Computational methods for predicting ligand affinity where no protein structure is known generally take the form of regression analysis based on molecular features that have only a tangential relationship to a protein/ligand binding event. Such methods have limited utility when structural variation moves beyond congeneric series. We present a novel approach based on the multiple-instance learning method of Compass, where a physical model of a binding site is induced from ligands and their corresponding activity data. The model consists of molecular fragments that can account for multiple positions of literal protein residues. We demonstrate the method on 5HT1a ligands by training on a series with limited scaffold variation and testing on numerous ligands with variant scaffolds. Predictive error was between 0.5 and 1.0 log units (0.7-1.4 kcal/mol), with statistically significant rank correlations. Accurate activity predictions of novel ligands were demonstrated using a validation approach where a small number of ligands of limited structural variation known at a fixed time point were used to make predictions on a blind test set of widely varying molecules, some discovered at a much later time point.