An Introduction to Variational Methods for Graphical Models
Machine Learning
Mean-field approaches to independent component analysis
Neural Computation
Information Theory, Inference & Learning Algorithms
Information Theory, Inference & Learning Algorithms
On the Slow Convergence of EM and VBEM in Low-Noise Linear Models
Neural Computation
A Variational Method for Learning Sparse and Overcomplete Representations
Neural Computation
Gaussian Processes for Classification: Mean-Field Algorithms
Neural Computation
Expectation Consistent Approximate Inference
The Journal of Machine Learning Research
State-Space Models: From the EM Algorithm to a Gradient Approach
Neural Computation
Bayesian independent component analysis: Variational methods and non-negative decompositions
Digital Signal Processing
Fast and robust fixed-point algorithms for independent component analysis
IEEE Transactions on Neural Networks
Bayesian independent component analysis: Variational methods and non-negative decompositions
Digital Signal Processing
Variational and stochastic inference for Bayesian source separation
Digital Signal Processing
Expert Systems with Applications: An International Journal
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In this paper we present an empirical Bayes method for flexible and efficient independent component analysis (ICA). The method is flexible with respect to choice of source prior, dimensionality and constraints of the mixing matrix (unconstrained or non-negativity), and structure of the noise covariance matrix. Parameter optimization is handled by variants of the expectation maximization (EM) algorithm: overrelaxed adaptive EM and the easy gradient recipe. These retain the simplicity of EM while converging faster. The required expectations over the source posterior, the sufficient statistics, are estimated with mean field methods: variational and the expectation consistent (EC) framework. We describe the derivation of the EC framework for ICA in detail and give empirical results demonstrating the improved performance. The paper is accompanied by the publicly available Matlab toolbox icaMF.