The rectified Gaussian distribution
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
Variational learning in nonlinear Gaussian belief networks
Neural Computation
An introduction to variational methods for graphical models
Learning in graphical models
Mean-field approaches to independent component analysis
Neural Computation
Learning from Incomplete Data
Sequential EM learning for subspace analysis
Pattern Recognition Letters
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Beyond independent components: trees and clusters
The Journal of Machine Learning Research
The Journal of Machine Learning Research
A "nonnegative PCA" algorithm for independent component analysis
IEEE Transactions on Neural Networks
Variational learning and bits-back coding: an information-theoretic view to Bayesian learning
IEEE Transactions on Neural Networks
Building Blocks for Variational Bayesian Learning of Latent Variable Models
The Journal of Machine Learning Research
A note on variational Bayesian factor analysis
Neural Networks
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Linear factor models with non-negativity constraints have received a great deal of interest in a number of problem domains. In existing approaches, positivity has often been associated with sparsity. In this paper we argue that sparsity of the factors is not always a desirable option, but certainly a technical limitation of the currently existing solutions. We then reformulate the problem in order to relax the sparsity constraint while retaining positivity. This is achieved by employing a rectification nonlinearity rather than a positively supported prior directly on the latent space. A variational learning procedure is derived for the proposed model and this is contrasted to existing related approaches. Both i.i.d. and first-order AR variants of the proposed model are provided and they are experimentally demonstrated with artificial data. Application to the analysis of galaxy spectra show the benefits of the method in a real-world astrophysical problem, where the existing approach is not a viable alternative.