Classification response times in probabilistic rule-based category structures: Contrasting exemplar-retrieval and decision-boundary models

Experiments were conducted to contrast the predictions from exemplar models and rule-based decisionboundary models of perceptual classification. Observers classified multidimensional stimuli into categories that could be described in terms of easily verbalized logical rules. The critical manipulation was that some pairs of stimuli received probabilistic feedback, whereas other control pairs received deterministic feedback. Despite the probabilistic feedback, the probabilistic pairs and the deterministic pairs were the same distance from idealobserver, rule-based decision boundaries. Across two experiments with varying category structures, observers classified the probabilistic pairs with slower response times (RTs) and lower accuracies than the comparison deterministic pairs. The effects were relatively long term, extending into test blocks in which all feedback was withheld. The results were as predicted by exemplar models, but challenged models that posit that RT is a function solely of the distance of a stimulus from rule-based boundaries. The studies add considerable generality to previous ones and suggest that, even in domains involving rule-based category structures, exemplar-retrieval processes play a significant role. Supplemental materials related to this article may be downloaded from http:// mc.psychonomic-journals.org/content/supplemental.     

Comparing exemplar-retrieval and decision-bound models of speeded perceptual classification

The authors compared the exemplar-based random-walk (EBRW) model of Nosofsky and Palmeri (1997) and the decision-bound model (DBM) of Ashby and Maddox (1994; Maddox & Ashby, 1996) on their ability to predict performance in Garner’s (1974) speeded classification tasks. A key question was the extent to which the models could predict facilitation in the correlated task and interference in the filtering task, in situations involving integral-dimension stimuli. To obtain rigorous constraints for model evaluation, the goal was to fit the detailed structure of the response time (RT) distribution data associated with each individual stimulus in each task. Both models yielded reasonably good global quantitative fits to the RT distribution and accuracy data. However, the DBM failed to properly characterize the interference effects in the filtering task. Apparently, a fundamental limitation of the DBM is that it predicts that the fastest RTs in the filtering task should be faster than the fastest RTs in the control task, whereas the opposite pattern was observed in our data.     

Comparisons between exemplar similarity and mixed prototype models using a linearly separable category structure

Nosofsky and Zaki (2002) found that an exemplar similarity model provided better accounts of individual subject classification and generalization performance than did a mixed prototype model proposed by Smith and Minda (1998; Minda & Smith, 2001). However, these previous tests used a nonlinearly separable category structure. In the present work, the authors extend the previous findings by demonstrating a superiority for the exemplar generalization model over the mixed prototype model in a case involving a linearly separable structure. Because this structure has numerous features that Minda and Smith argued should be conducive to prototype-based processing, the results pose a significant challenge to the mixed prototype view.     

Episodic and prototype models of category learning

The question of what processes are involved in the acquisition and representation of categories remains unresolved despite several decades of research. Studies using the well-known prototype distortion task (Posner and Keele in J Exp Psychol 77:353–363, 1968) delineate three candidate models. According to exemplar-based models, we memorize each instance of a category and when asked to decide whether novel items are category members or not, the decision is explicitly based on a similarity comparison with each stored instance. By contrast, prototype models assume that categorization is based on the similarity of the target item to an implicit abstraction of the central tendency or average of previously encountered instances. A third model suggests that the categorization of prototype distortions does not depend on pre-exposure to study exemplars at all and instead reflects properties of the stimuli that are easily learned during the test. The four experiments reported here found evidence that categorization in this task is predicated on the first and third of these models, namely transfer at test and the exemplar-based model. But we found no evidence for the second candidate model that assumed that categorization is based on implicit prototype abstraction.     

Influence of manipulated category knowledge on prototype classification and recognition

The recognition and classification of category members was explored, following a variable number of learning trials. In Experiment 1, subjects received 1 or 9 learning trials, followed by a recognition-then-classification test containing old, new, prototype, and foil patterns. In Experiment 2, subjects received 1, 6, or 12 trials, and made either classification or recognition judgments. In each experiment, classification accuracy for all item types was at near-chance -performance after a single trial but steadily increased with increased learning trials. On the transfer test, oldness judgments were highest for the category prototype after a single trial. However, with increased learning trials, oldness judgments increased for old instances and decreased for the category prototype and new instances. We suggest that false recognition of the category prototype, especially after a single learning trial, need not reflect an abstraction process. We discuss the possibility that an abstracted prototype may emerge with additional learning as an unfamiliar, ideal point.     

Prototypes in category learning: the effects of category size, category structure, and stimulus complexity

Although research in categorization has sometimes been motivated by prototype theory, recent studies have favored exemplar theory. However, some of these studies focused on small, poorly differentiated categories composed of simple, 4-dimensional stimuli. Some analyzed the aggregate data of entire groups. Some compared powerful multiplicative exemplar models to less powerful additive prototype models. Here, comparable prototype and exemplar models were fit to individual-participant data in 4 experiments that sampled category sets varying in size, level of category structure, and stimulus complexity (dimensionality). The prototype model always fit the observed data better than the exemplar model did. Prototype-based processes seemed especially relevant when participants learned categories that were larger or contained more complex stimuli.     

Stimulus dependence in probabilistic category learning

The current study investigates whether probabilistic categorization on the Weather Prediction task involves a single, modality/domain general learning mechanism or there are modality/domain differences. The same probabilistic categorization task was used in three modalities/domains and two modes of presentation. Cues consisted of visual, auditory-verbal or auditory-nonverbal stimuli, and were presented either sequentially or simultaneously. Results show that while there was no general difference in performance across modalities/domains, the mode of presentation affected them differently. In the visual modality, simultaneous performance had a general advantage over sequential presentation, while in the auditory conditions, there was an initial advantage of simultaneous presentation, which disappeared, and in the non-verbal condition, gave over to a sequential advantage in the later stages of learning. Data suggest that there are strong peripheral modality effects; however, there are no signs of modality/domain of stimuli centrally affecting categorization.     

Error discounting in probabilistic category learning

The assumption in some current theories of probabilistic categorization is that people gradually attenuate their learning in response to unavoidable error. However, existing evidence for this error discounting is sparse and open to alternative interpretations. We report 2 probabilistic-categorization experiments in which we investigated error discounting by shifting feedback probabilities to new values after different amounts of training. In both experiments, responding gradually became less responsive to errors, and learning was slowed for some time after the feedback shift. Both results were indicative of error discounting. Quantitative modeling of the data revealed that adding a mechanism for error discounting significantly improved the fits of an exemplar-based and a rule-based associative learning model, as well as of a recency-based model of categorization. We conclude that error discounting is an important component of probabilistic learning.     

Effects of contrasting category,conjoint frequency and typicality on categorization

Two experiments were conducted to investigate whether (a) experience with a contrasting category, (b) conjoint frequency of dimensional values, (c) range of typicality of values, and (d) type of information administered during learning influenced subsequent test performance. Each experiment began with an observational category learning task, employing faces as stimuli. This was followed by a classification test task and by pairwise comparisons of faces. Influence of a contrasting category was studied in experiment 1 by varying frequency of values of the contrasting category, and in experiment 2 by either including or not including a contrasting category in the learning task. Results indicated that (a) categorization is influenced by experience with a contrasting category, (b) conjoint frequency enhances the importance of values to a category, (c) broad typicality range experience reduces typicality differences among exemplars of a category, whereas small range experience diminishes differences in a contrasting category, and (d) information on representativeness of exemplars does not facilitate subsequent test performance. The implications of the results for categorization models are discussed.     

A probabilistic account of exemplar and category generation

People are capable of imagining and generating new category exemplars and categories. This ability has not been addressed by previous models of categorization, most of which focus on classifying category exemplars rather than generating them. We develop a formal account of exemplar and category generation which proposes that category knowledge is represented by probability distributions over exemplars and categories, and that new exemplars and categories are generated by sampling from these distributions. This sampling account of generation is evaluated in two pairs of behavioral experiments. In the first pair of experiments, participants were asked to generate novel exemplars of a category. In the second pair of experiments, participants were asked to generate a novel category after observing exemplars from several related categories. The results suggest that generation is influenced by both structural and distributional properties of the observed categories, and we argue that our data are better explained by the sampling account than by several alternative approaches.     

Features of graded category structure: Generalizing the family resemblance and polymorphous concept models

Many real-world categories contain graded structure: certain category members are rated as more typical or representative of the category than others. Research has shown that this graded structure can be well predicted by the degree of commonality across the feature sets of category members. We demonstrate that two prominent feature-based models of graded structure, the family resemblance (Rosch & Mervis, 1975) and polymorphous concept models (Hampton, 1979), can be generalized via the contrast model (Tversky, 1977) to include both common and distinctive feature information, and apply the models to the prediction of typicality in 11 semantic categories. The results indicate that both types of feature information play a role in the prediction of typicality, with common features weighted more heavily for within-category predictions, and distinctive features weighted more heavily for contrast-category predictions. The same pattern of results was found in additional analyses employing rated goodness and exemplar generation frequency. It is suggested that these findings provide insight into the processes underlying category formation and representation.     

Categorization reaction time,category structure,and category size in semantic memory using artificial categories

This study examined the effects of category structure and category size on categorization reaction time, artificial categories being used to obtain greater experimental control than is usually found in semantic memory research. Four artificial categories varying in structure (hierarchical and nonhierarchical) and size (8 or 16 instances) were introduced to 20 adolescent subjects over a 12-week period by means of stories, exercises, and discussions. Significantly longer categorization reaction times were required for instances from the hierarchical categories, but no set size effect was found. The application of clustering and multidimensional scaling procedures to subjects’ free recall data revealed that subjects had acquired the hierarchical structures but imposed their own structures on the other categories. These findings were interpreted within a spreading activation framework.     

Diagnosticity and prototypicality in category learning: a comparison of inference learning and classification learning

Category knowledge allows for both the determination of category membership and an understanding of what the members of a category are like. Diagnostic information is used to determine category membership; prototypical information reflects the most likely features given category membership. Two experiments examined 2 means of category learning, classification and inference learning, in terms of sensitivity to diagnostic and prototypical information. Classification learners were highly sensitive to diagnostic features but not sensitive to nondiagnostic, but prototypical, features. Inference learners were less sensitive to the diagnostic features than were classification learners and were also sensitive to the nondiagnostic, prototypical, features. Discussion focuses on aspects of the 2 learning tasks that might lead to this differential sensitivity and the implications for learning real-world categories.     

Effects of similarity and practice on speeded classification response times and accuracies: Further tests of an exemplar-retrieval model

Observers were tested in a perceptual category-learning experiment in which they were instructed to make classification decisions as rapidly as possible without making errors. Nosofsky and Palmeri's (1997b) exemplar-based random walk (EBRW) model of speeded classification was tested for its ability to fit the classification response times and accuracies. The authors demonstrated that the EBRW model provided good quantitative fits to the mean response times and accuracies associated with individual objects as a function of their locations in a multidimensional similarity space and as a function of practice in the task. Preliminary evidence was also obtained that stimulus-specific adjustments in the random walk response criteria may have occurred during the course of learning.     

Challenging the role of implicit processes in probabilistic category learning

Considerable interest in the hypothesis that different cognitive tasks recruit qualitatively distinct processing systems has led to the proposal of separate explicit (declarative) and implicit (procedural) systems. A popular probabilistic category learning task known as the weather prediction task is said to be ideally suited to examine this distinction because its two versions, “observation” and “feedback,” are claimed to recruit the declarative and procedural systems, respectively. In two experiments, we found results that were inconsistent with this interpretation. In Experiment 1, a concurrent memory task had a detrimental effect on the implicit (feedback) version of the task. In Experiment 2, participants displayed comparable and accurate insight into the task and their judgment processes in the feedback and observation versions. These findings have important implications for the study of probabilistic category learning in both normal and patient populations.     

The role of working memory and visual processing in prototype category learning

To investigate whether working memory and visual processing have the same role or different roles in A/B and A/not A prototype category learning, the present study adopted an A/B or A/not A category learning task in control and dual conditions. The results of Experiment 1 showed that an additional dual visual working memory task rather than a dual verbal working memory task reduced accuracy of the A/B task, whereas no dual tasks influenced accuracy of the A/not A task. The results of Experiment 2 revealed that an additional dual visual processing task impaired accuracy of the A/B task, whereas the dual visual processing task did not influence accuracy of the A/not A task. These results indicate that visual working memory and visual processing play different roles in A/B and A/not A prototype category learning, and support that these two types of prototype category learning are mediated by different memory systems.     

Overconfidence effects in category learning: a comparison of connectionist and exemplar memory models

Exemplar and connectionist models were compared on their ability to predict overconfidence effects in category learning data. In the standard task, participants learned to classify hypothetical patients with particular symptom patterns into disease categories and reported confidence judgments in the form of probabilities. The connectionist model asserts that classifications and confidence are based on the strength of learned associations between symptoms and diseases. The exemplar retrieval model (ERM) proposes that people learn by storing examples and that their judgments are often based on the first example they happen to retrieve. Experiments 1 and 2 established that overconfidence increases when the classification step of the process is bypassed. Experiments 2 and 3 showed that a direct instruction to retrieve many exemplars reduces overconfidence. Only the ERM predicted the major qualitative phenomena exhibited in these experiments.     

Mental models and probabilistic thinking

This paper outlines the theory of reasoning based on mental models, and then shows how this theory might be extended to deal with probabilistic thinking. The same explanatory framework accommodates deduction and induction: there are both deductive and inductive inferences that yield probabilistic conclusions. The framework yields a theoretical conception of strength of inference, that is, a theory of what the strength of an inference is objectively: it equals the proportion of possible states of affairs consistent with the premises in which the conclusion is true, that is, the probability that the conclusion is true given that the premises are true. Since there are infinitely many possible states of affairs consistent with any set of premises, the paper then characterizes how individuals estimate the strength of an argument. They construct mental models, which each correspond to an infinite set of possibilities (or, in some cases, a finite set of infinite sets of possibilities). The construction of models is guided by knowledge and beliefs, including lay conceptions of such matters as the “law of large numbers”. The paper illustrates how this theory can account for phenomena of probabilistic reasoning.