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Computational Intelligence and Neuroscience
Volume 2017, Article ID 9478952, 9 pages
Research Article

Robust and Adaptive Online Time Series Prediction with Long Short-Term Memory

1College of Command and Information System, PLA University of Science and Technology, Nanjing, Jiangsu 210007, China
21st Department, Army Officer Academy of PLA, Hefei, Anhui 230031, China

Correspondence should be addressed to Zhisong Pan; moc.liamtoh@szptoh

Received 27 August 2017; Revised 23 November 2017; Accepted 3 December 2017; Published 17 December 2017

Academic Editor: Pedro Antonio Gutierrez

Copyright © 2017 Haimin Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Online time series prediction is the mainstream method in a wide range of fields, ranging from speech analysis and noise cancelation to stock market analysis. However, the data often contains many outliers with the increasing length of time series in real world. These outliers can mislead the learned model if treated as normal points in the process of prediction. To address this issue, in this paper, we propose a robust and adaptive online gradient learning method, RoAdam (Robust Adam), for long short-term memory (LSTM) to predict time series with outliers. This method tunes the learning rate of the stochastic gradient algorithm adaptively in the process of prediction, which reduces the adverse effect of outliers. It tracks the relative prediction error of the loss function with a weighted average through modifying Adam, a popular stochastic gradient method algorithm for training deep neural networks. In our algorithm, the large value of the relative prediction error corresponds to a small learning rate, and vice versa. The experiments on both synthetic data and real time series show that our method achieves better performance compared to the existing methods based on LSTM.