Generalization and similarity in exemplar models of categorization: Insights from machine learning

Abstract

Exemplar theories of categorization depend on similarity for explaining subjects' ability to generalize to new stimuli. A major criticism of exemplar theories concerns their lack of abstraction mechanisms and thus, seemingly, of generalization ability. Here, we use insights from machine learning to demonstrate that exemplar models can actually generalize very well. Kernel methods in machine learning are akin to exemplar models and are very successful in real-world applications. Their generalization performance depends crucially on the chosen similarity measure. Although similarity plays an important role in describing generalization behavior, it is not the only factor that controls generalization performance. In machine learning, kernel methods are often combined with regularization techniques in order to ensure good generalization. These same techniques are easily incorporated in exemplar models. We show that the generalized context model (Nosofsky, 1986) and ALCOVE (Kruschke, 1992) are closely related to a statistical model called kernel logistic regression. We argue that generalization is central to the enterprise of understanding categorization behavior, and we suggest some ways in which insights from machine learning can offer guidance.

Does Cognitive Science Need Kernels?

“…The response of the perceptron to a stimulus can then be expressed as a weighted combination of the similarity of the stimulus to the training exemplars. This is what exemplar models in cognitive psychology do (Kruschke, 1992;Nosofsky, 1992;Jäkel, Schölkopf, & Wichmann, 2008a) (see Box 2 for details and Fig. 2 for an illustration of an exemplar model).…”

“…In a recent series of papers, we have spelled out explicitly the relationships between certain kernel methods in machine learning and common exemplar models in cognitive science (Jäkel et al, 2007(Jäkel et al, , 2008a(Jäkel et al, , 2008b. These studies provide groundwork for transferring insights from kernel methods to exemplar models.…”

“…As in the perceptron, learning in this representation can be understood as estimating weights. In cognitive science such a model is called an exemplar model (Kruschke, 1992;Nosofsky, 1992;Jäkel et al, 2008a). Hence, each set of feature detectors defines a natural similarity measure k such that any perceptron can equivalently be expressed as an exemplar model.…”

“…The similarity measure is called a kernel in machine learning, hence the term kernel methods. Interestingly, many similarity measures that are used in cognitive psychology are kernels in the machine learning sense (Jäkel et al, 2007(Jäkel et al, , 2008aJäkel, Schölkopf, & Wichmann, 2008b). In particular, radial basis functions (RBFs)-for example Gaussians or Laplaciansare used in models of categorization (Nosofsky, 1986;Kruschke, 1992;Love, Medin, & Gureckis, 2004) and object recognition (Poggio & Edelman, 1990;Bülthoff & Edelman, 1992).…”

“…In fact, there are already attempts to use insights on generalization for understanding human category learning (Jäkel et al, 2008a;Love et al, 2004;Briscoe & Feld-Box 4 Glossary Generalization: The response of a learner to previously unseen stimuli. Generalization is a crucial aspect of learning.…”