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Structure or Noise?
We show how rate-distortion theory provides a mechanism for automated theory
building by naturally distinguishing between regularity and randomness. We
start from the simple principle that model variables should, as much as
possible, render the future and past conditionally independent. From this, we
construct an objective function for model making whose extrema embody the
trade-off between a model's structural complexity and its predictive power. The
solutions correspond to a hierarchy of models that, at each level of
complexity, achieve optimal predictive power at minimal cost. In the limit of
maximal prediction the resulting optimal model identifies a process's intrinsic
organization by extracting the underlying causal states. In this limit, the
model's complexity is given by the statistical complexity, which is known to be
minimal for achieving maximum prediction. Examples show how theory building can
profit from analyzing a process's causal compressibility, which is reflected in
the optimal models' rate-distortion curve--the process's characteristic for
optimally balancing structure and noise at different levels of representation.Comment: 6 pages, 2 figures;
http://cse.ucdavis.edu/~cmg/compmech/pubs/son.htm
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