In this paper, we apply a weakly-supervised learning approach for slot tagging using con- ditional random fields by exploiting web search click logs. We extend the constrained lattice training of Tckstrm et al. (2013) to non-linear conditional random fields in which latent variables mediate between observations and labels. When combined with a novel initialization scheme that leverages unlabeled data, we show that our method gives signifi- cant improvement over strong supervised and weakly-supervised baselines.