24,240 research outputs found
Optimal embedding parameters: A modelling paradigm
Reconstruction of a dynamical system from a time series requires the
selection of two parameters, the embedding dimension and the embedding
lag . Many competing criteria to select these parameters exist, and all
are heuristic. Within the context of modeling the evolution operator of the
underlying dynamical system, we show that one only need be concerned with the
product . We introduce an information theoretic criteria for the
optimal selection of the embedding window . For infinitely long
time series this method is equivalent to selecting the embedding lag that
minimises the nonlinear model prediction error. For short and noisy time series
we find that the results of this new algorithm are data dependent and superior
to estimation of embedding parameters with the standard techniques
Learning by stochastic serializations
Complex structures are typical in machine learning. Tailoring learning
algorithms for every structure requires an effort that may be saved by defining
a generic learning procedure adaptive to any complex structure. In this paper,
we propose to map any complex structure onto a generic form, called
serialization, over which we can apply any sequence-based density estimator. We
then show how to transfer the learned density back onto the space of original
structures. To expose the learning procedure to the structural particularities
of the original structures, we take care that the serializations reflect
accurately the structures' properties. Enumerating all serializations is
infeasible. We propose an effective way to sample representative serializations
from the complete set of serializations which preserves the statistics of the
complete set. Our method is competitive or better than state of the art
learning algorithms that have been specifically designed for given structures.
In addition, since the serialization involves sampling from a combinatorial
process it provides considerable protection from overfitting, which we clearly
demonstrate on a number of experiments.Comment: Submission to NeurIPS 201
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