Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
Training products of experts by minimizing contrastive divergence
Neural Computation
Estimation of Non-Normalized Statistical Models by Score Matching
The Journal of Machine Learning Research
Topographic Product Models Applied to Natural Scene Statistics
Neural Computation
Topographic Independent Component Analysis
Neural Computation
Some extensions of score matching
Computational Statistics & Data Analysis
A two-layer ICA-like model estimated by score matching
ICANN'07 Proceedings of the 17th international conference on Artificial neural networks
IEEE Transactions on Neural Networks
The Journal of Machine Learning Research
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We consider a hierarchical two-layer model of natural signals in which both layers are learned from the data. Estimation is accomplished by score matching, a recently proposed estimation principle for energy-based models. If the first-layer outputs are squared and the second-layer weights are constrained to be nonnegative, the model learns responses similar to complex cells in primary visual cortex from natural images. The second layer pools a small number of features with similar orientation and frequency, but differing in spatial phase. For speech data, we obtain analogous results. The model unifies previous extensions to independent component analysis such as subspace and topographic models and provides new evidence that localized, oriented, phase-invariant features reflect the statistical properties of natural image patches.