Discriminative, or (structured) prediction, methods have proved effective for variety of problems in computer vision; a notable example is 3D monocular pose estimation. All methods to date, however, relied on an assumption that training (source) and test (target) data come from the same underlying joint distribution. In many real cases, including standard data sets, this assumption is flawed. In the presence of training set bias, the learning results in a biased model whose performance degrades on the (target) test set. Under the assumption of covariate shift, we propose an unsupervised domain adaptation approach to address this problem. The approach takes the form of training instance reweighting, where the weights are assigned based on the ratio of training and test marginals evaluated at the samples. Learning with the resulting weighted training samples alleviates the bias in the learned models. We show the efficacy of our approach by proposing weighted variants of kernel regression (KR) and twin Gaussian processes (TGP). We show that our weighted variants outperform their unweighted counterparts and improve on the state-of-the-art performance in the public (HumanEva) data set.