Skip to main content Accessibility help
×
Home
Hostname: page-component-78dcdb465f-jsbx8 Total loading time: 0.953 Render date: 2021-04-19T13:30:23.336Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

Multi-step prediction for influenza outbreak by an adjusted long short-term memory

Published online by Cambridge University Press:  02 April 2018

J. Zhang
Affiliation:
Department of Technology Management for Innovation, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-Ku, Tokyo 113-8656, Japan
K. Nawata
Affiliation:
Department of Technology Management for Innovation, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-Ku, Tokyo 113-8656, Japan
Corresponding
Rights & Permissions[Opens in a new window]

Abstract

Influenza results in approximately 3–5 million annual cases of severe illness and 250 000–500 000 deaths. We urgently need an accurate multi-step-ahead time-series forecasting model to help hospitals to perform dynamical assignments of beds to influenza patients for the annually varied influenza season, and aid pharmaceutical companies to formulate a flexible plan of manufacturing vaccine for the yearly different influenza vaccine. In this study, we utilised four different multi-step prediction algorithms in the long short-term memory (LSTM). The result showed that implementing multiple single-output prediction in a six-layer LSTM structure achieved the best accuracy. The mean absolute percentage errors from two- to 13-step-ahead prediction for the US influenza-like illness rates were all <15%, averagely 12.930%. To the best of our knowledge, it is the first time that LSTM has been applied and refined to perform multi-step-ahead prediction for influenza outbreaks. Hopefully, this modelling methodology can be applied in other countries and therefore help prevent and control influenza worldwide.

Type
Original Paper
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © Cambridge University Press 2018

Introduction

Influenza, commonly known as flu, circulates worldwide and places a substantial burden on people's health every year. The flu outbreak resulted in approximately 3–5 million annual cases of severe illness and 250 000–500 000 deaths [1]. In the USA, annual flu outbreak led to an average of 610 660 life-years lost, 3.1 million hospitalised days and 31.4 million outpatient visits. The total economic burden of annual flu outbreak using projected statistical life values amounted to $87.1 billion [Reference Molinari2]. Flu is one of the costliest epidemics worldwide.

The flu vaccine is one of the best ways to reduce the risk of getting sick with flu and spreading it to others [3]. During the 2015–2016 flu season, flu vaccine prevented an estimated 5.1 million illnesses, 2.5 million medical visits, 71 000 hospitalisations and 3000 pneumonia and influenza deaths [3]. However, because flu virus undergoes high mutation rates and frequent genetic re-assortment [Reference Lubeck, Schulman and Palese4Reference Suárez, Valcárcel and Ortín6], manufacturing flu vaccine suffers from a complicated process every year. In Februaries, World Health Organization (WHO) assesses the strains of flu virus that are most likely to be circulating over the following winter. Then, vaccine manufacturers produce flu vaccines in a very limited time [7]. Usually, the first batch of vaccine is unavailable until Septembers [8, Reference Gerdil9].

Moreover, hospital beds assignment to flu patients is also a challenging task due to the limited capacity of hospital beds, time dependencies of bed request arrivals and unique treatment requirements of flu patients [Reference Proudlove, Boaden and Jorgensen10]. Furthermore, flu seasons vary in timing, severity and duration from one season to another [7]. Therefore, flu hospitalisation also varies by sites and time in each season [Reference Puig-Barberà11, 12], which makes beds assignment to flu patients more difficult for hospitals.

To help hospitals and pharmaceutical companies better prepare for an annual flu outbreak, we need an accurate model to perform multi-step-ahead time-series prediction for flu outbreaks. Multi-step-ahead time-series prediction, or simply ‘multi-step prediction’, is an analytical task of predicting a sequence of values in future by analysing observed values in the past [Reference Weigend and Gershenfeld13]. Nonetheless, not many past papers studied multi-step prediction for flu outbreaks. The possible reason could be that multi-step prediction usually results in poor accuracy due to some insuperable problems, such as error accumulation. One compromising method is that one can aggregate raw data to a larger time unit and then use the single-step prediction to avoid performing multi-step prediction. For instance, if raw data are weekly based, we can aggregate weekly values to monthly values and then perform a single-step prediction for the coming month (that is roughly around 4 weeks). Although the single-step prediction avoids poor accuracy, it will hinder us from understanding the trend and variation during the coming month.

In this study, we leveraged the deep learning model of long short-term memory (LSTM). Our selection of LSTM was based on the theoretical and practical consideration. In theory, the LSTM is a special kind of RNN. Its elaborate structure (multilayers and gated cells) enables LSTM to learn simulate non-linear function, long-term dependencies [Reference Hochreiter and Schmidhuber14] and refine time-series prediction [Reference Gers, Schmidhuber and Cummins15]. In practice, we found that LSTM achieved the best accuracy in all the six models (autoregressive integrated moving average, support vector regression, random forest, gradient boosting, artificial neural network and LSTM) when we performed a single-step prediction for the US flu data (the same data source with those of this study) in one of our previous studies [Reference Zhang and Nawata16].

Methods

Source data and metrics

We used the US flu data from the 40th week of 2002 to the 30th week of 2017, collected from the ‘FluView’ Portal of Centre for Disease Control and Prevention (CDC) [17]. To remove any possible variations in populations, we used the influenza-like illness (ILI) rates as the response (y) of models.

$${\rm ILI}\,{\rm rate} = \displaystyle{{{\rm The}\,{\rm number}\,{\rm of}\,{\rm ILI}} \over {{\rm Total}\,{\rm number}\,{\rm of}\,{\rm Illness}}}.$$

Figure 1(a) illustrates the historical plot of the US flu data. We split the duration into two parts: the first 2/3 (from the 40th week of 2002 to the 44th week of 2012) for training and the last 1/3 (from the 45th week of 2012 to the 30th week of 2017) for testing.

Fig. 1. The US flu data from the 40th week of 2002 to the 30th week of 2017. (a) We split the data into the training set and the testing set. The y-axis represents the weekly ILI rates, and the x-axis represents the time series (from the 40th week of 2002 to the 30th week of 2017). The dashed line is the first 2/3 of the data (from the 40th week of 2002 to the 52nd week of 2012) that were used for training, and the solid line is the last 1/3 of the data (from the first week of 2013 to the 30th week of 2017) that were used for testing. (b) The histogram of the weekly ILI rates of the US flu data. The y-axis represents the frequency, and the x-axis represents weekly ILI rates. The histogram is right-skewed.

Figure 1(b) describes the histogram of the weekly ILI rates. The histogram is right-skewed. Generally, comparing accuracy of models by mean absolute percentage error (MAPE) mainly reflects the difference of the ‘median’; while comparing by root mean square error primarily reflects the difference of the ‘mean’. The right-skewed histogram and the Kolmogorov–Smirnov test (P < 0.05) showed that the US flu data followed a non-normal distribution. Therefore, we expected that the accuracy would reflect the difference of ‘median’ and thereby used MAPE as a key performance indicator (KPI) for comparing models.

$${\rm MAPE}\; = \; \displaystyle{1 \over n}\; \mathop \sum \limits_{t = 1}^n \; \; \left \vert {\displaystyle{{F_t - A_t} \over {A_t}}} \right \vert \; \times \; 100\%, $$

where A t is the actual value and F t is the forecast value.

Feature space and responses

For the feature space, we adopted the time lag of 52 weeks due to the result of one of our previous studies. In the previous study, we used the same US flu data and compared accuarcy of models of the different time lags of 2, 4, 9, 13, 26 and 52 weeks and found that of 52 weeks grew out the best accuracy [Reference Zhang and Nawata16]. Moreover, we calculated the first-order differences as a part of the feature spaces, since some past study found that first-order differences helped improve accuracy of the prediction models for flu data [Reference Wu18]. In brief, for feature spaces, we used (I) the ILI rate of the current week, (II) the ILI rates of the past 52 weeks and (III) the 52 first-order differences. Totally, we have 105 features.

Regarding responses, we were forecasting the two-, three-, four-, five-, six-, seven-, eight-, nine-, 10-, 11-, 12- and 13-step-ahead ILI rates.

Model

For multi-step prediction, there are mainly two types of methodologies: (I) ‘recursive’ prediction and (II) ‘jumping’ prediction. Generally, the methodology of (I) predicts values step-by-step; the methodology of (II) predicts some-step-ahead values independently. The following (a), (b), (c) and (d) explain four multi-step prediction algorithms [Reference Brownlee19].

  1. (a) Multi-stage prediction (MSP)

MSP is a ‘recursive’ prediction. MSP uses one single-output model, which is recursively applied in multiple-step prediction, feeding through the previous output as its new input [Reference Cheng, Ng, Kitsuregawa, Li and Chang20]. In this study, as the first step, we predict X t+1 using the 53 historical values, i.e. X t, X t−1, X t−2, … and X t−52; as the second step, we predict X t+2 based on X t+1 (X t+1 was predicted in the first step), X t, X t−1, X t−2, … and X t−51; as the third step, we predict X t+3 based on X t+2 (X t+2 was predicted in the second step), X t+1 (X t+1 was predicted in the first step), X t, X t−1, X t−2, … and X t−50, etc. Formula 1 describes the prediction process.

Formula 1. Algorithm of MSP

prediction(t+1) = LSTM_MSP_MODEL#01(observation(t), observation(t−1), observation(t−2), …, observation(t−52))

prediction(t+2) = LSTM_MSP_MODEL#01(prediction(t+1), observation(t), observation(t−1), …, observation(t−51))

prediction(t+3) = LSTM_MSP_MODEL#01(prediction(t+2), prediction(t+1), observation(t), observation(t−1), …, observation (t−50))

prediction(t+13) = LSTM_MSP_MODEL#01(prediction (t+12), prediction(t+11), prediction(t+10), …, prediction(t+1), observation(t), observation(t−1), …, observation(t−40))

  1. (b) Adjusted multi-stage prediction (AMSP)

AMSP is a refined version of MSP. Comparatively, when AMSP predicting X t+p (P ⩾ 2), it uses another model instead of using the same model repeatedly. Such a modification helps suppress error accumulation [Reference Venkatraman, Hebert and Bagnell21, Reference Akhlaghi and Zhou22]. Formula 2 illustrates the algorithm of AMSP.

Formula 2. Algorithm of AMSP

prediction(t+1) = LSTM_AMSP_MODEL#01(observation(t), observation(t−1), observation(t−2), …, observation(t−52))

prediction(t+2) = LSTM_AMSP_MODEL#02(prediction(t+1), observation(t), observation(t−1), …, observation(t−51))

prediction(t+3) = LSTM_MSP_MODEL#03(prediction(t+2), prediction(t+1), observation(t), observation(t−1), …, observation(t−50))

prediction(t+13) = LSTM_AMSP_MODEL#13(prediction(t+12), prediction(t+11), prediction(t+10), …, prediction(t+1), observation(t), observation(t−1), …, observation(t−40))

  1. (c) Multiple single-output prediction (MSOP)

MSOP is a ‘jumping’ prediction. MSOP directly predicts a p-step-ahead (P ⩾ 2) value only by historical values: X t, X t−1, X t−2, …, X tn. Formula 3 explains the algorithm of MSOP.

Formula 3. Algorithm of MSOP

prediction(t+1) = LSTM_MSOP_MODEL#01(observation(t), observation (t−1), observation(t−2), …, observation(t−52))

prediction(t+2) = LSTM_MSOP_MODEL#02(observation(t), observation(t−1), observation(t−2), …, observation(t−52))

prediction(t+3) = LSTM_MSOP_MODEL#03(observation(t), observation(t−1), observation(t−2), …, observation(t−52))

prediction(t+13) = LSTM_MSOP_MODEL#13(observation(t), observation(t−1), observation(t−2), …, observation(t−52))

  1. (d) Multiple-output prediction (MOP)

MOP can be regarded as a merged version of MSOP. MOP uses one model to predict many some-step-ahead values all at once. In other fields, MOP was also implemented by multiple support vector regression [Reference Cheng, Ng, Kitsuregawa, Li and Chang20, Reference Zhang23, Reference Bao, Xiong and Hu24]. Formula 4 outlines the algorithm of MOP.

Formula 4. Algorithm of MOP

prediction(t+1), prediction(t+2), …, prediction(t+13) = LSTM_MOP_MODEL#01(observation(t), observation(t−1), observation(t−2), …, observation(t−52))

Coding

We used Python and Keras package (Version 2.0.4) [Reference Chollet25] based on Tensorflow (Version 1.1.0) [26]. We adopted an ‘early-stopping’ algorithm with a ‘patience’ of 100 epochs (for a total of 1000 epochs) and compared the predicting accuracy of LSTM models of the number of layers: 3–6 and 10.

Results

Results of MSP

Table 1(a) illustrates the MAPEs of LSTM with MSP algorithm. The three-layer LSTM with MSP algorithm achieved the predicting MAPEs of 19.757, 32.969, 49.096, 67.866, 89.892, 114.977, 143.999, 177.719, 217.721, 267.335, 332.577 and 426.828%, when forecasting the ILI rates of the coming second to 13th weeks. The MAPE increased by nearly 22 times as the number of predicting steps increased. Comparatively, the MAPEs of the four-layer LSTM with MSP algorithm increased limitedly, from 9.57% to 13.77% with some slight setbacks in 10-, 11- and 12-step prediction. The similar phenomena occurred in the MAPEs of LSTM of five, six and 10 layers with MSP (Fig. 2).

Fig. 2. The MAPEs of LSTM with MSP. The y-axis represents the MAPE of the predictions and the x-axis represents multi-steps of the predictions. The (a–e) illustrate the MAPEs with the MSP algorithm of three-, four-, five-, six-, 10-layer LSTM, respectively.

Table 1. The MAPEs of LSTM with the multi-step predicting algorithms of MSP, AMSP, MSOP and MOP

MAPEs, mean absolute percentage errors; MSP, multi-stage prediction; LSTM, long short-term memory.

MAPEs, mean absolute percentage errors; AMSP, adjusted multi-stage prediction; LSTM, long short-term memory.

MAPEs, mean absolute percentage errors; MSOP, multiple single-output prediction; LSTM, long short-term memory.

MAPEs, mean absolute percentage errors; MOP, multiple-output prediction; LSTM, long short-term memory.

Results of AMSP, MSOP and MOP

Tables 1(b–d) display the MAPEs of LSTM with AMSP, MSOP and MOP algorithm. In AMSP, the average MAPE increased from 9.171% to 14.715% as the number of predicting steps increased from two to 13, and varied from 13.626% to 13.911% as the number of layers of LSTM increased from three to 10 layers.

The average MAPEs of LSTM of both MSOP and MOP had a slight upward trend as the number of predicting steps increased (from 8.911% to 14.064% in MSOP; from 10.747% to 26.389% in MOP); and varied limitedly as the number of layers of LSTM increased (from 12.935% to 13.386% in MSOP; from 17.9100% to 20.684% in MOP).

In sharp contrast to MSP, the accuracy of AMSP, MSOP and MOP had little improvement when we used more layers of LSTM.

Comparison of the average MAPE of MSP, AMSP, MSOP and MOP

Figure 3 compares the average MAPEs of LSTM with multi-step predicting algorithms of MSP, AMSP, MSOP and MOP. The different numbers of the layers impacted the predicting accuracy tremendously in MSP (from 13.315% to 161.728%); slightly in MOP (from 17.910% to 20.684%), and barely in AMSP (from 13.626% to 13.911%) and MSOP (from 12.930% to 13.386%). Implementing MSOP in the six-layer LSTM structure achieved the best accuracy in this study. The MAPEs from two-step-ahead to 13-step-ahead prediction for the US ILI rates were all <15%, averagely 12.930%.

Fig. 3. The average MAPEs of LSTM with MSP, AMSP, MSOP and MOP. The y-axis represents the MAPE of the predictions and the x-axis represents the models of three-, four-, five-, six- and 10-layer LSTM with the multi-step predicting algorithms of MSP, AMSP, MSOP and MOP. Implementing MSOP in the six-layer LSTM achieved the lowest average MAPE of 12.930% in this study.

Discussion

Past studies

We did not find past studies that performed auto-regression in the multi-step prediction for flu outbreaks. Regarding multi-step prediction for studies in other fields, MSP is one of the most popular methodologies probably because many types of models can be used for this purpose, such as linear regression, support vector regression [Reference Muller, Gerstner, Germond, Hasler and Nicoud27], random forest, gradient boosting, artificial neural network [Reference Narendra and Parthasarathy28], etc. However, any such model inevitably introduces errors and tends to suffer from error accumulation problem when the predicted period is long. This is because the bias and variance from previous predictions impact future predictions [Reference Cheng, Ng, Kitsuregawa, Li and Chang20]. These compounding errors change the input distribution for future prediction steps, breaking the train-test independent and identically distributed assumption common in supervised learning [Reference Cheng, Ng, Kitsuregawa, Li and Chang20].

Comparison of accuracy of MSP, AMSP, MSOP and MOP

When comparing four different multi-step predicting algorithms, we found that the MAPEs of AMSP were less than those of MSP, which demonstrated AMSP suppressed the accumulated errors effectively based on its refined algorithm. Besides, the MAPEs of MSOP are less than those of MOP. As we mentioned in section ‘Methods’, to predict the ILI rates of the coming second to 13th weeks, MOP trained only one model while MSOP trained 13 models. As a result, MSOP can predict with no necessity of sharing neurons in LSTM structure, while MOP has to share neurons in LSTM structure. Consequently, the accuracy of MSOP performed better. Moreover, the average MAPEs of MSOP are slightly less than those of AMSP. The explanation is that MSOP does not accumulate errors at all, while AMSP just adjusted its accumulated errors by training new models. Therefore, MSOP performed best.

Other features

In our opinion, including other features in multi-step predicting models impacts models’ accuracy positively and negatively. For one thing, when predicting future values, other features could help predict more accurately, especially at turning points, such as an abrupt decrease in temperature. For another thing, before forecasting future ILI rates, we need to forecast other features (e.g. we need weather forecast for temperature and humidity). The error in former prediction could enlarge the error in later prediction. The mechanism is similar to MSP, which accumulates error step by step. In conclusion, whether the accuracy improves or deteriorates might depend on different data in different season from different countries.

In this study, we only performed auto-regression based on two pieces of consideration. First, we regard historical values as a response of all related features, such as temperature, humidity, etc. Therefore, to some extent, taking historical values as feature space includes all related features/factors in models. Besides, how to include temperature or humidity of the whole country in the models is a challenge work. Simply averaging temperature or humidity of all the places (cities and towns) of the USA might bring other problems, such as overlooking in population size, population density, life styles, etc. in different places.

Conclusion

In this study, we adjusted the LSTM model by the four multi-step prediction algorithms. The result showed that implementing MSOP in a six-layer LSTM structure achieved the best accuracy. The MAPEs from two-step-ahead to 13-step-ahead prediction for the US ILI rates were all <15%, averagely 12.930%. Hopefully, this accurate modelling approach will positively help hospitals, pharmaceutical companies, individuals and governments better prepare for the flu seasons and therefore prevent and control flu outbreaks worldwide.

Declaration of Interest

None.

Ethical Standards

The authors assert that all procedures contributing to this work comply with the ethical standards of the relevant national and institutional committees on human experimentation and with the Helsinki Declaration of 1975, as revised in 2008.

References

1.World Health Organization (WHO) (2017) Influenza (seasonal) act sheet. Available at http://www.who.int/mediacentre/factsheets/fs211/en/ (Accessed 29 October 2017).Google Scholar
2.Molinari, NA, et al. (2007) The annual impact of seasonal influenza in the US: measuring disease burden and costs. Vaccine 25, 50865096.CrossRefGoogle ScholarPubMed
3.Centers for Disease Control and Prevention, National Center for Immunization and Respiratory Diseases (NCIRD) (2016). Estimated influenza illnesses, medical visits, hospitalizations, and deaths averted by vaccination in the United States. Available at https://www.cdc.gov/flu/about/disease/2015-16.htm (Accessed 29 October 2017).Google Scholar
4.Lubeck, MD, Schulman, JL and Palese, P (1980) Antigenic variants of influenza viruses: marked differences in the frequencies of variants selected with different monoclonal antibodies. Virology 102, 458462.CrossRefGoogle ScholarPubMed
5.Stech, J, et al. (1999) Independence of evolutionary and mutational rates after transmission of avian influenza viruses to swine. Journal of Virology 73, 18781884.CrossRefGoogle Scholar
6.Suárez, P, Valcárcel, J and Ortín, J (1992) Heterogeneity of the mutation rates of influenza A viruses: isolation of mutator mutants. Journal of Virology 66, 24912494.CrossRefGoogle ScholarPubMed
7.Centers for Disease Control and Prevention, National Center for Immunization and Respiratory Diseases (NCIRD) (2016) Summary of the 2015–2016 influenza season. Available at https://www.cdc.gov/flu/about/season/flu-season-2015-2016.htm (Accessed 29 October 2017).Google Scholar
8.National Health Service (NHS) (2016) How the flu jab works. Available at https://www.nhs.uk/Conditions/vaccinations/Pages/how-flu-vaccine-works.aspx (Accessed 29 October 2017).Google Scholar
9.Gerdil, C (2003) The annual production cycle for influenza vaccine. Vaccine 21, 17761779.CrossRefGoogle ScholarPubMed
10.Proudlove, N, Boaden, R and Jorgensen, J (2007) Developing bed managers: the why and the how. Journal of Nursing Management 15, 3442.CrossRefGoogle Scholar
11.Puig-Barberà, J, et al. (2014) First-year results of the global influenza hospital surveillance network: 2012–2013 northern hemisphere influenza season. BMC Public Health 14, 564575.CrossRefGoogle ScholarPubMed
12.Centers for Disease Control and Prevention, National Center for Immunization and Respiratory Diseases (NCIRD) (2016) Disease burden of influenza. Available at https://www.cdc.gov/flu/about/disease/burden.htm (Accessed 29 October 2017).Google Scholar
13.Weigend, AS and Gershenfeld, NA (1993) Time Series Prediction: Forecasting The Future And Understanding The Past. Santa Fe, New Mexico: Santa Fe Institute.Google Scholar
14.Hochreiter, S and Schmidhuber, J (1997) Long short-term memory. Neural Computation 9, 17351780.CrossRefGoogle ScholarPubMed
15.Gers, FA, Schmidhuber, J and Cummins, F (2000) Learning to forget: continual prediction with LSTM. Neural Computation 12, 24512471.CrossRefGoogle ScholarPubMed
16.Zhang, J and Nawata, K (2017) A comparative study on predicting influenza outbreaks. Bioscience Trends 11, 533541.CrossRefGoogle ScholarPubMed
17.FluView interactive. Available at https://www.cdc.gov/flu/about/disease/2015-16.htm (Accessed 29 October 2017).Google Scholar
18.Wu, H, et al. (2017) Time series analysis of weekly influenza-like illness rate using a one-year period of factors in random forest regression. Bioscience Trends 11, 292296.CrossRefGoogle ScholarPubMed
19.Brownlee, J (2017) Four strategies for multi-step time series forecasting. Available at https://machinelearningmastery.com/multi-step-time-series-forecasting/ (Accessed 29 October 2017).Google Scholar
20.Cheng, H, et al. (2006) Multistep-ahead time series prediction. In Ng, WK, Kitsuregawa, M, Li, J and Chang, K (eds). Proceedings of the 10th Pacific-Asia Conference on Advances in Knowledge Discovery and Data Mining. Singapore: Pacific-Asia Conference on Knowledge Discovery and Data Mining, pp. 765774.CrossRefGoogle Scholar
21.Venkatraman, A, Hebert, M and Bagnell, JA (2015) Improving multi-step prediction of learned time series models. Proceedings of the Twenty-Ninth Association for the Advancement of Artificial Intelligence Conference on Artificial Intelligence. Austin: Association for the Advancement of Artificial Intelligence, pp. 30243030.Google Scholar
22.Akhlaghi, S and Zhou, N (2017) Adaptive multistep prediction based EKF to power system dynamic state estimation. Power and Energy Conference. Illinois: Institute of Electrical and Electronics Engineers. doi: 10.1109/PECI.2017.7935748.CrossRefGoogle Scholar
23.Zhang, L, et al. (2013) Iterated time series prediction with multiple support vector regression models. Neurocomputing 99, 411422.CrossRefGoogle Scholar
24.Bao, Y, Xiong, T and Hu, Z (2014) Multi-step-ahead time series prediction using multiple-output support vector regression. Neurocomputing 129, 482493.CrossRefGoogle Scholar
25.Chollet, F (2017) Keras package. Available at https://keras.io/ (Accessed 29 October 2017).Google Scholar
26.Google Inc. (2017) Available at https://www.tensorflow.org/ (Accessed 29 October 2017).Google Scholar
27.Muller, K, et al. (1997) Predicting time series with support vector machines. In Gerstner, W, Germond, A, Hasler, M and Nicoud, JD (eds). International Conference on Artificial Neural Networks. Heidelberg: Artificial Neural Networks, pp. 9991004.Google Scholar
28.Narendra, KS and Parthasarathy, K (1990) Identification and control of dynamical systems using neural networks. Institute of Electrical and Electronics Engineers Transactions on Neural Networks 1, 427.Google ScholarPubMed

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 400
Total number of PDF views: 785 *
View data table for this chart

* Views captured on Cambridge Core between 02nd April 2018 - 19th April 2021. This data will be updated every 24 hours.

You have Access
Open access

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Multi-step prediction for influenza outbreak by an adjusted long short-term memory
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Multi-step prediction for influenza outbreak by an adjusted long short-term memory
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Multi-step prediction for influenza outbreak by an adjusted long short-term memory
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *