TY  - JOUR
A1  - Ty, Alexander J. A.
A1  - Fang, Zheng
A1  - Gonzalez, Rivver A.
A1  - Rozdeba, Paul J.
A1  - Abarbanel, Henry D.
T1  - Machine learning of time series using time-delay embedding and precision annealing
T2  - Neural Computation
N2  - Tasking machine learning to predict segments of a time series requires estimating the parameters of a ML model with input/output pairs from the time series. We borrow two techniques used in statistical data assimilation in order to accomplish this task: time-delay embedding to prepare our input data and precision annealing as a training method. The precision annealing approach identifies the global minimum of the action (-log[P]). In this way, we are able to identify the number of training pairs required to produce good generalizations (predictions) for the time series. We proceed from a scalar time series s(tn);tn=t0+n Delta t and, using methods of nonlinear time series analysis, show how to produce a DE>1-dimensional time-delay embedding space in which the time series has no false neighbors as does the observed s(tn) time series. In that DE-dimensional space, we explore the use of feedforward multilayer perceptrons as network models operating on DE-dimensional input and producing DE-dimensional outputs.
Y1  - 2019
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/48111
SN  - 0899-7667
SN  - 1530-888X
VL  - 31
IS  - 10
SP  - 2004
EP  - 2024
PB  - MIT Press
CY  - Cambridge
ER  -