Discovering Structure by Learning Sparse Graphs

Systems of concepts such as colors, animals, cities, and artifacts are richly structured, and people discover the structure of these domains throughout a lifetime of experience. Discovering structure can be formalized as probabilistic inference about the organization of entities, and previous work has operationalized learning as selection amongst specific candidate hypotheses such as rings, trees, chains, grids, etc. defined by graph grammars (Kemp & Tenenbaum, 2008). While this model makes discrete choices from a limited set, humans appear to entertain an unlimited range of hypotheses, many without an obvious grammatical description. In this paper, we approach structure discovery as optimization in a continuous space of all possible structures, while encouraging structures to be sparsely connected. When reasoning about animals and cities, the sparse model achieves performance equivalent to more structured approaches. We also explore a large domain of 1000 concepts with broad semantic coverage and no simple structure.