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
Source separation in post-nonlinear mixtures
IEEE Transactions on Signal Processing
Blind separation of mixture of independent sources through aquasi-maximum likelihood approach
IEEE Transactions on Signal Processing
Learning Deep Architectures for AI
Foundations and Trends® in Machine Learning
Gamma Markov random fields for audio source modeling
IEEE Transactions on Audio, Speech, and Language Processing
Interpretation and generalization of score matching
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
A two-layer model of natural stimuli estimated with score matching
Neural Computation
Phase coupling estimation from multivariate phase statistics
Neural Computation
A connection between score matching and denoising autoencoders
Neural Computation
Selecting β-divergence for nonnegative matrix factorization by score matching
ICANN'12 Proceedings of the 22nd international conference on Artificial Neural Networks and Machine Learning - Volume Part II
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Many probabilistic models are only defined up to a normalization constant. This makes maximum likelihood estimation of the model parameters very difficult. Typically, one then has to resort to Markov Chain Monte Carlo methods, or approximations of the normalization constant. Previously, a method called score matching was proposed for computationally efficient yet (locally) consistent estimation of such models. The basic form of score matching is valid, however, only for models which define a differentiable probability density function over R^n. Therefore, some extensions of the framework are proposed. First, a related method for binary variables is proposed. Second, it is shown how to estimate non-normalized models defined in the non-negative real domain, i.e. R"+^n. As a further result, it is shown that the score matching estimator can be obtained in closed form for some exponential families.