Making Inferences and Classifications Using Categories That Are Not Linearly Separable

Making Inferences and Classifications Using Categories That Are Not Linearly Separable Takashi Yamauchi Arthur B. Markman Texas AM Tversky & Kahneman, 1974; Yamauchi & Markman, 2000, in press). Another source of category-based induction comes from individual exemplars of a category. Many studies have shown that people classify items by retrieving information about specific exemplars from memory (Kruschke, 1992; Medin & Schaffer, 1978; Nosofsky, 1986). A similar process may be used to make feature inferences. In predicting an unknown feature of an item, people may predict characteristics of the new item based on exemplars stored in memory. Studies investigating classification have shown that exemplar information plays a crucial role in making classification judgments. Research on inductive inference, however, reveals that category-level abstract feature information (e.g., prototypes) is crucial for inference. For example, Anderson and Fincham (1996) demonstrated that people are capable of predicting the value for one feature given the value of another, based on the overall correlation between the features in the study phase of the experiment, rather than on the basis of seeing those specific values during the study phase. Yamauchi and Markman (2000) further showed that varying the appearance of exemplars during learning disrupts classification, but not inference. These findings suggest that, while classification and inference may be formally equivalent, they make use of different kinds of information in practice (Yamauchi & Markman, 1998). In this paper, we extend this hypothesis and examine the idea that category-level summary information provides a basis for inference (e.g., prototypes), while exemplar information plays a major role in classification. In the following sections, we describe the inference and classification tasks that were employed in our experiments. Then, we examine the role of exemplar and prototype information in two experiments. Classification and Inference In our experiments, classification is defined as a practice in which an item is placed into one of two groups based on its attributes. Inference is defined as a practice in which an attribute of an item is predicted given the category label of the item as well as information about its other attributes. For example, classification as we define it is akin to the prediction of a category to which a person belongs (e.g., Democrat) having observed his attributes (e.g., supports affirmative action and favors reduced defense spending). Inference is akin to predicting an attribute of a person (e.g., supports affirmative action) given a category to which he belongs, and other known attributes (e.g., is a Democrat and favors reducing defense spending). We further define the term category label as a symbol that represents category membership by denoting a particular group of exemplars, and the term category feature as a symbol that denotes a characteristic of an exemplar. Classification requires the prediction of the category label based on the features of the item; inference requires the prediction of a category feature based on the information about other features and the category label. In our experiments, subjects learn two categories (Table 1a) through a classification task or an inference task. On a classification trial, subjects are presented with a stimulus depicting the values of the form, size, color and position of the geometric figure, and they predict the category label of that stimulus (see Figure 1a). On an inference trial, subjects are presented with the values of the size, shape and position of the geometric figure along with the category label to which the stimulus belongs (e.g., Set A), and they predict the value of the missing feature (e.g., the color) (Figure 1b). On different trials, subjects predict different features. In this manner, classification and inference are formally equivalent if a category label is regarded as simply another feature (Anderson, 1990; but see Yamauchi & Markman, 1998, in press, for further discussion).