Unifying rational models of categorization via the hierarchical Dirichlet process (original) (raw)
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The Bayesian evaluation of categorization models: Comment on Wills and Pothos (2012)
2012
Abstract Wills and Pothos (2012) review approaches to evaluating formal models of categorization, raising a series of worthwhile issues, challenges, and goals. Unfortunately, in discussing these issues and proposing solutions, Wills and Pothos (2012) do not consider Bayesian methods in any detail. This means not only that their review excludes a major body of current work in the field, but also that it does not consider the body of work that provides the best current answers to the issues raised.
RELATION BETWEEN THE RATIONAL MODEL AND THE CONTEXT MODEL OF CATEGORIZATION
A formal proof is pnnided that Anderson's {1990) rational model of categorization generalizes the Medin and Schaffer {1978) context model. According to the context model, people represent categ<>ries by storing individual exemplars in memoiy. According to the rational mode!, people represent categories in terms of midtiple exemplarclusters or prototypes. In both models, a multiplicative rule is used to compute the similarity of an item to the underlying category representations. In certain special cases, each multiple prototype in the rational model corresponds to an individual exemplar, and in these cases the rational model reduces to the context model. Preliminary quantitative comparisons between the models are illustrated to test whether the multiple-prototype view adds significant explanatory power over the pure exemplar view.
A probabilistic model of cross-categorization
Cognition, 2011
Most natural domains can be represented in multiple ways: we can categorize foods in terms of their nutritional content or social role, animals in terms of their taxonomic groupings or their ecological niches, and musical instruments in terms of their taxonomic categories or social uses. Previous approaches to modeling human categorization have largely ignored the problem of cross-categorization, focusing on learning just a single system of categories that explains all of the features. Cross-categorization presents a difficult problem: how can we infer categories without first knowing which features the categories are meant to explain? We present a novel model that suggests that human cross-categorization is a result of joint inference about multiple systems of categories and the features that they explain. We also formalize two commonly proposed alternative explanations for cross-categorization behavior: a features-first and an objects-first approach. The features-first approach suggests that cross-categorization is a consequence of attentional processes, where features are selected by an attentional mechanism first and categories are derived second. The objects-first approach suggests that cross-categorization is a consequence of repeated, sequential attempts to explain features, where categories are derived first, then features that are poorly explained are recategorized. We present two sets of simulations and experiments testing the models' predictions about human categorization. We find that an approach based on joint inference provides the best fit to human categorization behavior, and we suggest that a full account of human category learning will need to incorporate something akin to these capabilities.
Two mathematical models of human categorization
The goal of the paper is mathematical verification of various hypotheses concerning the cognitive efficiency of human categorization. To this aim two calculus-based mathematical models are constructed to account for the crucial features of human categorization: prototypicality and basic level primacy. The first model allows to calculate and compare the cognitive efficiency of the prototype and definition based categories, while the second one explicates the cognitive prominence of the basic level categories. Additionally, the models account for cultural and specialist knowledge variability of categorization as well as the link between the limited human brain capacity and categorization. Both models can be also be used to predict and extrapolate the results of psycho-linguistic experiments.
A Random Categorization Model for Hierarchical Taxonomies
Scientific reports, 2017
A taxonomy is a standardized framework to classify and organize items into categories. Hierarchical taxonomies are ubiquitous, ranging from the classification of organisms to the file system on a computer. Characterizing the typical distribution of items within taxonomic categories is an important question with applications in many disciplines. Ecologists have long sought to account for the patterns observed in species-abundance distributions (the number of individuals per species found in some sample), and computer scientists study the distribution of files per directory. Is there a universal statistical distribution describing how many items are typically found in each category in large taxonomies? Here, we analyze a wide array of large, real-world datasets - including items lost and found on the New York City transit system, library books, and a bacterial microbiome - and discover such an underlying commonality. A simple, non-parametric branching model that randomly categorizes i...
A Causal-Model Theory of Categorization
Cognitive Science - COGSCI, 1999
In this article I propose that categorization decisions are often made relative to causal models of categories that people possess. According to this causal-model theory o f categorization, evidence of an exemplar's membership in a category consists of the likelihood that such an exemplar can be generated by the category's causal model. Bayesian networks are proposed as a representation of these causal models. Causal-model theory was fit to categorization data from a recent study, and yielded better fits than either the prototype model or the exemplar-based context model, b y accounting, for example, for the confirmation and violation of causal relationships and the asymmetries inherent in such relationships.
On the adequacy of current empirical evaluations of formal models of categorization
Psychological Bulletin, 2012
Categorization is one of the fundamental building blocks of cognition, and the study of categorization is notable for the extent to which formal modeling has been a central and influential component of research. However, the field has seen a proliferation of noncomplementary models with little consensus on the relative adequacy of these accounts. Progress in assessing the relative adequacy of formal categorization models has, to date, been limited because (a) formal model comparisons are narrow in the number of models and phenomena considered and (b) models do not often clearly define their explanatory scope. Progress is further hampered by the practice of fitting models with arbitrarily variable parameters to each data set independently. Reviewing examples of good practice in the literature, we conclude that model comparisons are most fruitful when relative adequacy is assessed by comparing well-defined models on the basis of the number and proportion of irreversible, ordinal, penetrable successes (principles of minimal flexibility, breadth, good-enough precision, maximal simplicity, and psychological focus).
Thirty categorization results in search of a model
Journal of Experimental Psychology: …, 2000
(2000) conducted a meta-analysis of 30 data sets reported in the classification literature that involved use of the "5-4" category structure introduced by D. L. Medin and M. M. Schaffer (1978). The meta-analysis was aimed at investigating exemplar and elaborated prototype models of categorization. In this commentary, the author argues that the meta-analysis is misleading because it includes many data sets from experimental designs that are inappropriate for distinguishing the models. Often, the designs involved manipulations in which the actual 5-4 structure was not, in reality, tested, voiding the predictions of the models. The commentary also clarifies various aspects of the workings of the exemplar-based context model. Finally, concerns are raised that the all-or-none exemplar processes that form part of Smith and Minda's (2000) elaborated prototype models are implausible and lacking in generality.
Estimation and testing of distributions in metric spaces are well known. R.A. Fisher, J. Neyman, W. Cochran and M. Bartlett achieved essential results on the statistical analysis of categorical data. In the last 40 years many other statisticians found important results in this field. Often data sets contain categorical data, e.g. levels of factors or names. There does not exist any ordering or any distance between these categories. At each level there are measured some metric or categorical values. We introduce a new method of scaling based on statistical decisions. For this we define empirical probabilities for the original observations and find a class of distributions in a metric space where these empirical probabilities can be found as approximations for equivalently defined probabilities. With this method we identify probabilities connected with the categorical data and probabilities in metric spaces. Here we get a mapping from the levels of factors or names into points of a metric space. This mapping yields the scale for the categorical data. From the statistical point of view we use multivariate statistical methods, we calculate maximum likelihood estimations and compare different approaches for scaling.