### Abstract

This paper makes use of long short-term memory (LSTM) neural networks for forecasting probability distributions of time series in terms of discrete symbols that are quantized from real-valued data. The developed framework formulates the forecasting problem into a probabilistic paradigm as h X × Y [0, 1] such that y Yh (x,y)=1, where X is the finite-dimensional state space, Y is the symbol alphabet, and is the set of model parameters. The proposed method is different from standard formulations (e.g., autoregressive moving average (ARMA)) of time series modeling. The main advantage of formulating the problem in the symbolic setting is that density predictions are obtained without any significantly restrictive assumptions (e.g., second-order statistics). The efficacy of the proposed method has been demonstrated by forecasting probability distributions on chaotic time series data collected from a laboratory-scale experimental apparatus. Three neural architectures are compared, each with 100 different combinations of symbol-alphabet size and forecast length, resulting in a comprehensive evaluation of their relative performances.

Original language | English (US) |
---|---|

Article number | 084502 |

Journal | Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME |

Volume | 140 |

Issue number | 8 |

DOIs | |

State | Published - Aug 1 2018 |

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### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Information Systems
- Instrumentation
- Mechanical Engineering
- Computer Science Applications

### Cite this

}

*Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME*, vol. 140, no. 8, 084502. https://doi.org/10.1115/1.4039281

**Neural Probabilistic Forecasting of Symbolic Sequences with Long Short-Term Memory.** / Hauser, Michael; Fu, Yiwei; Phoha, Shashi; Ray, Asok.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Neural Probabilistic Forecasting of Symbolic Sequences with Long Short-Term Memory

AU - Hauser, Michael

AU - Fu, Yiwei

AU - Phoha, Shashi

AU - Ray, Asok

PY - 2018/8/1

Y1 - 2018/8/1

N2 - This paper makes use of long short-term memory (LSTM) neural networks for forecasting probability distributions of time series in terms of discrete symbols that are quantized from real-valued data. The developed framework formulates the forecasting problem into a probabilistic paradigm as h X × Y [0, 1] such that y Yh (x,y)=1, where X is the finite-dimensional state space, Y is the symbol alphabet, and is the set of model parameters. The proposed method is different from standard formulations (e.g., autoregressive moving average (ARMA)) of time series modeling. The main advantage of formulating the problem in the symbolic setting is that density predictions are obtained without any significantly restrictive assumptions (e.g., second-order statistics). The efficacy of the proposed method has been demonstrated by forecasting probability distributions on chaotic time series data collected from a laboratory-scale experimental apparatus. Three neural architectures are compared, each with 100 different combinations of symbol-alphabet size and forecast length, resulting in a comprehensive evaluation of their relative performances.

AB - This paper makes use of long short-term memory (LSTM) neural networks for forecasting probability distributions of time series in terms of discrete symbols that are quantized from real-valued data. The developed framework formulates the forecasting problem into a probabilistic paradigm as h X × Y [0, 1] such that y Yh (x,y)=1, where X is the finite-dimensional state space, Y is the symbol alphabet, and is the set of model parameters. The proposed method is different from standard formulations (e.g., autoregressive moving average (ARMA)) of time series modeling. The main advantage of formulating the problem in the symbolic setting is that density predictions are obtained without any significantly restrictive assumptions (e.g., second-order statistics). The efficacy of the proposed method has been demonstrated by forecasting probability distributions on chaotic time series data collected from a laboratory-scale experimental apparatus. Three neural architectures are compared, each with 100 different combinations of symbol-alphabet size and forecast length, resulting in a comprehensive evaluation of their relative performances.

UR - http://www.scopus.com/inward/record.url?scp=85044967289&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85044967289&partnerID=8YFLogxK

U2 - 10.1115/1.4039281

DO - 10.1115/1.4039281

M3 - Article

VL - 140

JO - Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME

JF - Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME

SN - 0022-0434

IS - 8

M1 - 084502

ER -