Approximations of Gaussian Process Uncertainties for Visual Recognition Problems

Gaussian processes offer the advantage of calculating the classification uncertainty in terms of predictive variance associated with the classification result. This is especially useful to select informative samples in active learning and to spot samples of previously unseen classes known as novelty detection. However, the Gaussian process framework suffers from high computational complexity leading to computation times too large for practical applications. Hence, we propose an approximation of the Gaussian process predictive variance leading to rigorous speedups. The complexity of both learning and testing the classification model regarding computational time and memory demand decreases by one order with respect to the number of training samples involved. The benefits of our approximations are verified in experimental evaluations for novelty detection and active learning of visual object categories on the datasets C-Pascal of Pascal VOC 2008, Caltech-256, and ImageNet.

[1]  M. Overton.  On minimizing the maximum eigenvalue of a symmetric matrix , 1988 .

[2]  Radford M. Neal.  Pattern Recognition and Machine Learning , 2007, Technometrics.

[3]  Bernt Schiele,et al.  Extracting Structures in Image Collections for Object Recognition , 2010, ECCV.

[4]  Bernhard Schölkopf,et al.  Estimating the Support of a High-Dimensional Distribution , 2001, Neural Computation.

[5]  Thomas Deselaers,et al.  ClassCut for Unsupervised Class Segmentation , 2010, ECCV.

[6]  Carl E. Rasmussen,et al.  A Unifying View of Sparse Approximate Gaussian Process Regression , 2005, J. Mach. Learn. Res..

[7]  Chandan Srivastava,et al.  Support Vector Data Description , 2011 .

[8]  Zoubin Ghahramani,et al.  Sparse Gaussian Processes using Pseudo-inputs , 2005, NIPS.

[9]  Joachim Denzler,et al.  Rapid Uncertainty Computation with Gaussian Processes and Histogram Intersection Kernels , 2012, ACCV.

[10]  Carl E. Rasmussen,et al.  Gaussian Processes for Machine Learning (GPML) Toolbox , 2010, J. Mach. Learn. Res..

[11]  Trevor Darrell,et al.  Gaussian Processes for Object Categorization , 2010, International Journal of Computer Vision.

[12]  Francesca Odone,et al.  Histogram intersection kernel for image classification , 2003, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429).

[13]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[14]  Joachim Denzler,et al.  Large-Scale Gaussian Process Classification with Flexible Adaptive Histogram Kernels , 2012, ECCV.

[15]  C. V. Jawahar,et al.  Generalized RBF feature maps for Efficient Detection , 2010, BMVC.

[16]  Kok Lay Teo,et al.  Smooth Convex Approximation to the Maximum Eigenvalue Function , 2004, J. Glob. Optim..

[17]  Vittorio Ferrari,et al.  Appearance Sharing for Collective Human Pose Estimation , 2012, ACCV.

[18]  Matthieu Guillaumin,et al.  Segmentation Propagation in ImageNet , 2012, ECCV.

[19]  Joachim Denzler,et al.  An Efficient Approximation for Gaussian Process Regression , 2013 .

[20]  G. Griffin,et al.  Caltech-256 Object Category Dataset , 2007 .

[21]  C. Rasmussen,et al.  Approximations for Binary Gaussian Process Classification , 2008 .

[22]  Joachim Denzler,et al.  One-class classification with Gaussian processes , 2013, Pattern Recognit..

[23]  Li Fei-Fei,et al.  ImageNet: A large-scale hierarchical image database , 2009, CVPR.

[24]  Radim Sára,et al.  A Weak Structure Model for Regular Pattern Recognition Applied to Facade Images , 2010, ACCV.