Extreme Value Theory for Modeling Category Decision Boundaries in Visual Recognition
Several possibilities exist for modeling decision boundaries in category learning, with varying degrees of human fidelity. This paper finds evidence for preferentially focusing representational resources on the extremes of the distribution of visual inputs in a generative model as an alternative to the central tendency models that are commonly used for prototypes and exemplars. The notion of treating extrema near a decision boundary as features in visual recognition is not new, but a comprehensive statistical framework of recognition based on extrema has yet to emerge for category learning. Here we suggest that the statistical Extreme Value Theory [Coles et al., 2001] provides such a framework. In Experiment 1, line segment stimuli that vary in a single dimension of length [Hsu and Griffiths, 2010] are used to assess how human subjects and statistical models assign category membership to a gap region between two categories shown as reference stimuli. A Weibull fit better predicts an observed human shift when moving from uniform to enriched or long tails as reference stimuli. In Experiment 2, more complex 2D rendered face sequences drawn from morphspaces [Folstein et al., 2012] are used as stimuli. Again, the Weibull fit better predicts an observed human shift when reference stimuli are sampled differently. An extrema-based model lends new insight into how discriminative information may be encoded in the brain with implications for the understanding of how decision making works in category learning.