Causal Categorization with Bayes Nets

A theory of categorization is presented in which knowledge of causal relationships between category features is represented as a Bayesian network. Referred to as causal-model theory, this theory predicts that objects are classified as category members to the extent they are likely to have been produced by a categorys causal model. On this view, people have models of the world that lead them to expect a certain distribution of features in category members (e.g., correlations between feature pairs that are directly connected by causal relationships), and consider exemplars good category members when they manifest those expectations. These expectations include sensitivity to higher-order feature interactions that emerge from the asymmetries inherent in causal relationships. Research on the topic of categorization has traditionally focused on the problem of learning new categories given observations of category members. In contrast, the theory-based view of categories emphasizes the influence of the prior theoretical knowledge that learners often contribute to their representations of categories [1]. However, in contrast to models accounting for the effects of empirical observations, there have been few models developed to account for the effects of prior knowledge. The purpose of this article is to present a model of categorization referred to as causal-model theory or CMT [2, 3]. According to CMT, people 's know ledge of many categories includes not only features, but also an explicit representation of the causal mechanisms that people believe link the features of many categories. In this article I apply CMT to the problem of establishing objects category membership. In the psychological literature one standard view of categorization is that objects are placed in a category to the extent they have features that have often been observed in members of that category. For example, an object that has most of the features of birds (e.g., wings, fly, build nests in trees, etc.) and few features of other categories is thought to be a bird. This view of categorization is formalized by prototype models in which classification is a function of the similarity (i.e. , number of shared features) between a mental representation of a category prototype and a to-be-classified object. However , a well-known difficulty with prototype models is that a features contribution to category membership is independent of the presence or absence of other features. In contrast , consideration of a categorys theoretical knowledge is likely to influence which combinations of features make for acceptable category members. For example , people believe that birds have nests in trees because they can fly , and in light of this knowledge an animal that doesnt fly and yet still builds nests in trees might be considered a less plausible bird than an animal that builds nests on the ground and doesnt fly (e.g., an ostrich) even though the latter animal has fewer features typical of birds. To assess whether knowledge in fact influences which feature combinations make for good category members , in the following experiment undergraduates were taught novel categories whose four binary features exhibited either a common-cause or a common-effect schema (Figure 1). In the common-cause schema, one category feature (PI) is described as causing the three other features (F2, F3, and F4). In the common-effect schema one feature (F4) is described as being caused by the three others (F I, F2, and F3). CMT assumes that people represent causal knowledge such as that in Figure 1 as a kind of Bayesian network [4] in which nodes are variables representing binary category features and directed edges are causal relationships representing the presence of probabilistic causal mechanisms between features. Specifically , CMT assumes that when a cause feature is present it enables the operation of a causal mechanism that will, with some probability m , bring about the presence of the effect feature. CMT also allow for the possibility that effect features have potential background causes that are not explicitly represented in the network, as represented by parameter b which is the probability that an effect will be present even when its network causes are absent. Finally, each cause node has a parameter c that represents the probability that a cause feature will be present. Common-Cause Schema ~ ~ ® Common-Effect Schema Figure 1. . (~~) @ . .. : .... ~~:f·""""®1 ®"""::® " .... @/ ®'. F .• 3 Common-Cause Common-Effect Correlations Correlations