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Abstract:
modeling dynamic processes. The approach can learn a compact
and informative statistic which summarizes past states to predict
future observations. Furthermore, the uncertainty of the prediction
is characterized nonparametrically by a joint density over the
learned statistic and present observation. We discuss the
application of the technique to both noise driven dynamical systems
and random processes sampled from a density which is conditioned on
the past. In the first case we show results in which both the
dynamics of random walk and the statistics of the driving noise are
captured. In the second case we present results in which a
summarizing statistic is learned on noisy random telegraph waves
with differing dependencies on past states. In both cases the
algorithm yields a principled approach for discriminating processes
with differing dynamics and/or dependencies. The method is grounded
in ideas from information theory and nonparametric
statistics.
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