Stochastic Variational Inference via Upper Bound
This work addresses the need for more efficient and accurate variational inference methods in Bayesian deep learning, representing an incremental improvement over existing approaches.
The authors tackled the problem of designing a tighter surrogate loss for stochastic variational inference in Bayesian deep learning by introducing an evidence upper bound (EUBO), which outperformed previous methods in simulation studies and achieved state-of-the-art results for Bayesian neural networks.
Stochastic variational inference (SVI) plays a key role in Bayesian deep learning. Recently various divergences have been proposed to design the surrogate loss for variational inference. We present a simple upper bound of the evidence as the surrogate loss. This evidence upper bound (EUBO) equals to the log marginal likelihood plus the KL-divergence between the posterior and the proposal. We show that the proposed EUBO is tighter than previous upper bounds introduced by $χ$-divergence or $α$-divergence. To facilitate scalable inference, we present the numerical approximation of the gradient of the EUBO and apply the SGD algorithm to optimize the variational parameters iteratively. Simulation study with Bayesian logistic regression shows that the upper and lower bounds well sandwich the evidence and the proposed upper bound is favorably tight. For Bayesian neural network, the proposed EUBO-VI algorithm outperforms state-of-the-art results for various examples.