Complexity Measures and Concept Learning

The nature of concept learning is a core question in cognitive science. Theories must account for the relative difficulty of acquiring different concepts by supervised learners. For a canonical set of six category types, two distinct orderings of classification difficulty have been found. One ordering, which we call paradigm-specific, occurs when adult human learners classify objects with easily distinguishable characteristics such as size, shape, and shading. The general order occurs in all other known cases: when adult humans classify objects with characteristics that are not readily distinguished (e.g., brightness, saturation, hue); for children and monkeys; and when categorization difficulty is extrapolated from errors in identification learning. The paradigm-specific order was found to be predictable mathematically by measuring the logical complexity of tasks, i.e., how concisely the solution can be represented by logical rules. However, logical complexity does not explain the general order. Here we show that a new difficulty measurement, i.e., the amount of uncertainty remaining when a subset of the dimensions are specified, can correctly predict the general order. This result contrasts with the logical-complexity-based task ordering because our proposed measurement captures statistical, not logical, complexity. This suggests that, when learners do not/cannot form logical rules about the characteristics of objects, they may be using statistical means in their category learning. It is known in information science that logical (algorithmic) and statistical (information theoretic) complexities are fundamentally linked. Our proposed statistical Preprint submitted to Elsevier July 1, 2014 complexity measurement, therefore, naturally complements the logical complexity one and extends the overall applicability of the complexity-based approach to understanding concept learning.