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The Generalized Reparameterization Gradient
Francisco Ruiz · Michalis Titsias · David Blei

Tue Dec 06 09:00 AM -- 12:30 PM (PST) @ Area 5+6+7+8 #149 #None

The reparameterization gradient has become a widely used method to obtain Monte Carlo gradients to optimize the variational objective. However, this technique does not easily apply to commonly used distributions such as beta or gamma without further approximations, and most practical applications of the reparameterization gradient fit Gaussian distributions. In this paper, we introduce the generalized reparameterization gradient, a method that extends the reparameterization gradient to a wider class of variational distributions. Generalized reparameterizations use invertible transformations of the latent variables which lead to transformed distributions that weakly depend on the variational parameters. This results in new Monte Carlo gradients that combine reparameterization gradients and score function gradients. We demonstrate our approach on variational inference for two complex probabilistic models. The generalized reparameterization is effective: even a single sample from the variational distribution is enough to obtain a low-variance gradient.

Author Information

Francisco Ruiz (Columbia University)
Michalis Titsias (DeepMind)
David Blei (Columbia University)

David Blei is a Professor of Statistics and Computer Science at Columbia University, and a member of the Columbia Data Science Institute. His research is in statistical machine learning, involving probabilistic topic models, Bayesian nonparametric methods, and approximate posterior inference algorithms for massive data. He works on a variety of applications, including text, images, music, social networks, user behavior, and scientific data. David has received several awards for his research, including a Sloan Fellowship (2010), Office of Naval Research Young Investigator Award (2011), Presidential Early Career Award for Scientists and Engineers (2011), Blavatnik Faculty Award (2013), and ACM-Infosys Foundation Award (2013). He is a fellow of the ACM.

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