Hierarchical mixtures of experts and the EM algorithm
Neural Computation
Neural Computation
Multiple paired forward and inverse models for motor control
Neural Networks - Special issue on neural control and robotics: biology and technology
Training products of experts by minimizing contrastive divergence
Neural Computation
Robust blind source separation by beta divergence
Neural Computation
Divergence function, duality, and convex analysis
Neural Computation
Information geometry of U-Boost and Bregman divergence
Neural Computation
Stochastic reasoning, free energy, and information geometry
Neural Computation
Means of Positive Numbers and Matrices
SIAM Journal on Matrix Analysis and Applications
The α-EM algorithm: surrogate likelihood maximization using α-logarithmic information measures
IEEE Transactions on Information Theory
IEEE Transactions on Neural Networks
Non-negative matrix factorization with α-divergence
Pattern Recognition Letters
α-Gaussian mixture modelling for speaker recognition
Pattern Recognition Letters
Parameter estimation for α-gmm based on maximum likelihood criterion
Neural Computation
Sided and symmetrized Bregman centroids
IEEE Transactions on Information Theory
α-divergence is unique, belonging to both f-divergence and Bregman divergence classes
IEEE Transactions on Information Theory
PRICAI'10 Proceedings of the 11th Pacific Rim international conference on Trends in artificial intelligence
A generalization of independence in naive bayes model
IDEAL'10 Proceedings of the 11th international conference on Intelligent data engineering and automated learning
An estimation of generalized bradley-terry models based on the em algorithm
Neural Computation
Unsupervised Weight Parameter Estimation Method for Ensemble Learning
Journal of Mathematical Modelling and Algorithms
Sequential spectral learning to hash with multiple representations
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part V
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When there are a number of stochastic models in the form of probability distributions, one needs to integrate them. Mixtures of distributions are frequently used, but exponential mixtures also provide a good means of integration. This letter proposes a one-parameter family of integration, called α-integration, which includes all of these well-known integrations. These are generalizations of various averages of numbers such as arithmetic, geometric, and harmonic averages. There are psychophysical experiments that suggest that α-integrations are used in the brain. The α-divergence between two distributions is defined, which is a natural generalization of Kullback-Leibler divergence and Hellinger distance, and it is proved that α-integration is optimal in the sense of minimizing α-divergence. The theory is applied to generalize the mixture of experts and the product of experts to the α-mixture of experts. The α-predictive distribution is also stated in the Bayesian framework.