The discovery of structural form

Abstract

Algorithms for finding structure in data have become increasingly important both as tools for scientific data analysis and as models of human learning, yet they suffer from a critical limitation. Scientists discover qualitatively new forms of structure in observed data: For instance, Linnaeus recognized the hierarchical organization of biological species, and Mendeleev recognized the periodic structure of the chemical elements. Analogous insights play a pivotal role in cognitive development: Children discover that object category labels can be organized into hierarchies, friendship networks are organized into cliques, and comparative relations (e.g., ''bigger than'' or ''better than'') respect a transitive order. Standard algorithms, however, can only learn structures of a single form that must be specified in advance: For instance, algorithms for hierarchical clustering create tree structures, whereas algorithms for dimensionality-reduction create low-dimensional spaces. Here, we present a computational model that learns structures of many different forms and that discovers which form is best for a given dataset. The model makes probabilistic inferences over a space of graph grammars representing trees, linear orders, multidimensional spaces, rings, dominance hierarchies, cliques, and other forms and successfully discovers the underlying structure of a variety of physical, biological, and social domains. Our approach brings structure learning methods closer to human abilities and may lead to a deeper computational understanding of cognitive development.cognitive development ͉ structure discovery ͉ unsupervised learning

The discovery and comparison of symbolic magnitudes

“…Without clear constraints, it is hard to derive testable predictions. However, we can evaluate the specific model of linear orderings that Kemp and Tenenbaum (2008) provided. This model has two basic problems as a psychological proposal.…”

The origins of inquiry: inductive inference and exploration in early childhood

“…Recent advances in computational modeling have provided formal accounts of how abstract knowledge can both be learned and support learning from sparse data across content domains [60][61][62][63][64][65]. Some of children's inferential abilities can be captured with these models (see, e.g., [61,66], for reviews and analysis).…”

“…However, the likelihood favors h1 and h3, because colds and lung cancer are more likely than the flu to generate coughing. Thus the posterior probability favors the hypothesis that the child has a cold (example from, and detailed account available in [62]). Bayes' law also provides a formal account unifying what might otherwise seem like very different routes to uncertainty and exploration.…”

“…Hierarchical Bayesian inference models provide a formal account of our ability to jointly infer such abstract 'over-hypotheses', together with subordinate hypotheses that constrain the interpretation of subsequent data, showing for instance that learners can simultaneously infer a specific tree-structure and the fact that the data are organized as a tree (e.g., rather than a ring or a chain) [60][61][62][63][64]. Recently researchers have shown that even infants can infer over hypotheses from sparse data [65].…”

Connectionist modeling of developmental changes in infancy: Approaches, challenges, and contributions.

“…The model was successful in simulating infants' behavior, which suggested that a common mechanism may operate during category learning throughout the life span. This type of modeling that uses the same mechanism to model child and adult behavior has been an active area of research in other modeling approaches as well (e.g., probabilistic modeling: Kemp & Tenenbaum, 2008; dynamic field theory: Perone et al, 2011).…”