Scalable and Incremental Learning of Gaussian Mixture Models

This work presents a fast and scalable algorithm for incremental learning of Gaussian mixture models. By performing rank-one updates on its precision matrices and determinants, its asymptotic time complexity is of \BigO{NKD^2} for $N$ data points, $K$ Gaussian components and $D$ dimensions. The resulting algorithm can be applied to high dimensional tasks, and this is confirmed by applying it to the classification datasets MNIST and CIFAR-10. Additionally, in order to show the algorithm's applicability to function approximation and control tasks, it is applied to three reinforcement learning tasks and its data-efficiency is evaluated.

[1]  Nitish Srivastava,et al.  Improving neural networks by preventing co-adaptation of feature detectors , 2012, ArXiv.

[2]  Stephen Grossberg,et al.  Competitive Learning: From Interactive Activation to Adaptive Resonance , 1987, Cogn. Sci..

[3]  Paulo Martins Engel,et al.  Dealing with continuous-state reinforcement learning for intelligent control of traffic signals , 2011, 2011 14th International IEEE Conference on Intelligent Transportation Systems (ITSC).

[4]  Rafael C. Pinto,et al.  Echo State Incremental Gaussian Mixture Network for Spatio-Temporal Pattern Processing , 2011 .

[5]  François Le Gall,et al.  Powers of tensors and fast matrix multiplication , 2014, ISSAC.

[6]  François Fleuret,et al.  Jointly Informative Feature Selection , 2014, AISTATS.

[7]  José Santos-Victor,et al.  An online algorithm for simultaneously learning forward and inverse kinematics , 2012, 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[8]  Rafael C. Pinto,et al.  Recursive Incremental Gaussian Mixture Network For Spatio-Temporal Pattern Processing , 2016 .

[9]  Paulo Martins Engel,et al.  IGMN: An incremental connectionist approach for concept formation, reinforcement learning and robotics , 2011 .

[10]  Paulo Martins Engel,et al.  Learning Abstract Behaviors with the Hierarchical Incremental Gaussian Mixture Network , 2012, 2012 Brazilian Symposium on Neural Networks.

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

[12]  Leandro Krug Wives,et al.  Location-Based Events Detection on Micro-Blogs , 2012, ArXiv.

[13]  Joao Henrique F. Flores,et al.  Autocorrelation and partial autocorrelation functions to improve neural networks models on univariate time series forecasting , 2012, The 2012 International Joint Conference on Neural Networks (IJCNN).

[14]  Marc Schlipsing,et al.  Efficient update of the covariance matrix inverse in iterated linear discriminant analysis , 2010, Pattern Recognit. Lett..

[15]  Peder A. Olsen,et al.  Extended MLLT for Gaussian Mixture Models , 2001 .

[16]  Yoshua Bengio,et al.  Gradient-based learning applied to document recognition , 1998, Proc. IEEE.

[17]  Pinto Rafael.  Experiment Data for "A Fast Incremental Gaussian Mixture Model" , 2015 .

[18]  Paulo Martins Engel,et al.  One-shot learning in the road sign problem , 2012, The 2012 International Joint Conference on Neural Networks (IJCNN).

[19]  Paulo Martins Engel,et al.  A Fast Incremental Gaussian Mixture Model , 2015, PloS one.

[20]  Paulo Martins Engel.  INBC : an incremental algorithm for dataflow segmentation based on a probabilistic approach , 2009 .

[21]  D. Harville.  Matrix Algebra From a Statistician's Perspective , 1998 .

[22]  Paulo Martins Engel,et al.  Using a Gaussian mixture neural network for incremental learning and robotics , 2012, The 2012 International Joint Conference on Neural Networks (IJCNN).

[23]  James L. McClelland.  Parallel Distributed Processing , 2005 .

[24]  Tom Schaul,et al.  Dueling Network Architectures for Deep Reinforcement Learning , 2015, ICML.

[25]  Alex Krizhevsky,et al.  Learning Multiple Layers of Features from Tiny Images , 2009 .

[26]  H. Robbins.  A Stochastic Approximation Method , 1951 .

[27]  J. Sherman,et al.  Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix , 1950 .

[28]  Paulo Martins Engel,et al.  IGMN : An Incremental Gaussian Mixture Network that Learns Instantaneously from Data Flows , 2011 .

[29]  Ian H. Witten,et al.  The WEKA data mining software: an update , 2009, SKDD.

[30]  Sergey Levine,et al.  Trust Region Policy Optimization , 2015, ICML.

[31]  Milton Roberto Heinen,et al.  A connectionist approach for incremental function approximation and on-line tasks , 2011 .

[32]  Michael I. Jordan,et al.  Supervised learning from incomplete data via an EM approach , 1993, NIPS.

[33]  Paulo Martins Engel,et al.  Incremental Learning of Multivariate Gaussian Mixture Models , 2010, SBIA.