In cheminformatics, compound-target binding profiles has been a main source of data for research. For data repositories that only provide positive profiles, a popular assumption is that unreported profiles are all negative. In this paper, we caution audience not to take this assumption for granted, and present empirical evidence of its ineffectiveness from a machine learning perspective. Our examination is based on a setting where binding profiles are used as features to train predictive models; we show (1) prediction performance degrades when the assumption fails and (2) explicit recovery of unreported profiles improves prediction performance. In particular, we propose a framework that jointly recovers profiles and learns predictive model, and show it achieves further performance improvement. The presented study not only suggests applying matrix recovery methods to recover unreported profiles, but also initiates a new missing feature problem which we called Learning with Positive and Unknown Features.