The Variational Predictive Natural Gradient

Variational inference requires choosing an approximating Variational inference transforms posterior inference family. The variational family plus the model together define into parametric optimization thereby enabling the variational objective. The variational objective can the use of latent variable models where be optimized with stochastic gradients for a broad range of otherwise impractical. However, variational inference models (Kingma & Welling, 2014; Ranganath et al., 2014; can be finicky when different variational Rezende et al., 2014). When the posterior has correlations, parameters control variables that are strongly correlated dimensions of the optimization problem become tied, i.e., under the model. Traditional natural gradients there is curvature. One way to correct for curvature in optimization based on the variational approximation fail to is to use natural gradients (Amari, 1998; Ollivier correct for correlations when the approximation et al., 2011; Thomas et al., 2016) . Natural gradients for is not the true posterior. To address this, we construct variational inference (Hoffman et al., 2013) adjust for the a new natural gradient called the variational non-Euclidean nature of probability distributions.