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A Rational Account of Categorization Based on Information Theory

Christophe J. MacLellan, Karthik Singaravadivelan, Xin Lian, Zekun Wang, Pat Langley

Abstract

We present a new theory of categorization based on an information-theoretic rational analysis. To evaluate this theory, we investigate how well it can account for key findings from classic categorization experiments conducted by Hayes-Roth and Hayes-Roth (1977), Medin and Schaffer (1978), and Smith and Minda (1998). We find that it explains the human categorization behavior at least as well (or better) than the independent cue and context models (Medin & Schaffer, 1978), the rational model of categorization (Anderson, 1991), and a hierarchical Dirichlet process model (Griffiths et al., 2007).

A Rational Account of Categorization Based on Information Theory

Abstract

We present a new theory of categorization based on an information-theoretic rational analysis. To evaluate this theory, we investigate how well it can account for key findings from classic categorization experiments conducted by Hayes-Roth and Hayes-Roth (1977), Medin and Schaffer (1978), and Smith and Minda (1998). We find that it explains the human categorization behavior at least as well (or better) than the independent cue and context models (Medin & Schaffer, 1978), the rational model of categorization (Anderson, 1991), and a hierarchical Dirichlet process model (Griffiths et al., 2007).

Paper Structure

This paper contains 16 sections, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Instantiating the Proposed Theory
  3. Preliminary Tests of the Theory
  4. Central Tendencies of Categories
  5. Human Study Design
  6. Simulation Methodology
  7. Results & Discussion
  8. Non-Linearly & Linearly Separable Categories
  9. Human Study Design
  10. Simulation Methodology
  11. Results & Discussion
  12. Prototype-Exemplar Transition
  13. Human Study Design
  14. Simulation Methodology
  15. Results & Discussion
  16. ...and 1 more sections

Figures (5)

  • Figure 1: Probabilities of the Club 1 category for the test items from the hayesroth1977role experiment, aggregated by item type. The types along the x-axis are ordered according to the human classification ratings. The error bars represent the 95% confidence intervals.
  • Figure 2: The loglikelihood of the test items from the hayesroth1977role experiment according to our system, aggregated by item type. The types along the x-axis are ordered according to the human recognition scores. The error bars represent the 95% confidence intervals.
  • Figure 3: Predicted probability of category A from our system and the RMC for exp 1. The circles denote training items, the triangles denote novel test items. The fill denotes the type of item (A=white, B=black). The lines connect items of the same category and type for each approach. The error bars denote 95% confidence intervals.
  • Figure 4: Predicted probability of category A from our system and the context model for exp 2. The circles denote training items, the triangles denote novel test items. The fill denotes the type of item (A=white, B=black). The lines connect items of the same category and type for each approach. The error bars denote 95% confidence intervals.
  • Figure 5: Predictions and human data for smith1998prototypes's second experiment. Each line is a stimuli with Category A denoted by white, Category B denoted by black, and exception items denoted by triangles. Figures (a) and (b) are reproduced from griffiths2007unifying, showing the human and HDP model data respectively. Our system's predictions are shown in (c).