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
JF  - 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
U6  - https://doi.org/10.1162/neco_a_01224
SN  - 0899-7667
SN  - 1530-888X
VL  - 31
IS  - 10
SP  - 2004
EP  - 2024
PB  - MIT Press
CY  - Cambridge
ER  - 
TY  - JOUR
A1  - Nüsken, Nikolas
A1  - Reich, Sebastian
A1  - Rozdeba, Paul J.
T1  - State and parameter estimation from observed signal increments
JF  - Entropy : an international and interdisciplinary journal of entropy and information studies
N2  - The success of the ensemble Kalman filter has triggered a strong interest in expanding its scope beyond classical state estimation problems. In this paper, we focus on continuous-time data assimilation where the model and measurement errors are correlated and both states and parameters need to be identified. Such scenarios arise from noisy and partial observations of Lagrangian particles which move under a stochastic velocity field involving unknown parameters. We take an appropriate class of McKean-Vlasov equations as the starting point to derive ensemble Kalman-Bucy filter algorithms for combined state and parameter estimation. We demonstrate their performance through a series of increasingly complex multi-scale model systems.
KW  - parameter estimation
KW  - continuous-time data assimilation
KW  - ensemble Kalman filter
KW  - correlated noise
KW  - multi-scale diffusion processes
Y1  - 2019
U6  - https://doi.org/10.3390/e21050505
SN  - 1099-4300
VL  - 21
IS  - 5
PB  - MDPI
CY  - Basel
ER  -