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Efficient bounds for the Softmax and applications to approximate inference in hybrid models

Guillaume Bouchard
The softmax link is used in many probabilistic model dealing with both discrete and continuous data. However, efficient Bayesian inference for this type of model is till an open problem due to the lack of efficient upper bound for the sum of exponentials. We propose three different bounds for this function and study their approximation properties. We give a direct application to the Bayesian treatment of multiclass logistic regression and discuss its generalization to deterministic approximate inference in hybrid probabilistic graphical models
NIPS 2007 Neural Information Processing Systems Conference, Whistler, Canada, December 7-8, 2007