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Erschienen in: International Journal of Machine Learning and Cybernetics 7/2019

20.06.2018 | Original Article

Deep Boltzmann machine for nonlinear system modelling

verfasst von: Wen Yu, Erick de la Rosa

Erschienen in: International Journal of Machine Learning and Cybernetics | Ausgabe 7/2019

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Abstract

Deep Boltzmann machine (DBM) has been successfully applied in classification, regression and time series modeling. For nonlinear system modelling, DBM should also have many advantages over the other neural networks, such as input features extraction and noise tolerance. In this paper, we use DBM to model nonlinear systems by calculating the probability distributions of the input and output. Two novel weight updating algorithms are proposed to obtain these distributions. We use binary encoding and conditional probability transformation methods. The proposed methods are validated with two benchmark nonlinear systems.

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Literatur
1.
Zurück zum Zitat LeCun Y, Bengio Y, Hinton GE (2015) Deep learning. Nature 521(7553):436–444CrossRef LeCun Y, Bengio Y, Hinton GE (2015) Deep learning. Nature 521(7553):436–444CrossRef
2.
Zurück zum Zitat Wang Z, Wang X (2018) A deep stochastic weight assignment network and its application to chess playing. J Parall Distrib Comput 117:205–211CrossRef Wang Z, Wang X (2018) A deep stochastic weight assignment network and its application to chess playing. J Parall Distrib Comput 117:205–211CrossRef
3.
4.
Zurück zum Zitat LeCun Y, Bottou L, Bengio Y, Haffner P (1998) Gradient-based learning applied to document recognition. Proc IEEE 86(11):2278–2324CrossRef LeCun Y, Bottou L, Bengio Y, Haffner P (1998) Gradient-based learning applied to document recognition. Proc IEEE 86(11):2278–2324CrossRef
5.
Zurück zum Zitat Salakhutdinov R, Hinton GE (2009) Deep boltzmann machines. In: 12th International conference on artificial intelligence and statistics (AISTATS). Clearwater Beach, Florida, USA Salakhutdinov R, Hinton GE (2009) Deep boltzmann machines. In: 12th International conference on artificial intelligence and statistics (AISTATS). Clearwater Beach, Florida, USA
6.
7.
Zurück zum Zitat Larochelle H, Bengio Y (2008) Classification using discriminative restricted Boltzmann machines. In: 25th International conference on machine learning, Helsinki, Finland, pp 536–543 Larochelle H, Bengio Y (2008) Classification using discriminative restricted Boltzmann machines. In: 25th International conference on machine learning, Helsinki, Finland, pp 536–543
8.
Zurück zum Zitat Le Roux N, Bengio Y (2008) Representational power of restricted Boltzmann machines and deep belief networks. Neural Comput 20:1631–1649MathSciNetCrossRefMATH Le Roux N, Bengio Y (2008) Representational power of restricted Boltzmann machines and deep belief networks. Neural Comput 20:1631–1649MathSciNetCrossRefMATH
9.
Zurück zum Zitat Erhan D, Bengio Y, Courville A, Manzagol P-A, Vincent P (2010) Why does unsupervised pre-training help deep learning? J Mach Learn Res 11:625–660MathSciNetMATH Erhan D, Bengio Y, Courville A, Manzagol P-A, Vincent P (2010) Why does unsupervised pre-training help deep learning? J Mach Learn Res 11:625–660MathSciNetMATH
11.
Zurück zum Zitat Hinton GE, Sejnowski TJ (1986) Learning and relearning in Boltzmann machines. In: Parallel distributed processing: explorations in the microstructure of cognition, vol 1: foundations, pp 282–317, MIT Press, Cambridge, MA Hinton GE, Sejnowski TJ (1986) Learning and relearning in Boltzmann machines. In: Parallel distributed processing: explorations in the microstructure of cognition, vol 1: foundations, pp 282–317, MIT Press, Cambridge, MA
12.
Zurück zum Zitat Qiu L, Zhang L, Ren Y, Suganthan PN, Amaratunga G (2014) Ensemble deep learning for regression and time series forecasting. In: 2014 IEEE symposium on computational intelligence in ensemble learning (CIEL), pp 1–6, Orlando, FL, USA Qiu L, Zhang L, Ren Y, Suganthan PN, Amaratunga G (2014) Ensemble deep learning for regression and time series forecasting. In: 2014 IEEE symposium on computational intelligence in ensemble learning (CIEL), pp 1–6, Orlando, FL, USA
13.
Zurück zum Zitat Busseti E, Osband I, Wong S (2012) Deep learning for time series modeling. Technical report, Stanford University Busseti E, Osband I, Wong S (2012) Deep learning for time series modeling. Technical report, Stanford University
14.
Zurück zum Zitat Längkvist M, Karlsson L, Loutfi A (2014) A review of unsupervised feature learning and deep learning for time-series modeling. Pattern Recogn Lett 42:11–24CrossRef Längkvist M, Karlsson L, Loutfi A (2014) A review of unsupervised feature learning and deep learning for time-series modeling. Pattern Recogn Lett 42:11–24CrossRef
15.
Zurück zum Zitat Romeu P et al (2013) Time-series forecasting time-series, of indoor temperature using pre-trained deep neural networks. Artificial Neural Networks and Machine Learning-ICANN. Springer, Berlin Heidelberg, pp 451–458 Romeu P et al (2013) Time-series forecasting time-series, of indoor temperature using pre-trained deep neural networks. Artificial Neural Networks and Machine Learning-ICANN. Springer, Berlin Heidelberg, pp 451–458
16.
Zurück zum Zitat Ljung L (1987) System identification-theory for user. Prentice Hall, Englewood CliffsMATH Ljung L (1987) System identification-theory for user. Prentice Hall, Englewood CliffsMATH
17.
18.
Zurück zum Zitat Bengio Y, Lamblin P, Popovici D, Larochelle H (2007) Greedy layer-wise training of deep networks. In: Advances in neural information processing systems (NIPS’06). MIT Press, Cambridge, pp 153–160 Bengio Y, Lamblin P, Popovici D, Larochelle H (2007) Greedy layer-wise training of deep networks. In: Advances in neural information processing systems (NIPS’06). MIT Press, Cambridge, pp 153–160
19.
Zurück zum Zitat de la Rosa E, Yu W (2016) Randomized algorithms for nonlinear system identification with deep learning modification. Inform Sci 364:197–212CrossRef de la Rosa E, Yu W (2016) Randomized algorithms for nonlinear system identification with deep learning modification. Inform Sci 364:197–212CrossRef
20.
Zurück zum Zitat Narendra KS, Parthasarathy K (1990) Identification and control of dynamical systems using neural networks. IEEE Trans Neural Netw 1(1):4-2CrossRef Narendra KS, Parthasarathy K (1990) Identification and control of dynamical systems using neural networks. IEEE Trans Neural Netw 1(1):4-2CrossRef
21.
Zurück zum Zitat Jagannathan S, Lewis FL (1996) Identification of nonlinear dynamical systems using multilayered neural networks. Automatica 32(12):1707–1712MathSciNetCrossRefMATH Jagannathan S, Lewis FL (1996) Identification of nonlinear dynamical systems using multilayered neural networks. Automatica 32(12):1707–1712MathSciNetCrossRefMATH
22.
Zurück zum Zitat Busseti E, Osband I, Wong S (2012) Deep learning for time series modeling. CS 229 Technical Report, Stanford University Busseti E, Osband I, Wong S (2012) Deep learning for time series modeling. CS 229 Technical Report, Stanford University
23.
Zurück zum Zitat de la Rosa E, Yu W (2015) Restricted Boltzmann machine for nonlinear system modeling. In: 14th IEEE international conference on machine learning and applications (ICMLA15), Miami, USA de la Rosa E, Yu W (2015) Restricted Boltzmann machine for nonlinear system modeling. In: 14th IEEE international conference on machine learning and applications (ICMLA15), Miami, USA
24.
Zurück zum Zitat de la Rosa E, Yu W, Li X (2016) Nonlinear system modeling with deep neural networks and autoencoders algorithm. In: 2016 IEEE international conference on systems, man, and cybernetics (SMC16), Budapest, Hungary, pp 2157–2162 de la Rosa E, Yu W, Li X (2016) Nonlinear system modeling with deep neural networks and autoencoders algorithm. In: 2016 IEEE international conference on systems, man, and cybernetics (SMC16), Budapest, Hungary, pp 2157–2162
25.
Zurück zum Zitat de la Rosa E, Yu W (2015) Nonlinear system identification using deep learning and randomized algorithms. In: 2015 IEEE international conference on information and automation, Lijing, China, pp 274–279 de la Rosa E, Yu W (2015) Nonlinear system identification using deep learning and randomized algorithms. In: 2015 IEEE international conference on information and automation, Lijing, China, pp 274–279
26.
27.
Zurück zum Zitat Cybenko G (1989) Approximation by superposition of sigmoidal activation function. Math Control Sig Syst 2:303–314CrossRefMATH Cybenko G (1989) Approximation by superposition of sigmoidal activation function. Math Control Sig Syst 2:303–314CrossRefMATH
28.
Zurück zum Zitat Huang GB, Chen L, Siew CK (2006) Universal approximation using incremental constructive feedforward networks with random hidden nodes. IEEE Trans Neural Netw. 17(4):879–92CrossRef Huang GB, Chen L, Siew CK (2006) Universal approximation using incremental constructive feedforward networks with random hidden nodes. IEEE Trans Neural Netw. 17(4):879–92CrossRef
29.
Zurück zum Zitat Ackley DH, Hinton GE, Sejnowski TJ (1985) A learning algorithm for boltzmann machines. Cogn Sci 9:147–169CrossRef Ackley DH, Hinton GE, Sejnowski TJ (1985) A learning algorithm for boltzmann machines. Cogn Sci 9:147–169CrossRef
31.
Zurück zum Zitat Box G, Jenkins G, Reinsel G (2008) Time series analysis: forecasting and control, 4th edn. Wiley, New YorkCrossRefMATH Box G, Jenkins G, Reinsel G (2008) Time series analysis: forecasting and control, 4th edn. Wiley, New YorkCrossRefMATH
32.
Zurück zum Zitat Bergstra J, Bengio Y (2011) Random search for hyper-parameter optimization. J Machine Learn Res 13:281–305MathSciNetMATH Bergstra J, Bengio Y (2011) Random search for hyper-parameter optimization. J Machine Learn Res 13:281–305MathSciNetMATH
33.
Zurück zum Zitat Schoukens J, Suykens J, Ljung L (2009) Wiener-Hammerstein benchmark, 15th IFAC symposiumon system identification. Saint-Malo, France Schoukens J, Suykens J, Ljung L (2009) Wiener-Hammerstein benchmark, 15th IFAC symposiumon system identification. Saint-Malo, France
34.
Zurück zum Zitat Erhan D, Manzagol PA, Bengio Y, Bengio S, Vincent P (2009) The difficulty of training deep architectures and the effect of unsupervised pretraining. In: 12th International conference on artificial intelligence and statistics (AISTATS’09), pp 153–160 Erhan D, Manzagol PA, Bengio Y, Bengio S, Vincent P (2009) The difficulty of training deep architectures and the effect of unsupervised pretraining. In: 12th International conference on artificial intelligence and statistics (AISTATS’09), pp 153–160
35.
Zurück zum Zitat Bartlett PL (1997) For valid generalization, the size of the weights is more important than the size of the network. In: Mozer M, Jordan M, Petsche T (eds) Advances in neural information processing systems’ 1996, vol 9. MIT Press, Cambridge, pp 134–140 Bartlett PL (1997) For valid generalization, the size of the weights is more important than the size of the network. In: Mozer M, Jordan M, Petsche T (eds) Advances in neural information processing systems’ 1996, vol 9. MIT Press, Cambridge, pp 134–140
36.
Zurück zum Zitat Jang JS (1993) ANFIS: Adaptive-network-based fuzzy inference system. IEEE Trans Syst Man Cybern 23:665–685CrossRef Jang JS (1993) ANFIS: Adaptive-network-based fuzzy inference system. IEEE Trans Syst Man Cybern 23:665–685CrossRef
37.
Zurück zum Zitat Mitra S, Hayashi Y (2000) Neuro-fuzzy rule generation: survey in soft computing framework. IEEE Trans Neural Netw 11(3):748–769CrossRef Mitra S, Hayashi Y (2000) Neuro-fuzzy rule generation: survey in soft computing framework. IEEE Trans Neural Netw 11(3):748–769CrossRef
38.
Zurück zum Zitat Rivals I, Personnaz L (2003) Neural-network construction and selection in nonlinear modeling. IEEE Trans Neural Netw 14(4):804–820CrossRefMATH Rivals I, Personnaz L (2003) Neural-network construction and selection in nonlinear modeling. IEEE Trans Neural Netw 14(4):804–820CrossRefMATH
40.
Zurück zum Zitat Leung FHF, Lam HK, Ling SH, Tam PKS (2003) Tuning of the structure and parameters of a neural network using an improved genetic algorithm. IEEE Transact Neural Netw 14:79–88CrossRef Leung FHF, Lam HK, Ling SH, Tam PKS (2003) Tuning of the structure and parameters of a neural network using an improved genetic algorithm. IEEE Transact Neural Netw 14:79–88CrossRef
Metadaten
Titel
Deep Boltzmann machine for nonlinear system modelling
verfasst von
Wen Yu
Erick de la Rosa
Publikationsdatum
20.06.2018
Verlag
Springer Berlin Heidelberg
Erschienen in
International Journal of Machine Learning and Cybernetics / Ausgabe 7/2019
Print ISSN: 1868-8071
Elektronische ISSN: 1868-808X
DOI
https://doi.org/10.1007/s13042-018-0847-0

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