The paper introduces a "black box" variational inference algorithm that can be quickly applied to many models with minimal additional derivation. The method is based on stochastic optimization of the variational objective, where the noisy gradient is computed from Monte Carlo samples of the variational distribution. The authors develop techniques to reduce the variance of the gradient, including Rao-Blackwellization and control variates, while maintaining the goal of avoiding model-specific derivations. They evaluate their method against sampling-based methods and demonstrate that it reaches better predictive likelihoods faster. The method is also shown to enable easy exploration of a wide range of models, as demonstrated through applications to longitudinal healthcare data. The paper includes extensions to adaptive learning rates and stochastic optimization in hierarchical Bayesian models, and provides empirical results to support the effectiveness of the proposed approach.The paper introduces a "black box" variational inference algorithm that can be quickly applied to many models with minimal additional derivation. The method is based on stochastic optimization of the variational objective, where the noisy gradient is computed from Monte Carlo samples of the variational distribution. The authors develop techniques to reduce the variance of the gradient, including Rao-Blackwellization and control variates, while maintaining the goal of avoiding model-specific derivations. They evaluate their method against sampling-based methods and demonstrate that it reaches better predictive likelihoods faster. The method is also shown to enable easy exploration of a wide range of models, as demonstrated through applications to longitudinal healthcare data. The paper includes extensions to adaptive learning rates and stochastic optimization in hierarchical Bayesian models, and provides empirical results to support the effectiveness of the proposed approach.