Predictive inference uses a model to analyze a dataset and make predictions about new observations. When a model does not match the data, predictive accuracy suffers. To miti-gate this effect, we develop the profile predic-tive, a predictive density that incorporates the population distribution of data into Bayesian inference. This leads to a practical method for reducing the effect of model mismatch. We extend this method into variational infer-ence and propose a stochastic optimization algorithm, called bumping variational infer-ence (bump-vi). We demonstrate improved predictive accuracy over classical variational inference in two models: a Bayesian mixture model of image histograms and a latent Dirich-let allocation topic model of a text corpus. 1