时间序列预测方法综述
|
摘要
时间序列是按照时间排序的一组随机变量,它通常是在相等间隔的时间段内依照给定的采样率对某种潜在过程进行观测的结果。时间序列数据本质上反映的是某个或者某些随机变量随时间不断变化的趋势,而时间序列预测方法的核心就是从数据中挖掘出这种规律,并利用其对将来的数据做出估计。针对时间序列预测方法,着重介绍了传统的时间序列预测方法、基于机器学习的时间序列预测方法和基于参数模型的在线时间序列预测方法,并对未来的研究方向进行了进一步的展望。
Time series is a set of random variables ordered in timestamp.It is often the observation of an underlying process,in which values are collected from uniformly spaced time instants,according to a given sampling rate.Time series data essentially reflects the trend that one or some random variables change with time.The core of time series prediction is mining the rule from data and making use of it to estimate future data.This paper emphatically introduced a summary of time series prediction method,namely the traditional time series prediction method,machine learning based time series prediction method and online time series prediction method based on parameter model,and further prospected the future research direction.
Time series is a set of random variables ordered in timestamp.It is often the observation of an underlying process,in which values are collected from uniformly spaced time instants,according to a given sampling rate.Time series data essentially reflects the trend that one or some random variables change with time.The core of time series prediction is mining the rule from data and making use of it to estimate future data.This paper emphatically introduced a summary of time series prediction method,namely the traditional time series prediction method,machine learning based time series prediction method and online time series prediction method based on parameter model,and further prospected the future research direction.
引文
[1]YUAN J D,WANG Z H.Review of Time Series Representation and Classification Techniques[J].Computer Science,2015,42(3):1-7.(in Chinese)原继东,王志海.时间序列的表示与分类算法综述[J].计算机科学,2015,42(3):1-7.
[2]GAO J,SULTAN H,HU J,et al.Denoising Nonlinear Time Series by Adaptive Filtering and Wavelet Shrinkage:A Comparison[J].IEEE Signal Processing Letters,2010,17(3):237-240.
[3]ROJO-ALVAREZ J L,MARTINEZ-RAMON M,PRADO-CUMPLIDO M,et al.Support Vector Method for Robust AR-MA System Identification[J].IEEE Transactions on Signal Processing,2004,52(1):155-164.
[4]GRANGER C W J,NEWBOLD P.Forecasting Economic Time Series[M].New York:Academic Press,1986.
[5]BOX G,JENKINS G.Time Series Analysis,Forecasting and Control[M].Holden-Day,1990.
[6]HAMILTON J.Time Series Analysis[M].Princeton:Princeton University Press,1994.
[7]DEMPSTER A P,LAIRD N M,RUBIN D B.Maximum Likelihood from Incomplete Data via the EM Algorithm[J].Journal of the Royal Statistical Society,Series B(Methodological),1977,39(1):1-38.
[8]DURBIN J,KOOPMAN S J.Time Series Analysis by State Space Methods[M].Oxford:Oxford University Press,2012.
[9]KALMAN R E.A New Approach to Linear Filtering and Prediction Problems[J].Journal of Fluids Engineering,1960,82(1):35-45.
[10]ALQUIER P,LI X,WINTENBERGER O.Prediction of Time Series by Statistical Learning:General Losses and Fast Rates[J].Dependence Modelling,2014,1:65-93.
[11]KUZNETSOV V,MOHRI M.Generalization Bounds for Time Series Prediction with Non-Stationary Processes[M]∥Algorithmic Learning Theory.Springer International Publishing,2014:260-274.
[12]CRISTIANINI N,TAYLOR J S.Introduction to Support Vector Machines[M].李国正,王猛,曾华军,译.北京:电子工业出版社,2004.
[13]ZHANG X G.Introduction to Statistical Learning Theory and Support Vector Machines[J].Acta Automatica Sinica,2000,26(1):32-41.(in Chinese)张学工.关于统计学习理论与支持向量机[J].自动化学报,2000,26(1):32-41.
[14]VAPNIK V N.The Nature of Statistical Learning Theory[M].张学工,译.北京:清华大学出版社,2000.
[15]VAPNIK V N.Statistical Learning Theory[M].许建华,张学工,译.北京:电子工业出版社,2004.
[16]CRISTIANINI N,TAYLOR J S.An Introduction to Support Vector Machines[M].Cambridge:Cambridge University Press,2000.
[17]KIM K.Financial Time Series Forecasting Using Support Vector Machines[J].Neurocomputing,2003,55(1):307-319.
[18]GESTEL T V,SUYKENS J A K,BAESTAENS D E,et al.Financial Time Series Prediction Using Least Squares Support Vector Machines within The Evidence Framework[J].IEEETransactions on Neural Networks,2001,12(4),809-821.
[19]MACKAY D J C.Bayesian Interpolation[J].Neural Computation,1992,4(3):415-447.
[20]MACKAY D J C.Probable Networks and Plausible PredictionsA Review of Practical Bayesian Methods for Supervised Neural Networks[J].Network Computation in Neural Systems,1995,6(3):469-505.
[21]SUYKENS J A K,VANDEWALLE J.Least Squares Support Vector Machine Classifiers[J].Neural Processing Letters,1999,9(3):293-300.
[22]SUYKENS J A K.Least Squares Support Vector Machines for Classification and Nonlinear Modeling[J].Neural Network World,2000,10(1):29-48.
[23]MELLIT A,PAVAN A M,BENGHANEM M.Least Squares Support Vector Machine For Short-Term Prediction of Meteorological Time Series[J].Theoretical Applied Climatology,2013,111(1):297-307.
[24]TAY F E H,CAO L.Application of Support Vector Machines in Financial Time Series Forecasting[J].Omega,2001,29(4):309-317.
[25]JACOBS R A,JORDAN M A,NOWLAN S J,et al.Adaptive Mixtures of Local Experts[J].Neural Computation,1991,3(1):79-87.
[26]JORDAN M I,JACOBS R A.Hierarchical Mixtures of Experts and the EM Algorithm[J].Neural Computation,1994,6(2):181-214.
[27]WEIGEND A S,MANAGEAS M.Analysis and Prediction of Multi-Stationary Time Series[C]∥Proceedings of the Third International Conference on Neural Networks in the Capital Markets.1995.
[28]WEIGEND A S,MANAGEAS M,SRIVASTAVA A N.Nonlinear Gated Experts for Time Series:Discovering Regimes and Avoiding Over-fitting[J].International Journal of Neural Systems,1995,6(4):373-399.
[29]KOHONEN T.Self-Organization and Associative Memory[M].Springer,1989.
[30]PEARL J.Fusion,Propagation and Structuring In Belief Networks[J].Artificial Intelligence,1986,2(3):241-288.
[31]COOPER G F,HERSKOVITS E.A Bayesian Method for the Induction of Probabilistic Networks from Data[J].Machine Learning,2008,9(4):309-347.
[32]ZHANG M,ZHOU Z.Multi-Label Neural Networks with Application to Function Genomics and Text Categorization[J].IEEE Transactions on Knowledge and Data Engineering,2006,18(10):1338-1351.
[33]MEZ J,MATEO J L,PUERTA J.Learning Bayesian Networks by Hill Climbing:Efficient Methods Based on Progressive Restriction of the Neighborhood[J].Data Mining Knowledge Discovery,2011,22(1-2):106-148.
[34]DAS M,GHOSH S K.A Probabilistic Approach for Weather Forecast Using Spatio-temporal Inter-relationship among Climate Variables[C]∥International Conference on Industrial and Information Systems.IEEE,2015.
[35]DAS M,GHOSH S K.SemBnet:A Semantic Bayesian Network for Multivariate Prediction of Meteorological Time Series Data[J].Pattern Recognition Letters,2017,93:192-201.
[36]KOREN Y,BELL R,VOLINSKY C.Matrix Factorization Techniques for Recommender Systems[J].Computer,2009,42(8):30-37.
[37]KOREN K.Factorization Meets The Neighborhood:A Multifaceted Collaborative Filtering Model[C]∥ACM SIGKDD International Conference on Knowledge Discovery and Data Mining.ACM,2008:426-434.
[38]SALAKHUTDINOV R,MNIH A.Probabilistic Matrix Factorization[C]∥International Conference on Neural Information Processing Systems.Curran Associates Inc.,2007:1257-1264.
[39]XU M,ZHU J,ZHANG B.Bayesian Nonparametric Maximum Margin Matrix Factorization for Collaborative Prediction[C]∥Advances in Neural Information Processing Systems.2012.
[40]SREBRO N.Maximum margin matrix factorization[J].Advances in Nips,2005,37(2):1329-1336.
[41]BALAKRISHNAN S,CHOPRA S.Collaborative Ranking[C]∥ACM International Conference on Web Search and Data Mining.ACM,2012:143-152.
[42]WEIMER M,KARATZOGLOU A,LE Q,et al.CoFiRankMaximum Margin Matrix Factorization for Collaborative Ranking[C]∥Neural Information Processing Systems.2007:1593-1600.
[43]KROHN-GRIMBERGHE A,DRUMOND L,FREUDENTHA-LER C.Multi-Relational Matrix Factorization Using Bayesian Personalized Ranking for Social Network Data[C]∥Proceedings of the Fifth International Conference on Web Search and Web Data Mining(WSDM 2012).Seattle,WA,USA,2012.
[44]ZHANG Y,ROUGHAN M,WILLINGER W,et al.Spatio-temporal Compressive Sensing and Internet Traffic Matrices[C]∥ACM Sigcomm Conference on Data Communication.2009.
[45]RALLAPALLI S,QIU L,ZHANG Y,et al.Exploiting Temporal Stability and Low-Rank Structure for Localization in Mobile Networks[C]∥International Conference on Mobile Computing and Networking(Mobicom’10).2010.
[46]YU H F,RAO N,DHILLON I S.Temporal Regularized Matrix Factorization for High-Dimensional Time Series Prediction[C]∥NIPS.2016.
[47]XIONG L,CHEN X,HUANG T K,et al.Temporal Collaborative Filtering with Bayesian Probabilistic Tensor Factorization[C]∥Siam International Conference on Data Mining(SDM2010).Columbus,Ohio,USA,DBLP,2010:211-222.
[48]RASMUSSEN C E,WILLIAMS C K I.Gaussian Processes for Machine Learning[M].The MIT Press,2006.
[49]ALEXE B,DESELAERS T,FERRARI V.What is An Object[C]∥Computer Vision and Pattern Recognition.IEEE,2010:73-80.
[50]EVERINGHAM M,GOOL L V,WILLIAMS C K I,et al.The Pascal,Visual Object Classes(VOC)Challenge[J].International Journal of Computer Vision,2010,88(2):303-338.
[51]FELZENSZWALB P F,GIRSHICK R B,MCALLESTER D,et al.Object Detection with Discriminatively Trained Part-Based Models[J].IEEE Transactions on Pattern Analysis&Machine Intelligence,2010,32(9):1627-1645.
[52]KAPOOR A,GRAUMAN K,URTASUNR,et al.Gaussian Processes for Object Categorization[J].International Journal of Computer Vision,2010,88(2):169-188.
[53]CHUM O,ZISSERMAN A.An Exemplar Model for Learning Object Classes[C]∥IEEE Conference on Computer Vision and Pattern Recognition,2007(CVPR’07).IEEE,2007:1-8.
[54]DIOSAN L,ROGOZAN A,PECUCHET J P.Evolving Kernel Functions for SVMs by Genetic Programming[C]∥International Conference on Machine Learning and Applications.IEEE,2007:19-24.
[55]WU B,ZHANG W,CHEN L,et al.A GP-based Kernel Construction and Optimization Method for RVM[C]∥The International Conference on Computer and Automation Engineering.IEEE,2010:419-423.
[56]KLENSKE E D,ZEILINGER M N,SCHOLKOPF B,et al.Nonparametric Dynamics Estimation for Time Periodic Systems[C]∥Communication,Control,and Computing.IEEE,2014:486-493.
[57]LLOYD J R,DUVENAUD D,GROSSE R,et al.Automatic Construction and Natural-Language Description of Nonparametric Regression Models[C]∥Twenty-Eighth AAAI Conference on Artificial Intelligence.AAAI Press,2014:1242-1250.
[58]TOBAR F,BUI T D,TURNER R E.Learning Stationary Time Series Using Gaussian Processes with Nonparametric Kernels[C]∥Advances in Neural Information Processing Systems 28(NIPS 2015).2015.
[59]HWANG Y,TONG A,CHOI J.Automatic Construction of Nonparametric Relational Regression Models for Multiple Time Series[C]∥International Conference on International Conference on Machine Learning.JMLR.org,2016:3030-3039.
[60]KUREMOTO T,KIMURA S,KOBAYASHI K,et al.Time Series Forecasting Using a Deep Belief Network with Restricted Boltzman Machines[J].Neurocomputing,2014,137(15):47-56.
[61]TURNER J T.Time Series Analysis Using Deep Feed Forward Neural Networks[D].Baltimore:University of Maryland,2014.
[62]ROMEU P,ZAMORA-MARTINEZ F,BOTELLA-ROCAMO-RA P,et al.Time-Series Forecasting of Indoor Temperature Using Pre-trained Deep Neural Networks[C]∥International Conference on Artificial Neural Networks.Berlin:Springer,2013:451-458.
[63]LV Y,DUAN Y,KANG W,et al.Traffic Flow Prediction with Big Data:A Deep Learning Approach[J].IEEE Transactions on Intelligent Transportation Systems,2015,16(2):865-873.
[64]LANGKVIST M,KARLSSON L,LOUTFI A.A Review of Unsupervised Feature Learning and Deep Learning for Time-Series Modeling[J].Pattern Recognition Letters,2014,42(1):11-24.
[65]GAMBOA J C B.Deep Learning for Time-Series Analysis[J].Arxiv:1701.01887,2017.
[66]HEATON J B,POLSON N G,WITTE J H.Deep Learning in Finance[J].Arxiv:1602.06561,2016.
[67]BOROVYKH A,BOHTE S,OOSTERLEE C W.Conditional Time Series Forecasting with Convolutional Neural Networks[J].Arxiv:1703.04691,2017.
[68]OORD A,DIELEMAN S,ZEN H,et al.Wavenet:A Generative Model for Raw Audio[J].Arxiv:1609.03499,2016.
[69]JAIN A,KUMAR A M.Hybrid Neural Network Models for Hydrologic Time Series Forecasting[J].Applied Soft Computing,2007,7(2):585-592.
[70]ZHANG G,PATUWO B E,HU M.Forecasting with Artificial Neural Networks:The State of The Art[J].International Journal of Forecasting,1998,14(1):35-62.
[71]ZHANG G.Time Series Forecasting Using a Hybrid ARIMAand Neural Network Model[J].Neurocomputing,2003,50(1):159-175.
[72]BINKOWSKI M,MARTI G,DONNAT P.Autoregressive Convolutional Neural Networks for Asynchronous Time Series[J].Arxiv:1703.04122,2017.
[73]GOEL H,MELNYK I,BANERJEE A.R2N2:Residual Recurrent Neural Networks for Multivariate Time Series Forecasting[J].Arxiv:1709.03159,2017.
[74]LAI G,CHANG W,YANG Y,et al.Modeling Long-And ShortTerm Temporal Patterns with Deep Neural Networks[J].Arxiv:1703.07015,2017.
[75]ANAVA O,HAZAN E,MANNOR S,et al.Online Learning for Time Series Prediction[J].Journal of Machine Learning Research,2013,30:172-184.
[76]SHWARTZ S S.Online Learning and Online Convex Optimization[J].Foundations and Trends in Machine Learning,2011,4(2):107-194.
[77]ZINKEVICH M.Online Convex Programming and Generalized Infinitesimal Gradient Ascent[C]∥Proceedings of the Twentieth International Conference on Machine Learning(ICML).2003:928-936.
[78]HAZAN E,AGARWAL A,KALE S.Logarithmic regret algorithms for online convex optimization[J].Machine Learning,2007,69(2-3):169-192.
[2]GAO J,SULTAN H,HU J,et al.Denoising Nonlinear Time Series by Adaptive Filtering and Wavelet Shrinkage:A Comparison[J].IEEE Signal Processing Letters,2010,17(3):237-240.
[3]ROJO-ALVAREZ J L,MARTINEZ-RAMON M,PRADO-CUMPLIDO M,et al.Support Vector Method for Robust AR-MA System Identification[J].IEEE Transactions on Signal Processing,2004,52(1):155-164.
[4]GRANGER C W J,NEWBOLD P.Forecasting Economic Time Series[M].New York:Academic Press,1986.
[5]BOX G,JENKINS G.Time Series Analysis,Forecasting and Control[M].Holden-Day,1990.
[6]HAMILTON J.Time Series Analysis[M].Princeton:Princeton University Press,1994.
[7]DEMPSTER A P,LAIRD N M,RUBIN D B.Maximum Likelihood from Incomplete Data via the EM Algorithm[J].Journal of the Royal Statistical Society,Series B(Methodological),1977,39(1):1-38.
[8]DURBIN J,KOOPMAN S J.Time Series Analysis by State Space Methods[M].Oxford:Oxford University Press,2012.
[9]KALMAN R E.A New Approach to Linear Filtering and Prediction Problems[J].Journal of Fluids Engineering,1960,82(1):35-45.
[10]ALQUIER P,LI X,WINTENBERGER O.Prediction of Time Series by Statistical Learning:General Losses and Fast Rates[J].Dependence Modelling,2014,1:65-93.
[11]KUZNETSOV V,MOHRI M.Generalization Bounds for Time Series Prediction with Non-Stationary Processes[M]∥Algorithmic Learning Theory.Springer International Publishing,2014:260-274.
[12]CRISTIANINI N,TAYLOR J S.Introduction to Support Vector Machines[M].李国正,王猛,曾华军,译.北京:电子工业出版社,2004.
[13]ZHANG X G.Introduction to Statistical Learning Theory and Support Vector Machines[J].Acta Automatica Sinica,2000,26(1):32-41.(in Chinese)张学工.关于统计学习理论与支持向量机[J].自动化学报,2000,26(1):32-41.
[14]VAPNIK V N.The Nature of Statistical Learning Theory[M].张学工,译.北京:清华大学出版社,2000.
[15]VAPNIK V N.Statistical Learning Theory[M].许建华,张学工,译.北京:电子工业出版社,2004.
[16]CRISTIANINI N,TAYLOR J S.An Introduction to Support Vector Machines[M].Cambridge:Cambridge University Press,2000.
[17]KIM K.Financial Time Series Forecasting Using Support Vector Machines[J].Neurocomputing,2003,55(1):307-319.
[18]GESTEL T V,SUYKENS J A K,BAESTAENS D E,et al.Financial Time Series Prediction Using Least Squares Support Vector Machines within The Evidence Framework[J].IEEETransactions on Neural Networks,2001,12(4),809-821.
[19]MACKAY D J C.Bayesian Interpolation[J].Neural Computation,1992,4(3):415-447.
[20]MACKAY D J C.Probable Networks and Plausible PredictionsA Review of Practical Bayesian Methods for Supervised Neural Networks[J].Network Computation in Neural Systems,1995,6(3):469-505.
[21]SUYKENS J A K,VANDEWALLE J.Least Squares Support Vector Machine Classifiers[J].Neural Processing Letters,1999,9(3):293-300.
[22]SUYKENS J A K.Least Squares Support Vector Machines for Classification and Nonlinear Modeling[J].Neural Network World,2000,10(1):29-48.
[23]MELLIT A,PAVAN A M,BENGHANEM M.Least Squares Support Vector Machine For Short-Term Prediction of Meteorological Time Series[J].Theoretical Applied Climatology,2013,111(1):297-307.
[24]TAY F E H,CAO L.Application of Support Vector Machines in Financial Time Series Forecasting[J].Omega,2001,29(4):309-317.
[25]JACOBS R A,JORDAN M A,NOWLAN S J,et al.Adaptive Mixtures of Local Experts[J].Neural Computation,1991,3(1):79-87.
[26]JORDAN M I,JACOBS R A.Hierarchical Mixtures of Experts and the EM Algorithm[J].Neural Computation,1994,6(2):181-214.
[27]WEIGEND A S,MANAGEAS M.Analysis and Prediction of Multi-Stationary Time Series[C]∥Proceedings of the Third International Conference on Neural Networks in the Capital Markets.1995.
[28]WEIGEND A S,MANAGEAS M,SRIVASTAVA A N.Nonlinear Gated Experts for Time Series:Discovering Regimes and Avoiding Over-fitting[J].International Journal of Neural Systems,1995,6(4):373-399.
[29]KOHONEN T.Self-Organization and Associative Memory[M].Springer,1989.
[30]PEARL J.Fusion,Propagation and Structuring In Belief Networks[J].Artificial Intelligence,1986,2(3):241-288.
[31]COOPER G F,HERSKOVITS E.A Bayesian Method for the Induction of Probabilistic Networks from Data[J].Machine Learning,2008,9(4):309-347.
[32]ZHANG M,ZHOU Z.Multi-Label Neural Networks with Application to Function Genomics and Text Categorization[J].IEEE Transactions on Knowledge and Data Engineering,2006,18(10):1338-1351.
[33]MEZ J,MATEO J L,PUERTA J.Learning Bayesian Networks by Hill Climbing:Efficient Methods Based on Progressive Restriction of the Neighborhood[J].Data Mining Knowledge Discovery,2011,22(1-2):106-148.
[34]DAS M,GHOSH S K.A Probabilistic Approach for Weather Forecast Using Spatio-temporal Inter-relationship among Climate Variables[C]∥International Conference on Industrial and Information Systems.IEEE,2015.
[35]DAS M,GHOSH S K.SemBnet:A Semantic Bayesian Network for Multivariate Prediction of Meteorological Time Series Data[J].Pattern Recognition Letters,2017,93:192-201.
[36]KOREN Y,BELL R,VOLINSKY C.Matrix Factorization Techniques for Recommender Systems[J].Computer,2009,42(8):30-37.
[37]KOREN K.Factorization Meets The Neighborhood:A Multifaceted Collaborative Filtering Model[C]∥ACM SIGKDD International Conference on Knowledge Discovery and Data Mining.ACM,2008:426-434.
[38]SALAKHUTDINOV R,MNIH A.Probabilistic Matrix Factorization[C]∥International Conference on Neural Information Processing Systems.Curran Associates Inc.,2007:1257-1264.
[39]XU M,ZHU J,ZHANG B.Bayesian Nonparametric Maximum Margin Matrix Factorization for Collaborative Prediction[C]∥Advances in Neural Information Processing Systems.2012.
[40]SREBRO N.Maximum margin matrix factorization[J].Advances in Nips,2005,37(2):1329-1336.
[41]BALAKRISHNAN S,CHOPRA S.Collaborative Ranking[C]∥ACM International Conference on Web Search and Data Mining.ACM,2012:143-152.
[42]WEIMER M,KARATZOGLOU A,LE Q,et al.CoFiRankMaximum Margin Matrix Factorization for Collaborative Ranking[C]∥Neural Information Processing Systems.2007:1593-1600.
[43]KROHN-GRIMBERGHE A,DRUMOND L,FREUDENTHA-LER C.Multi-Relational Matrix Factorization Using Bayesian Personalized Ranking for Social Network Data[C]∥Proceedings of the Fifth International Conference on Web Search and Web Data Mining(WSDM 2012).Seattle,WA,USA,2012.
[44]ZHANG Y,ROUGHAN M,WILLINGER W,et al.Spatio-temporal Compressive Sensing and Internet Traffic Matrices[C]∥ACM Sigcomm Conference on Data Communication.2009.
[45]RALLAPALLI S,QIU L,ZHANG Y,et al.Exploiting Temporal Stability and Low-Rank Structure for Localization in Mobile Networks[C]∥International Conference on Mobile Computing and Networking(Mobicom’10).2010.
[46]YU H F,RAO N,DHILLON I S.Temporal Regularized Matrix Factorization for High-Dimensional Time Series Prediction[C]∥NIPS.2016.
[47]XIONG L,CHEN X,HUANG T K,et al.Temporal Collaborative Filtering with Bayesian Probabilistic Tensor Factorization[C]∥Siam International Conference on Data Mining(SDM2010).Columbus,Ohio,USA,DBLP,2010:211-222.
[48]RASMUSSEN C E,WILLIAMS C K I.Gaussian Processes for Machine Learning[M].The MIT Press,2006.
[49]ALEXE B,DESELAERS T,FERRARI V.What is An Object[C]∥Computer Vision and Pattern Recognition.IEEE,2010:73-80.
[50]EVERINGHAM M,GOOL L V,WILLIAMS C K I,et al.The Pascal,Visual Object Classes(VOC)Challenge[J].International Journal of Computer Vision,2010,88(2):303-338.
[51]FELZENSZWALB P F,GIRSHICK R B,MCALLESTER D,et al.Object Detection with Discriminatively Trained Part-Based Models[J].IEEE Transactions on Pattern Analysis&Machine Intelligence,2010,32(9):1627-1645.
[52]KAPOOR A,GRAUMAN K,URTASUNR,et al.Gaussian Processes for Object Categorization[J].International Journal of Computer Vision,2010,88(2):169-188.
[53]CHUM O,ZISSERMAN A.An Exemplar Model for Learning Object Classes[C]∥IEEE Conference on Computer Vision and Pattern Recognition,2007(CVPR’07).IEEE,2007:1-8.
[54]DIOSAN L,ROGOZAN A,PECUCHET J P.Evolving Kernel Functions for SVMs by Genetic Programming[C]∥International Conference on Machine Learning and Applications.IEEE,2007:19-24.
[55]WU B,ZHANG W,CHEN L,et al.A GP-based Kernel Construction and Optimization Method for RVM[C]∥The International Conference on Computer and Automation Engineering.IEEE,2010:419-423.
[56]KLENSKE E D,ZEILINGER M N,SCHOLKOPF B,et al.Nonparametric Dynamics Estimation for Time Periodic Systems[C]∥Communication,Control,and Computing.IEEE,2014:486-493.
[57]LLOYD J R,DUVENAUD D,GROSSE R,et al.Automatic Construction and Natural-Language Description of Nonparametric Regression Models[C]∥Twenty-Eighth AAAI Conference on Artificial Intelligence.AAAI Press,2014:1242-1250.
[58]TOBAR F,BUI T D,TURNER R E.Learning Stationary Time Series Using Gaussian Processes with Nonparametric Kernels[C]∥Advances in Neural Information Processing Systems 28(NIPS 2015).2015.
[59]HWANG Y,TONG A,CHOI J.Automatic Construction of Nonparametric Relational Regression Models for Multiple Time Series[C]∥International Conference on International Conference on Machine Learning.JMLR.org,2016:3030-3039.
[60]KUREMOTO T,KIMURA S,KOBAYASHI K,et al.Time Series Forecasting Using a Deep Belief Network with Restricted Boltzman Machines[J].Neurocomputing,2014,137(15):47-56.
[61]TURNER J T.Time Series Analysis Using Deep Feed Forward Neural Networks[D].Baltimore:University of Maryland,2014.
[62]ROMEU P,ZAMORA-MARTINEZ F,BOTELLA-ROCAMO-RA P,et al.Time-Series Forecasting of Indoor Temperature Using Pre-trained Deep Neural Networks[C]∥International Conference on Artificial Neural Networks.Berlin:Springer,2013:451-458.
[63]LV Y,DUAN Y,KANG W,et al.Traffic Flow Prediction with Big Data:A Deep Learning Approach[J].IEEE Transactions on Intelligent Transportation Systems,2015,16(2):865-873.
[64]LANGKVIST M,KARLSSON L,LOUTFI A.A Review of Unsupervised Feature Learning and Deep Learning for Time-Series Modeling[J].Pattern Recognition Letters,2014,42(1):11-24.
[65]GAMBOA J C B.Deep Learning for Time-Series Analysis[J].Arxiv:1701.01887,2017.
[66]HEATON J B,POLSON N G,WITTE J H.Deep Learning in Finance[J].Arxiv:1602.06561,2016.
[67]BOROVYKH A,BOHTE S,OOSTERLEE C W.Conditional Time Series Forecasting with Convolutional Neural Networks[J].Arxiv:1703.04691,2017.
[68]OORD A,DIELEMAN S,ZEN H,et al.Wavenet:A Generative Model for Raw Audio[J].Arxiv:1609.03499,2016.
[69]JAIN A,KUMAR A M.Hybrid Neural Network Models for Hydrologic Time Series Forecasting[J].Applied Soft Computing,2007,7(2):585-592.
[70]ZHANG G,PATUWO B E,HU M.Forecasting with Artificial Neural Networks:The State of The Art[J].International Journal of Forecasting,1998,14(1):35-62.
[71]ZHANG G.Time Series Forecasting Using a Hybrid ARIMAand Neural Network Model[J].Neurocomputing,2003,50(1):159-175.
[72]BINKOWSKI M,MARTI G,DONNAT P.Autoregressive Convolutional Neural Networks for Asynchronous Time Series[J].Arxiv:1703.04122,2017.
[73]GOEL H,MELNYK I,BANERJEE A.R2N2:Residual Recurrent Neural Networks for Multivariate Time Series Forecasting[J].Arxiv:1709.03159,2017.
[74]LAI G,CHANG W,YANG Y,et al.Modeling Long-And ShortTerm Temporal Patterns with Deep Neural Networks[J].Arxiv:1703.07015,2017.
[75]ANAVA O,HAZAN E,MANNOR S,et al.Online Learning for Time Series Prediction[J].Journal of Machine Learning Research,2013,30:172-184.
[76]SHWARTZ S S.Online Learning and Online Convex Optimization[J].Foundations and Trends in Machine Learning,2011,4(2):107-194.
[77]ZINKEVICH M.Online Convex Programming and Generalized Infinitesimal Gradient Ascent[C]∥Proceedings of the Twentieth International Conference on Machine Learning(ICML).2003:928-936.
[78]HAZAN E,AGARWAL A,KALE S.Logarithmic regret algorithms for online convex optimization[J].Machine Learning,2007,69(2-3):169-192.