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Published in:
2009 | OriginalPaper | Chapter
Non-sufficient Memories That Are Sufficient for Prediction
Authors : Wolfgang Löhr, Nihat Ay
Published in: Complex Sciences
Publisher: Springer Berlin Heidelberg
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The causal states of computational mechanics define the minimal sufficient (prescient) memory for a given stationary stochastic process. They induce the
ε
-machine which is a hidden Markov model (HMM) generating the process. The
ε
-machine is, however, not the minimal generative HMM and minimal internal state entropy of a generative HMM is a tighter upper bound for excess entropy than provided by statistical complexity. We propose a notion of prediction that does not require sufficiency. The corresponding models can be substantially smaller than the
ε
-machine and are closely related to generative HMMs.