Online inference for time-varying temporal dependency discovery from time series

Large-scale time series data are prevalent across diverse application domains including system management, biomedical informatics, social networks, finance, etc. Temporal dependency discovery performs an essential part to identify the hidden interactions among the observed time series and helps to gain more insight into the behavior of the applications. However, the time-varying sparsity of the interactions among time series often poses a big challenge to temporal dependency discovery in practice. This paper formulates the temporal dependency problem with a novel Bayesian model allowing for both the sparsity and evolution of the hidden interactions among the observed time series. Taking advantage of the Bayesian modeling, an online inference method is proposed for time-varying temporal dependency discovery. Extensive empirical studies on both the synthetic and real application time series data are conducted to demonstrate the effectiveness and the efficiency of the proposed method.

[1]  Andrew P. Bradley,et al.  The use of the area under the ROC curve in the evaluation of machine learning algorithms , 1997, Pattern Recognit..

[2]  Le Song,et al.  Time-Varying Dynamic Bayesian Networks , 2009, NIPS.

[3]  Nicholas G. Polson,et al.  Particle Filtering , 2006 .

[4]  Andrew Harvey,et al.  Forecasting, Structural Time Series Models and the Kalman Filter , 1990 .

[5]  Yan Liu,et al.  FBLG: a simple and effective approach for temporal dependence discovery from time series data , 2014, KDD.

[6]  G. Casella,et al.  The Bayesian Lasso , 2008 .

[7]  Nando de Freitas,et al.  Sequential Monte Carlo Methods in Practice , 2001, Statistics for Engineering and Information Science.

[8]  Timothy J. Robinson,et al.  Sequential Monte Carlo Methods in Practice , 2003 .

[9]  B. Ripley,et al.  Pattern Recognition , 1968, Nature.

[10]  渡辺 亮平,et al.  Sequential Monte Carlo , 2005, Nonlinear Time Series Analysis.

[11]  Stuart J. Russell,et al.  Dynamic bayesian networks: representation, inference and learning , 2002 .

[12]  Freda Kemp,et al.  An Introduction to Sequential Monte Carlo Methods , 2003 .

[13]  Jianfeng Feng,et al.  Granger causality vs. dynamic Bayesian network inference: a comparative study , 2009, BMC Bioinformatics.

[14]  Bruno Carpentieri,et al.  Sparse pattern selection strategies for robust Frobenius-norm minimization preconditioners in electromagnetism , 2000 .

[15]  Ming Lei,et al.  FIU-Miner: a fast, integrated, and user-friendly system for data mining in distributed environment , 2013, KDD.

[16]  Liang Tang,et al.  Mining temporal lag from fluctuating events for correlation and root cause analysis , 2014, 10th International Conference on Network and Service Management (CNSM) and Workshop.

[17]  Jian Xu,et al.  Real time contextual collective anomaly detection over multiple data streams , 2014 .

[18]  Robert P. W. Duin,et al.  A simplified extension of the Area under the ROC to the multiclass domain , 2006 .

[19]  Simon J. Godsill,et al.  On sequential Monte Carlo sampling methods for Bayesian filtering , 2000, Stat. Comput..

[20]  M. Gerstein,et al.  A Bayesian Networks Approach for Predicting Protein-Protein Interactions from Genomic Data , 2003, Science.

[21]  Jianpeng Xu,et al.  ORION: Online Regularized Multi-task Regression and Its Application to Ensemble Forecasting , 2014, 2014 IEEE International Conference on Data Mining.

[22]  Yan Liu,et al.  An Examination of Practical Granger Causality Inference , 2013, SDM.

[23]  Nicholas G. Polson,et al.  Particle Learning and Smoothing , 2010, 1011.1098.

[24]  C. Granger.  Investigating causal relations by econometric models and cross-spectral methods , 1969 .

[25]  Yan Liu,et al.  On Causality Inference in Time Series , 2012, AAAI Fall Symposium: Discovery Informatics.

[26]  Yan Liu,et al.  Learning dynamic temporal graphs for oil-production equipment monitoring system , 2009, KDD.

[27]  Nando de Freitas,et al.  An Introduction to Sequential Monte Carlo Methods , 2001, Sequential Monte Carlo Methods in Practice.

[28]  C. Granger.  Testing for causality: a personal viewpoint , 1980 .

[29]  David Heckerman,et al.  A Tutorial on Learning with Bayesian Networks , 1999, Innovations in Bayesian Networks.

[30]  Yan Liu,et al.  Temporal causal modeling with graphical granger methods , 2007, KDD '07.

[31]  Qing Wang,et al.  Online Context-Aware Recommendation with Time Varying Multi-Armed Bandit , 2016, KDD.

[32]  C. Granger.  Testing for causality: a personal viewpoint , 1980 .

[33]  M. Eichler.  GRAPHICAL MODELLING OF MULTIVARIATE TIME SERIES WITH LATENT VARIABLES , 2006 .