Non-sufficient Memories That Are Sufficient for Prediction

Wolfgang Löhr; Nihat Ay

Complex Sciences. First International Conference, Complex 2009, Shanghai, China, February 23-25, 2009. Revised Papers, Part 1

Research Article

Non-sufficient Memories That Are Sufficient for Prediction

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@INPROCEEDINGS{10.1007/978-3-642-02466-5_25,
    author={Wolfgang L\o{}hr and Nihat Ay},
    title={Non-sufficient Memories That Are Sufficient for Prediction},
    proceedings={Complex Sciences. First International Conference, Complex 2009, Shanghai, China, February 23-25, 2009. Revised Papers, Part 1},
    proceedings_a={COMPLEX PART 1},
    year={2012},
    month={5},
    keywords={hidden Markov models HMM computational mechanics causal states 
                -machine prediction},
    doi={10.1007/978-3-642-02466-5_25}
}

Wolfgang Löhr
Nihat Ay
Year: 2012
Non-sufficient Memories That Are Sufficient for Prediction
COMPLEX PART 1
Springer
DOI: 10.1007/978-3-642-02466-5_25

Wolfgang Löhr¹^,*, Nihat Ay^,*

1: Max Planck Institute for Mathematics in the Sciences

*Contact email: Wolfgang.Loehr@mis.mpg.de, Nihat.Ay@mis.mpg.de

Abstract

The causal states of computational mechanics define the minimal sufficient (prescient) memory for a given stationary stochastic process. They induce the -machine which is a hidden Markov model (HMM) generating the process. The -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 -machine and are closely related to generative HMMs.

Keywords: hidden Markov models HMM computational mechanics causal states -machine prediction

Published: 2012-05-11

: http://dx.doi.org/10.1007/978-3-642-02466-5_25