John K. Kruschke

ALCOVE : An exemplar-based connectionist model of category learning

ALCOVE (attention learning covering map) is a connectionist model of category learning that incorporates an exemplar-based representation (Medin & Schaffer, 1978; Nosofsky, 1986) with error-driven learning (Gluck & Bower, 1988; Rumelhart, Hinton, & Williams, 1986). Alcove selectively attends to relevant stimulus dimensions, is sensitive to correlated dimensions, can account for a form of base-rate neglect, does not suffer catastrophic forgetting, and can exhibit 3-stage (U-shaped) learning of high-frequency exceptions to rules, whereas such effects are not easily accounted for by models using other combinations of representation and learning method.

RULES AND EXEMPLARS IN CATEGORY LEARNING

Psychological theories of categorization generally focus on either rule- or exemplar-based explanations. We present 2 experiments that show evidence of both rule induction and exemplar encoding as well as a connectionist model, ATRIUM, that specifies a mechanism for combining rule- and exemplar-based representation. In 2 experiments participants learned to classify items, most of which followed a simple rule, although there were a few frequently occurring exceptions. Experiment 1 examined how people extrapolate beyond the range of training. Experiment 2 examined the effect of instance frequency on generalization. Categorization behavior was well described by the model, in which exemplar representation is used for both rule and exception processing. A key element in correctly modeling these results was capturing the interaction between the rule- and exemplar-based representations by using shifts of attention between rules and exemplars.

Bayesian Estimation Supersedes the t Test

Bayesian estimation for 2 groups provides complete distributions of credible values for the effect size, group means and their difference, standard deviations and their difference, and the normality of the data. The method handles outliers. The decision rule can accept the null value (unlike traditional t tests) when certainty in the estimate is high (unlike Bayesian model comparison using Bayes factors). The method also yields precise estimates of statistical power for various research goals. The software and programs are free and run on Macintosh, Windows, and Linux platforms.

The Time Has Come Bayesian Methods for Data Analysis in the Organizational Sciences

The use of Bayesian methods for data analysis is creating a revolution in fields ranging from genetics to marketing. Yet, results of our literature review, including more than 10,000 articles published in 15 journals from January 2001 and December 2010, indicate that Bayesian approaches are essentially absent from the organizational sciences. Our article introduces organizational science researchers to Bayesian methods and describes why and how they should be used. We use multiple linear regression as the framework to offer a step-by-step demonstration, including the use of software, regarding how to implement Bayesian methods. We explain and illustrate how to determine the prior distribution, compute the posterior distribution, possibly accept the null value, and produce a write-up describing the entire Bayesian process, including graphs, results, and their interpretation. We also offer a summary of the advantages of using Bayesian analysis and examples of how specific published research based on frequentist analysis-based approaches failed to benefit from the advantages offered by a Bayesian approach and how using Bayesian analyses would have led to richer and, in some cases, different substantive conclusions. We hope that our article will serve as a catalyst for the adoption of Bayesian methods in organizational science research.

What to believe: Bayesian methods for data analysis

Although Bayesian models of mind have attracted great interest from cognitive scientists, Bayesian methods for data analysis have not. This article reviews several advantages of Bayesian data analysis over traditional null-hypothesis significance testing. Bayesian methods provide tremendous flexibility for data analytic models and yield rich information about parameters that can be used cumulatively across progressive experiments. Because Bayesian statistical methods can be applied to any data, regardless of the type of cognitive model (Bayesian or otherwise) that motivated the data collection, Bayesian methods for data analysis will continue to be appropriate even if Bayesian models of mind lose their appeal.

Bayesian Assessment of Null Values Via Parameter Estimation and Model Comparison

Psychologists have been trained to do data analysis by asking whether null values can be rejected. Is the difference between groups nonzero? Is choice accuracy not at chance level? These questions have been traditionally addressed by null hypothesis significance testing (NHST). NHST has deep problems that are solved by Bayesian data analysis. As psychologists transition to Bayesian data analysis, it is natural to ask how Bayesian analysis assesses null values. The article explains and evaluates two different Bayesian approaches. One method involves Bayesian model comparison (and uses Bayes factors). The second method involves Bayesian parameter estimation and assesses whether the null value falls among the most credible values. Which method to use depends on the specific question that the analyst wants to answer, but typically the estimation approach (not using Bayes factors) provides richer information than the model comparison approach.

Blocking and backward blocking involve learned inattention.

Four experiments examine blocking of associative learning by human participants in a disease diagnosis procedure. The results indicate that after a cue is blocked, subsequent learning about the cue is attenuated. This attenuated learning after blocking is obtained for both standard blocking and for backward blocking. Attenuated learning after blocking cannot be accounted for by theories such as the Rescorla-Wagner model that rely on lack of learning about a redundant cue, nor can it be accounted for by extensions of the Rescorla-Wagner model designed to address backward blocking that encode absent cues with negative values. The results are predicted by the hypothesis that people learn not to attend to the blocked cue.

BASE RATES IN CATEGORY LEARNING

Previous researchers have discovered perplexing inconsistencies in how people appear to utilize category base rates when making category judgments. In particular, D.L. Medin and S.M. Edelson (1988) found an inverse base-rate effect, in which participants tended to select a rare category when tested with a combination of conflicting cues, and M.A. Gluck and G.H. Bower (1988) reported apparent base-rate neglect, in which participants tended to select a rare category when tested with a single symptom for which objective diagnosticity was equal for all categories. This article suggests that common principles underlie both effects: First, base-rate information is learned and consistently applied to all training and testing cases. Second, the crucial effect of base rates is to cause frequent categories to be learned before rare categories so that the frequent categories are encoded by their typical features and the rare categories are encoded by their distinctive features. Four new experiments provide evidence consistent with those principles. The principles are formalized in a new connectionist model that can rapidly shift attention to distinctive features.

Attention in Learning

Learners exhibit many apparently irrational behaviors in their use of cues, sometimes learning to ignore relevant cues or to attend to irrelevant ones. A learning phenomenon called highlighting seems especially to demand explanation in terms of learned attention. Highlighting complements the classic phenomenon of conditioned blocking, which has been shown to involve learned inattention. Highlighting and blocking, along with a wide spectrum of other perplexing learning phenomena, can be accounted for by recent connectionist models in which both attentional shifting and associative learning are driven by the rational goal of rapid error reduction.

Eye Gaze and Individual Differences Consistent with Learned Attention in Associative Blocking and Highlighting.

The associative learning effects called blocking and highlighting have previously been explained by covert learned attention, but evidence for learned attention has been indirect, via models of response choice. The present research reports results from eye tracking consistent with the attentional hypothesis: Gaze duration is diminished for blocked cues and augmented for highlighted cues. If degree of attentional learning varies across individuals but is relatively stable within individuals, then the magnitude of blocking and highlighting should covary across individuals. This predicted correlation is obtained for both choice and eye gaze. A connectionist model that implements attentional learning is shown to fit the data and account for individual differences by variation in its attentional parameters.