Naïve and Robust: Class‐Conditional Independence in Human Classification Learning

Abstract

Humans excel in categorization. Yet from a computational standpoint, learning a novel probabilistic classification task involves severe computational challenges. The present paper investigates one way to address these challenges: assuming class-conditional independence of features. This feature independence assumption simplifies the inference problem, allows for informed inferences about novel feature combinations, and performs robustly across different statistical environments. We designed a new Bayesian classification learning model (the dependence-independence structure and category learning model, DISC-LM) that incorporates varying degrees of prior belief in class-conditional independence, learns whether or not independence holds, and adapts its behavior accordingly. Theoretical results from two simulation studies demonstrate that classification behavior can appear to start simple, yet adapt effectively to unexpected task structures. Two experiments-designed using optimal experimental design principles-were conducted with human learners. Classification decisions of the majority of participants were best accounted for by a version of the model with very high initial prior belief in class-conditional independence, before adapting to the true environmental structure. Class-conditional independence may be a strong and useful default assumption in category learning tasks.

Do Additional Features Help or Hurt Category Learning? The Curse of Dimensionality in Human Learners

“…First, we describe the details of an ideal statistical learner which we call OPTIMAL. In our experiments, the stimuli were generated by following the principle of class-conditional independence (e.g., Anderson, 1990;Jarecki, Meder, & Nelson, 2013). As long as one knows the true category label y, then the probability of any particular feature value xi is completely independent of any other feature.…”

Towards a theory of heuristic and optimal planning for sequential information search

“…From a mathematical standpoint, the genes are class-conditionally-independent (Domingos & Pazzani, 1997;Jarecki, Meder & Nelson, 2018) and identically distributed across specimens.…”

Do additional features help or hurt category learning? The curse of dimensionality in human learners

“…First, we describe the details of an ideal statistical learner which we call optimal. In our experiments, the stimuli were generated by following the principle of class-conditional independence (e.g., Anderson, 1990;Jarecki, Meder, & Nelson, 2013). As long as one knows the true category label y, then the probability of any particular feature value x i is completely independent of any other feature.…”

“…, θ D ) where θ i = p(x i |y) describes the probability that feature i will have value x i . Although class-conditional independence is not always satisfied in real life where feature correlations are possible (Malt & Smith, 1984), it is a reasonable simplification in many situations (Jarecki et al, 2013), and one that is appropriate to our experimental design. Moreover, because the category can be represented in terms of a single idealised vector θ that describes the central tendency of the category, it is broadly similar to standard prototype models (Posner & Keele, 1968).…”