% generate some random data
n=200; m=20;
beta_true=randn(m,1); epsilon=1E-1;
X=rand(n,m)-.5; 
y=X*beta_true+randn(n,1)*epsilon;

% normalize everything
[n,m]=size(X);
y=y-mean(y); 
y=y/std(y);
X=X-repmat(mean(X,1),n,1);
stdX=std(X,0,1); %sqrt(sum(X.^2,1));
X=X./repmat(stdX,n,1);
beta_true=beta_true.*stdX';

% feed it to LARS
[betas]=lars(X,y);

% look at the betas as they change
figure(1);
s=sum(abs(betas),1);
plot(s, betas'); 
xlabel('|\beta|'); ylabel('\beta_i'); title('coefficients(\beta''s) as they change');

% look at performance of regression, i.e. estimating the true beta
figure(2);
plot(sqrt(sum((repmat(beta_true,1,m)-betas).^2,1))); 
xlabel('number of features'); ylabel('L_2 norm with true \beta'); title('regression performance vs number of features');