Simplicity and complexity of probabilistically defined concepts

Area of Science:

• Cognitive Psychology
• Machine Learning
• Information Theory

Background:

• Human concept learning is hindered by complexity, favoring simpler concepts.
• Existing research primarily focuses on deterministic Boolean features, neglecting probabilistic continuous features.
• Understanding complexity in probabilistic concept learning is crucial for broader applications.

Purpose of the Study:

• To investigate the impact of conceptual complexity on human learning of probabilistic concepts defined over continuous features.
• To explore how the positioning of Gaussian mixture components influences learning difficulty.
• To introduce and validate an information-theoretic framework for quantifying probabilistic concept complexity.

Main Methods:

• Subjects learned probabilistic concepts in a novel 2D continuous feature space.
• Concepts were Gaussian mixtures with varying component positions but a constant number of components.
• Statistical separability of concepts was independently manipulated.

Main Results:

• Component positioning significantly affected concept learning, irrespective of statistical separability.
• The study identified a link between concept complexity and the ability to represent concepts in lower dimensions.
• Results support the proposed framework for measuring probabilistic concept complexity.

Conclusions:

• The positioning of probabilistic concept components is a key factor in learning difficulty.
• Compressive complexity, based on dimensionality reduction, offers a robust measure for probabilistic concepts.
• This framework provides a consistent and applicable method for quantifying concept complexity.