Structures and properties of many inorganic compounds have been collected historically. However, it only covers a very small portion of possible inorganic crystals, which implies the presence of numerous currently unknown compounds. A powerful machine-learning strategy is mandatory to discover new inorganic compounds from all chemical combinations. Herein we propose a descriptor-based recommender-system approach to estimate the relevance of chemical compositions where crystals can be formed [i.e., chemically relevant compositions (CRCs)]. In addition to data-driven compositional similarity used in the literature, the use of compositional descriptors as a prior knowledge is helpful for the discovery of new compounds. We validate our recommender systems in two ways. First, one database is used to construct a model, while another is used for the validation. Second, we estimate the phase stability for compounds at expected CRCs using density functional theory calculations.