xtr(1:15,:); Y=Ytr(1:15);
 for p=0:10,
   th = regress( Y, polyx(X,p) );
   Yhat = polyx(X,p)*th;
   mseTrain(p+1) = mean( (Y-Yhat).^2 );
 end ;
 figure; semilogy(0:10,mseTrain,'r-'); 

 Dtest = load('mcycleTest.txt');
 Xtest=Dtest(:,2); Ytest=Dtest(:,1);
 for p=0:10,
   th = regress( Y, polyx(X,p) );
   Yhat = polyx(Xtest,p)*th;
   mseTest(p+1) = mean( (Ytest-Yhat).^2 );
 end;
 hold on; semilogy(0:10,mseTest,'g-');

 Dtrain = load('mcycleTrain.txt');
 Xtr=Dtrain(1:15,2); Ytr=Dtrain(1:15,1);
 Dtest = load('mcycleTest.txt');
 Xtest=Dtest(:,2); Ytest=Dtest(:,1);

 mseTrain=[]; mseTest=[];
 p=10; alpha=10.^[-5 -4 -3 -2 -1 0 1]
 for j=1:length(alpha),
   X1 = polyx(Xtr,p);
   th = Ytr'*X1*inv(X1'*X1 + alpha(j)*eye(p+1)),
   Yhat = polyx(Xtr,p)*th';
   mseTrain(j) = mean( (Ytr-Yhat).^2 );
   Yhat = polyx(Xtest,p)*th';
   mseTest(j) = mean( (Ytest-Yhat).^2 );
 end ;
 figure; loglog(alpha,mseTrain,'r-',alpha,mseTest,'g-');

 % L1-regularized models
 addpath('../downloads/glmnet_matlab');
 which glmnet

Xtr = polyx(Xtrain(1:15,:),10); Ytr=Ytrain(1:15,:); Xtr = polyx(Xtrain,10); Ytr=Ytrain;

fit = glmnet(Xtr,Ytr); % default: gaussian lasso glmnetPrint(fit); % show penalties corresponding to changes in feature set theta = glmnetCoef(fit,lambda); % get actual coefficients at some value of lambda lambda=1.5; Yhat = glmnetPredict(fit, 'response', Xtest, lambda) % make predictions

Xp = [0:.01:2]'; Xp1= polyx( Xp , 10); rfun=glmnetPredict(fit,'response',Xp1,1.5); figure; plot(Xp,rfun,'k-',Xtr,Ytr,'r.')

===================================

D=load('iris.txt'); X=D(:,1:2); Y=D(:,end);

I0=find(Y==0); I1=find(Y==1); I2=find(Y==2); figure; plot(X(I0,1),X(I0,2),'bo'); hold on; plot(X(I1,1),X(I1,2),'gx'); hold on; plot(X(I2,1),X(I2,2),'rs');

knn = knnClassifyC(1,X,Y); knn = knn.setK(1); class2DPlot(knn,X,Y);

 % Logistic regression

 %Y=D(:,end); X=D(Y~=0,1:2); Y=Y(Y~=0);
 %coeff = glmfit(X, Y-1, 'binomial', 'link','logit');
 %phat  = glmval(coeff, Xtest, 'logit');

 D=load('iris.txt');
 Y=D(:,end); X=D(Y~=0,1:2); Y=Y(Y~=0);
 lR = logRegC(X,Y-1);
 class2DPlot(lR,X,Y-1);

 lR = logRegPC(X,Y-1);
 class2DPlot(lR,X,Y-1);


 lR=logRegL1C(.1,X,Y-1)
 class2DPlot(lR,X,Y-1);

 Dtrain = load('ALL_AML_train.csv');
 Dtest  = load('ALL_AML_test.csv');
 Ytr = Dtrain(1,:)';  Xtr = Dtrain(2:end,:)';
 Yte = Dtest(1,:)';   Xte = Dtest(2:end,:)';


 fit = glmnet(Xtr,Ytr+1,'binomial');
 glmnetPrint(fit);
 % 2 features at lambda = .35
 coef = glmnetCoef(fit, .35);
 find(coef ~= 0)   % find non-zero feature coefficients

 lR = logRegC( Xtr(:,[3321 4848]), Ytr );
 class2DPlot(lR, Xtr(:,[3321 4848]), Ytr);

 Decision trees:
 classregtree

 N=50000; M=20;   % many examples of 20 variables in a Markov chain
 x=zeros(N,M);
 x(:,1)  = rand(N,1) > .5;
 for j=2:M,
   x(:,j) = mod(x(:,j-1) + (rand(N,1) > .9) ,2);
 end;
 x = x + .1*randn(size(x));

 C = cov(x);
 D=diag(diag(C)); C=D^(-.5) * C * D^(-.5);
 J=inv(C);
 D=diag(diag(J)); J=D^(-.5) * J * D^(-.5);
 figure(1); imagesc(C);
 figure(2); imagesc(J);



 N=50; M=20;   % many examples of 20 variables in a Markov chain
 x=zeros(N,M);
 x(:,1)  = rand(N,1) > .5;
 for j=2:M,
  x(:,j) = mod(x(:,j-1) + (rand(N,1) > .9) ,2);
 end;
 x = x + .1*randn(size(x));

 C = cov(x);
 D=diag(diag(C)); C=D^(-.5) * C * D^(-.5);
 J=inv(C);
 D=diag(diag(J)); J=D^(-.5) * J * D^(-.5);
 figure(1); imagesc(C);
 figure(2); imagesc(J);


 C=cov(x);


 fit = glmnet(x(:,2:end),x(:,1)); % default: gaussian lasso
 glmnetPrint(fit);   % show penalties corresponding to changes in feature set
 theta = glmnetCoef(fit,lambda);  % get actual coefficients at some value of lambda


 % Regression version of network estimation
 idx=10; rest=[1:idx-1,idx+1:M];
 fit = glmnet(x(:,rest),x(:,idx)); % default: gaussian lasso
 glmnetPrint(fit);   % show penalties corresponding to changes in feature set
 lambda = .11;      % gives 3 non-zero terms
 theta = glmnetCoef(fit,lambda);  % get actual coefficients at some value of  lambda
 rest(find(theta~=0)),


 % Graphical lasso