Non-sufficient Memories That Are Sufficient for Prediction

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.

• Type: Conference
• Year: 2009
• Where: COMPLEX
• Authors: Wolfgang Löhr, Nihat Ay
• Keywords: COMPLEX 2009, Generative Hmms, Minimal Generative Hmm, Stationary Stochastic Process, Theoretical Computer Science