--- /dev/null
+%X is generated following a gaussian mixture \sum pi_r N(meanX_k, covX_r)
+%Y is generated then, with Y_i ~ \sum pi_r N(Beta_r.X_i, covY_r)
+function[X,Y,Z] = generateIO(meanX, covX, covY, pi, beta, n)
+
+ [p, ~, k] = size(covX);
+ [m, ~, ~] = size(covY);
+ if exist('octave_config_info')
+ %Octave statistics package doesn't have gmdistribution()
+ X = zeros(n, p);
+ Z = zeros(n);
+ cs = cumsum(pi);
+ for i=1:n
+ %TODO: vectorize ? http://stackoverflow.com/questions/2977497/weighted-random-numbers-in-matlab
+ tmpRand01 = rand();
+ [~,Z(i)] = min(cs - tmpRand01 >= 0);
+ X(i,:) = mvnrnd(meanX(Z(i),:), covX(:,:,Z(i)), 1);
+ end
+ else
+ gmDistX = gmdistribution(meanX, covX, pi);
+ [X, Z] = random(gmDistX, n);
+ end
+
+ Y = zeros(n, m);
+ BX = zeros(n,m,k);
+ for i=1:n
+ for r=1:k
+ %compute beta_r . X_i
+ BXir = zeros(1, m);
+ for mm=1:m
+ BXir(mm) = dot(X(i,:), beta(:,mm,r));
+ end
+ %add pi(r) * N(beta_r . X_i, covY) to Y_i
+ Y(i,:) = Y(i,:) + pi(r) * mvnrnd(BXir, covY(:,:,r), 1);
+ end
+ end
+
+end