A simulated data for the illustration. Covariates \(x_i\) are drawn from \(N(\mu,I_{5\times 5})\) or \(N(-\mu,I_{5\times5})\) with probability 0.5. To make the first two variables active,\(\mu = [\mu_1,\dots,\mu_2,0,0,0]^T, \theta = [\theta_0,\dots,\theta_2,0,0,0]^T\) and we set \(\mu_i=1.5, \theta_i \sim Unif[0.5,1]\) Responses \(y_i\) is simulated via \(P_\theta(y=1|x) = 1/exp(-\theta^Tx)\). 1000 observations are sampled from the sub-population of positives(y=1) and labeled, and another 1000 observations are sampled from the original population and unlabeled.
data('simulPU')A list containing model matrix X, true response y, labeled/unlabeled response vector z, and a true positive probability truePY1.