Tracking Variability in Learning: Contrasting Statistical and Similarity-Based Accounts

Tracking Variability in Learning: Contrasting Statistical and Similarity-Based Accounts Yasuaki Sakamoto (yasu@psy.utexas.edu) Bradley C. Love (love@psy.utexas.edu) Matt Jones (mattj@psy.utexas.edu) Department of Psychology, The University of Texas at Austin Austin, TX 78712 USA Abstract between the nearest trained members (L6 and H1) of the low- variability and high-variability categories. Both prototype and exemplar models strongly predict that participants will classify border item N6 into the low-variance category because the same similarity metric is used for the low-variance and the high-variance categories, and the pro- totype for the low-variance category is closer to N6 as are the exemplars forming the low-variance category. In con- trast, distributional approaches, such as general recognition theory (Ashby & Townsend, 1986) and the category density model (Fried & Holyoak, 1984), predict that item N6 should belong to the high-variance category. These distributional ap- proaches are descendants of the unequal variance signal de- tection model (Green & Swets, 1966) and represent variabil- ity information separately for each category. Distributional approaches seem normative in that they use information about how members of a category vary from one another and this information can potentially improve accuracy. In Figure 1, the density functions of unequal variance depict the category representations of a distributional model. The density func- tion for the high-variability category is above the curve for the low-variability category at N6’s location. Therefore, the dis- tributional model predicts N6 belongs to the high-variability category. To foreshadow the results, participants are sensitive to the variability across category members as predicted by distri- butional models and classify the border item N6 into the high-variance category. This result seems to undermine ex- isting similarity-based approaches and favor distributional approaches. However, given the remarkable success of similarity-based models of categorization, it would be impru- dent to discard this class of models out of hand. The core in- tuitions underlying similarity-based models encompass con- structs like the representativeness heuristic (Tversky & Kah- neman, 1974). Moreover, findings like the inverse base rate effect (Medin & Edelson, 1988) are problematic for distribu- tional approaches. To reconcile this impasse, we present a simple extension to a similarity-based model that allow it to develop category representations that are sensitive to distribu- tional information that unequal variance models can exploit. In General Discussion, we will present related work in light of our findings. We should briefly note that although numer- ous studies have explored the effects of variability on cate- gorization, the true nature and extent of these effects is far from clear. Earlier work exploring the influence of category variability has not been diagnostic in evaluating similarity- based and distributional accounts (e.g., Homa & Vosburgh, 1976; Posner & Keele, 1968). Fried and Holyoak (1984) Learning to categorize objects involves learning which sources of variability are meaningful and which should be ignored or generalized. In this light, theories and models of category learning can be viewed as accounts of how people capture and represent meaningful variation. Similarity-based models, such as prototype and exemplar models, cannot correctly pre- dict that humans classify a stimulus halfway between the near- est members of a low-variability and high-variability category into the high-variability category. Distributional accounts, de- scending from the unequal variance signal detection model, can accommodate the result. We present a simple extension to similarity-based models that allows them to display the sensi- tivity to category variability that humans display. We conclude by discussing what constitutes similarity-based representations and processes and noting the points of convergence between similarity-based and distributional approaches. Humans operate in environments marked by variability. For instance, categorizing a novel stimulus (e.g., determining whether a person is friend or foe) involves generalizing from past experiences that differ from one another and the current situation. In this light, models of category learning are accounts of which sources of variability are meaningful and which should be ignored (i.e., generalized). For instance, prototype models abstract (i.e., average) across previous category members to form a central tendency or prototype (Posner & Keele, 1968). In prototype models, the meaningful way in which items vary is in their similarity (i.e., distance) to category prototypes. Exemplar models deem other sources of variability mean- ingful. Rather than storing a summary of previously experi- enced items as prototype models do, exemplar models store every experienced example in memory (Medin & Schaffer, 1978). In exemplar models, the meaningful way in which items vary is in the sum of their pairwise similarities (i.e., distances) to the exemplars representing each category. Although prototype and exemplar models offer quite dif- ferent accounts of how categories are represented, they both use similarity-based processing and can make overlapping predictions. Figure 1 illustrates a case in which these mod- els’ predictions converge. Participants learned to classify lines varying in length into one of two categories. Training items are illustrated as dark triangles. The six items (L1–L6) forming one category are relatively less variable than the six items (H1–H6) forming the contrasting category. Following training, participants classified a variety of items, including some items that were not experienced during training, such as item N6. These novel items are tests of how participants generalize. Item N6 is of particular interest as it is halfway