Statistical complexity

Complexity metrics
(Crutchfield and Young 1989)

One interpretation of the statistical complexity is that it is the minimum amount of historical information required to make optimal forecasts of bits in \(x\) at the error rate \(h_\mu\).

For periodic sequences, \(C_\mu(x) = 0\) and for ideal random sequences \(C_\mu(x) = 0\) too.

Several researchers have tried to capture the properties of statistical complexity with practical alternatives. The resulting complexity metrics include:


Crutchfield, James P., and Karl Young. 1989. “Inferring Statistical Complexity.” Physical Review Letters 63 (2):105–8.

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