Nearly maximally predictive features and their dimensions
Name
PhysRevE.95.051301.pdf
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341.72 KB
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Adobe PDF
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Author(s)
Marzen, Sarah E.
Crutchfield, James P.
Date Issued
May 2017
Journal
Physical Review E
Publisher
American Physical Society
Citation
Marzen, Sarah E. and Crutchfield, James P. "Nearly maximally predictive features and their dimensions." Physical Review E 95, 051301(R) (May 2017): 1-6 ©2017 American Physical Society
Version
Final published version
Abstract
Scientific explanation often requires inferring maximally predictive features from a given data set. Unfortunately, the collection of minimal maximally predictive features for most stochastic processes is uncountably infinite. In such cases, one compromises and instead seeks nearly maximally predictive features. Here, we derive upper bounds on the rates at which the number and the coding cost of nearly maximally predictive features scale with desired predictive power. The rates are determined by the fractal dimensions of a process' mixed-state distribution. These results, in turn, show how widely used finite-order Markov models can fail as predictors and that mixed-state predictive features can offer a substantial improvement.
MIT Department
Massachusetts Institute of Technology. Department of Physics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
http://dx.doi.org/10.1103/PhysRevE.95.051301
