Implicitly adaptive optimal proposal in variational inference for Bayesian learning

Overdispersed black-box variational inference uses importance sampling to decrease the variance of the Monte Carlo gradient in variational inference. This is achieved by using an overdispersed proposal distribution that belongs to the same exponential family as the variational distribution. This paper seeks to dynamically improve this proposal distribution during the learning process using implicit adaptive importance sampling. This method involves matching the moments of the Monte Carlo samples to those of the theoretical optimal proposal distribution by applying an affine transformation on the samples. Furthermore, our approach will incorporate the implicit reparameterization method to further mitigate the variance of the gradients. We run our method to Bayesian logistic regression for binary classification and Bayesian multinomial logistic regression for multiclass classification on several datasets. Our experimental results show that our method outperforms several existing importance sampling methods.