From Algorithmic to Subjective Randomness

Part of Advances in Neural Information Processing Systems 16 (NIPS 2003)

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Thomas Griffiths, Joshua Tenenbaum


We explore the phenomena of subjective randomness as a case study in understanding how people discover structure embedded in noise. We present a rational account of randomness perception based on the statis- tical problem of model selection: given a stimulus, inferring whether the process that generated it was random or regular. Inspired by the mathe- matical definition of randomness given by Kolmogorov complexity, we characterize regularity in terms of a hierarchy of automata that augment a finite controller with different forms of memory. We find that the reg- ularities detected in binary sequences depend upon presentation format, and that the kinds of automata that can identify these regularities are in- formative about the cognitive processes engaged by different formats.