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Journal of Data Analysis and Information Processing, 2017, 5, 115-130

http://www.scirp.org/journal/jdaip

ISSN Online: 2327-7203

ISSN Print: 2327-7211

DOI: 10.4236/jdaip.2017.53009

August 29, 2017

Time Series Forecasting with Multiple Deep

Learners: Selection from a Bayesian Network

Shusuke Kobayashi, Susumu Shirayama

Graduate School of Engineering, the University of Tokyo, Tokyo, Japan

Abstract

Considering the recent developments in deep learning, it has become incre

singly important to verify what methods are valid for the prediction of mult

variate time-series data. In this study, we propose a novel method of time-se

ries

prediction employing multiple deep learners combined with a Bayesian ne

work where training data is divided into clusters using K-

means clustering.

We decided how many clusters are the best for K-

means with the Bayesian

information criteria. Depending on each cluster, the multiple deep learners

are trained. We used three types of deep learners:

deep neural network

(DNN), recurrent neural network (RNN), and long short-

term memory

(LSTM). A naive Bayes classifier is used to determine which deep learner is in

charge of predicting a particular time-series. Our propos

ed method will be

applied to a set of financial time-

series data, the Nikkei Average Stock price,

to assess the accuracy of the predictions made. Compared with the conve

tional method of employing a single deep learner to acquire all the data, it is

demonstrated by our proposed method that F-value and accuracy are i

proved.

Keywords

Time-Series Data, Deep Learning, Bayesian Network, Recurrent Neural

Network, Long Short-Term Memory, Ensemble Learning, K-Means

1. Introduction

Deep learning has been developed to compensate for the shortcomings of pre-

vious neural networks [1] and is well known for its high performance in the

fields of character and image recognition [2]. In addition, deep learning’s influ-

ence is impacting various other fields [3] [4] [5], and its efficiency and accuracy

have been much bolstered by recent research. However, deep learning is subject

to three main drawbacks. For instance, obtaining and generating appropriate

How to cite this paper:

Kobayashi, S

. and

Shirayama

, S. (2017) Time Series

Forecasting

with Multiple Deep Learners: Selection

from a Bayesian Network

Journal of Data

Analysis and Information Processing

115

-130.

https://doi.org/10.4236/jdaip.2017.53009

Received:

July 10, 2017

Accepted:

August 26, 2017

Published:

August 29, 2017

7 by authors and

Scientific

Research Publishing Inc.

This work is licensed

under the Creative

Commons Attribution International

License (CC BY

4.0).

http://creativecommons.org/licenses/by/4.0/

Open Access

S. Kobayashi, S. Shirayama

116

training data is problematic, it suffers from excessively long calculation times.

Moreover, parameter selection is also difficult. While researchers are progressing

toward overcoming such issues, according to some reports, dealing with these

problems is difficult except for subjects in which the formation of feature spaces

such as images and sounds are the key to success [6].

However, while it is clear that deep learning is considered to underpin artifi-

cial intelligence and because the brain’s information processing mechanism is

not fully understood, it is possible to develop new learners by imitating what is

known about the information processing mechanisms of the brain. One way to

develop new learners is to use a Bayesian network [7]. Moreover, it is also con-

ceivable to combine multiple deep learners to create a single new learner. For ex-

ample, ensemble learning and complementary learning are representative learning

methods using multiple learners [8] [9] [10]. In addition, to realize a hierarchical

control mechanism, there are cases where multiple learners are used.

In this research, we develop a new learner using multiple deep learners in

combination with Bayesian networks as the selection method to choose the most

suitable type of learner for each set of test data.

In time-series data prediction with deep learning, overly long calculation times

are required for training. Moreover, a deep learner does not converge due to the

randomness of the time-series data. There is also an issue with employing a Baye-

sian network. In this paper, we try to reduce the computation time and improve

convergence by dividing training data into specific clusters using the K-means

method and creating multiple deep learners from the learning derived from the

divided training data. We also simplify the problem of ambiguity by using a Baye-

sian network to select a suitable deep learner for the task of prediction.

To demonstrate our model, we use a real-life application: predicting the Nik-

kei Average Stock price by taking into consideration the influence of multiple

stock markets. Specifically, we estimate the Nikkei Stock Average of the current

term based on the Nikkei Stock Average of the previous term as well as overseas

major stock price indicators such as NY Dow and FTSE 100. We evaluate the va-

lidity of our proposed method based on the accuracy of the estimation results.

2. Related Works

In this section, we introduce the related works of multiple learners.

In ensemble learning, outputs from each learner are integrated by weighted

averaging or a voting method [8]. In complementary learning, each learner is

combined with the group to compensate for each other’s disadvantages. Com-

plementary learning is a concept arising from the role sharing in the memory

mechanism of the hippocampus and cortex [9]. These learning methods tend to

mainly use weak learners. Conversely, to realize a hierarchical control mechan-

ism, there are cases where multiple learners are used. When the behavior of a

robot or multi-agent entity is controlled, a hierarchical control mechanism is of-

ten adopted as attention is paid to the fact that such task can be divided into

subtasks. Takahashi and Asada have proposed a robot behavior-acquisition me-

S. Kobayashi, S. Shirayama

117

thod by hierarchically constructing multiple learners of the same structure [10]. A

lower-level learner is responsible for different subtasks and learns low-level ac-

tions. A higher-level learner learns higher-level actions by exploiting a lower-level

learner’s knowledge.

Our proposed method, which will be described later, is based on the same

notion as the bagging method used in ensemble learning where training data

are divided and independently learned. The difference between our proposed

method and the bagging method is the division method, the integration of

multiple learners (the method of selecting suitable learners for each set of test

data) to improve learners’ accuracies in their acquisition of the material.

Therefore, similar to Takahashi and Asada [10], we do not hold to the premise

that tasks can be divided into subtasks. Our learner selection method is differ-

ent. However, our use of deep learning entities as learners is different to Ta-

kahashi and Asada’s approach as they simply used learners, which is a

Q-learning algorithm extended to a continuous state behavior space. Further-

more, prior research of learning methods has not fully established a method of

dividing training data, a method of integrating multiple learners, or a method

of hierarchizing learners. In addition, it has also failed to improve each learn-

er’s performance after learning.

3. Proposed Method

As we mentioned, because the information processing mechanism of the brain is

not fully understood, it is possible to develop new learners by imitating the in-

formation processing mechanism of the brain. In this research, we hypothesize

that the brain forms multiple learners in the initial stage of learning and im-

proves the performance of each learner in subsequent learning while selecting a

suitable learner.

To design learners based on this hypothesis, it is necessary to find ways of

constructing multiple learners, selecting a suitable learner, and improving the

accuracy of each learner by using feedback from a particular selected learner.

Hence, we assume that multiple learners have the same structure. The learners

are constructed by the clustering of input data. Selection of a suitable learner is

conducted with a naive Bayes classifier that forms the simplest Bayesian net-

work. Furthermore, after fixing learners, we construct a Bayesian network and

predict outcomes without changing the Bayesian network’s construction. How-

ever, it is preferable to improve each learner’s performance and the Bayesian

network by using feedback gained from the selected learners. This will form one

of our future research topics.

In the next section, we propose a method of constructing a single, unified

learner by using multiple deep learners. Moreover, in Section 3.2, we propose a

method of selecting a suitable learner with a naive Bayes classifier.

3.1. Learning with Multiple Deep Learners

In the analysis of time-series data with a deep learner, the prediction accuracy is

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