Efficient learning in Boltzmann machines using linear response theory
Neural Computation
Independent component analysis: theory and applications
Independent component analysis: theory and applications
Neural Computation
Advances in Independent Component Analysis
Advances in Independent Component Analysis
Learning Overcomplete Representations
Neural Computation
Gaussian Processes for Classification: Mean-Field Algorithms
Neural Computation
Mean field theory for sigmoid belief networks
Journal of Artificial Intelligence Research
Analytical method for blind binary signal separation
IEEE Transactions on Signal Processing
The Problem of Sparse Image Coding
Journal of Mathematical Imaging and Vision
Variational learning of clusters of undercomplete nonsymmetric independent components
The Journal of Machine Learning Research
On the Effect of the Form of the Posterior Approximation in Variational Learning of ICA Models
Neural Processing Letters
On the Slow Convergence of EM and VBEM in Low-Noise Linear Models
Neural Computation
Expectation Consistent Approximate Inference
The Journal of Machine Learning Research
Variational learning for rectified factor analysis
Signal Processing
State-Space Models: From the EM Algorithm to a Gradient Approach
Neural Computation
Linear State-Space Models for Blind Source Separation
The Journal of Machine Learning Research
Building Blocks for Variational Bayesian Learning of Latent Variable Models
The Journal of Machine Learning Research
A parametric density model for blind source separation
Neural Processing Letters
Bayesian independent component analysis: Variational methods and non-negative decompositions
Digital Signal Processing
Variational and stochastic inference for Bayesian source separation
Digital Signal Processing
Blind separation of nonlinear mixtures by variational Bayesian learning
Digital Signal Processing
Separation capability of overcomplete ICA approaches
SIP'07 Proceedings of the 6th Conference on 6th WSEAS International Conference on Signal Processing - Volume 6
Bayesian Inference and Optimal Design for the Sparse Linear Model
The Journal of Machine Learning Research
Audio Watermark Detection Using Undetermined ICA
ICA '09 Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Image denoising by sparse code shrinkage
WiCOM'09 Proceedings of the 5th International Conference on Wireless communications, networking and mobile computing
Lattice independent component analysis for functional magnetic resonance imaging
Information Sciences: an International Journal
Lattice independent component analysis for mobile robot localization
HAIS'10 Proceedings of the 5th international conference on Hybrid Artificial Intelligence Systems - Volume Part II
A comparison of VBM results by SPM, ICA and LICA
HAIS'10 Proceedings of the 5th international conference on Hybrid Artificial Intelligence Systems - Volume Part II
Unsupervised learning of spatio-temporal primitives of emotional gait
PIT'06 Proceedings of the 2006 international tutorial and research conference on Perception and Interactive Technologies
Bayesian inference of latent causes in gene regulatory dynamics
LVA/ICA'12 Proceedings of the 10th international conference on Latent Variable Analysis and Signal Separation
Review: A review of novelty detection
Signal Processing
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We develop mean-field approaches for probabilistic independent component analysis (ICA). The sources are estimated from the mean of their posterior distribution and the mixing matrix (and noise level) is estimated by maximum a posteriori (MAP). The latter requires the computation Of (a good approximation to) the correlations between sources. For this purpose, we investigate three increasingly advanced mean-field methods: the variational (also known as naive mean field) approach, linear response corrections, and an adaptive version of the Thouless, Anderson and Palmer (1977) (TAP) mean-field approach, which is due to Opper and Winther (2001). The resulting algorithms are tested on a number of problems. On synthetic data, the advanced mean-field approaches are able to recover the correct mixing matrix in cases where the variational mean-field theory fails. For handwritten digits, sparse encoding is achieved using nonnegative source and mixing priors. For speech, the mean-field method is able to separate in the underdetermined (overcomplete) case of two sensors and three sources. One major advantage of the proposed method is its generality and algorithmic simplicity. Finally, we point out several possible extensions of the approaches developed here.