Incorporating temporal smoothness and group structure in learning with incomplete data

Learning with incomplete data remains challenging in many real-world applications especially when the data is high-dimensional and dynamic. Many imputation based algorithms have been proposed to handle with incomplete data, where these algorithms use statistics of the historical information to remedy the missing parts. However, these methods merely use the structural information existed in the data, which are very helpful for sharing between the complete entries and the missing ones. For example, in traffic system, some group information and temporal smoothness exist in the data structure. In this paper, we propose to incorporate these structural information and develop a Structural Feature Leaning method for learning with InComplete data (SFLIC). The SFLIC model adopts a fused Lasso based regularizer and a group Lasso style regularizer to enlarge the data sharing along both the temporal smoothness level and the feature group level to fill the gap where the data entries are missing. The proposed SFLIC model is non-smooth function according to the model parameters, and we adopt the smoothing proximal gradient (SPG) method to seek for an efficient solution. We evaluate our model on both synthetic and real-world highway traffic datasets. Experimental results show that our method outperforms the state-of-the-art methods.

[1]  Yurii Nesterov,et al.  Smooth minimization of non-smooth functions , 2005, Math. Program..

[2]  Phil D. Green,et al.  Missing data techniques for robust speech recognition , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[3]  G. McLachlan,et al.  The EM algorithm and extensions , 1996 .

[4]  M. Yuan,et al.  Model selection and estimation in regression with grouped variables , 2006 .

[5]  T. Schneider Analysis of Incomplete Climate Data: Estimation of Mean Values and Covariance Matrices and Imputation of Missing Values. , 2001 .

[6]  Yi Zhang,et al.  PPCA-Based Missing Data Imputation for Traffic Flow Volume: A Systematical Approach , 2009, IEEE Transactions on Intelligent Transportation Systems.

[7]  Li Li,et al.  Efficient missing data imputing for traffic flow by considering temporal and spatial dependence , 2013 .

[8]  Roderick J. A. Little,et al.  Statistical Analysis with Missing Data: Little/Statistical Analysis with Missing Data , 2002 .

[9]  Wooi-Boon Goh,et al.  A new spatio-temporal MRF model for the detection of missing data in image sequences , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[10]  Trevor Hastie,et al.  Imputing Missing Data for Gene Expression Arrays , 2001 .

[11]  Lei Han,et al.  Overlapping decomposition for causal graphical modeling , 2012, KDD.

[12]  Jieping Ye,et al.  Feature grouping and selection over an undirected graph , 2012, KDD.

[13]  D. Rubin,et al.  Statistical Analysis with Missing Data , 1988 .

[14]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[15]  Xi Chen,et al.  Smoothing proximal gradient method for general structured sparse regression , 2010, The Annals of Applied Statistics.

[16]  R. Tibshirani Regression Shrinkage and Selection via the Lasso , 1996 .

[17]  Jaume Barceló,et al.  A Kalman Filter Approach for the Estimation of Time Dependent OD Matrices Exploiting Bluetooth Traffic Data Collection , 2012 .

[18]  Seung-Jae Lee,et al.  Dynamic OD Estimation Using Three Phase Traffic Flow Theory , 2011 .

[19]  Angshuman Guin,et al.  Multiple Imputation Scheme for Overcoming the Missing Values and Variability Issues in ITS Data , 2005 .

[20]  Paul M. Thompson,et al.  Multi-source learning with block-wise missing data for Alzheimer's disease prediction , 2013, KDD.

[21]  Lynne E. Parker,et al.  Nearest neighbor imputation using spatial-temporal correlations in wireless sensor networks , 2014, Inf. Fusion.