#logistic-regression

To correct covariate shift, you train logistic regression to distinguish training inputs (label $-1$) from equally many test inputs (label $+1$). For a training example $\mathbf{x}_i$ the classifier outputs $P(z{=}1 \mid \mathbf{x}_i) = 0.75$. Which importance weight $\beta_i = p(\mathbf{x}_i)/q(\mathbf{x}_i)$ should that example get in weighted empirical risk minimization, where $p$ is the test and $q$ the training input distribution?