Searching for novel materials involves identifying potential candidates and selecting those that have desirable properties and facile synthesis. It is relatively easy to generate large numbers of potential candidates, for instance, by computational searches or elemental substitution. The identification of synthesizable compounds, however, is a needle-in-a-haystack problem. Conventionally, the screening is based on a convex hull construction, which identifies structures stabilized by a particular thermodynamic constraint, such as pressure, chosen based on prior experimental evidence or intuition. We introduce a generalized convex hull framework that instead relies on data-driven coordinates, and represents the full structural diversity of the candidate compounds in an unbiased way. Its probabilistic construction addresses the inevitable uncertainty in input structure data and provides a superior measure of stability compared to the input (free) energies, that can, for instance, also be used to assist experimental crystal structure determination. It efficiently identifies candidates with high probabilities of being synthesizable and suggests the relevant experimentally realizable constraints, thereby providing a much needed starting point for the determination of viable synthetic pathways.