Bayesian Approaches to Color Category Learning

One of the challenges that children face as they acquire a language is discovering how words are used to refer to different colors. While human languages demonstrate variation in how they partition the space of colors, there are also clear regularities in the kinds of systems of color categories that are used [1]. This raises two important questions: How might color categories be learned? And how might regularities in systems of color categories across languages be explained? Learning color categories is an inductive problem, requiring learners to make an inference from labeled examples of colors to a full system of color categories. As in other domains of perception [2], an “ideal observer” model can be used to explore the optimal solution to this problem. Let h denote a hypothesis about a possible system of color categories and d the observed data – a set of labeled examples (such as “This color is blue, and this color is yellow”). If learners represent the degree of belief in the truth of each hypothesis with a probability, P(h), then the ideal solution to the problem of updating these beliefs in light of the data d is provided by Bayes’ rule: