Sequential Monte Carlo for Inclusive KL Minimization in Amortized Variational Inference
This work addresses a bottleneck in variational inference for probabilistic modeling, offering an incremental improvement over prior methods by reducing bias and improving approximation accuracy.
The paper tackles the challenge of minimizing the inclusive KL divergence in amortized variational inference, which is difficult due to biased gradients and concentrated distributions in existing methods like Reweighted Wake-Sleep. The proposed SMC-Wake method uses sequential Monte Carlo samplers to provide asymptotically unbiased gradient estimators, resulting in more accurate posterior approximations in experiments with simulated and real datasets.
For training an encoder network to perform amortized variational inference, the Kullback-Leibler (KL) divergence from the exact posterior to its approximation, known as the inclusive or forward KL, is an increasingly popular choice of variational objective due to the mass-covering property of its minimizer. However, minimizing this objective is challenging. A popular existing approach, Reweighted Wake-Sleep (RWS), suffers from heavily biased gradients and a circular pathology that results in highly concentrated variational distributions. As an alternative, we propose SMC-Wake, a procedure for fitting an amortized variational approximation that uses likelihood-tempered sequential Monte Carlo samplers to estimate the gradient of the inclusive KL divergence. We propose three gradient estimators, all of which are asymptotically unbiased in the number of iterations and two of which are strongly consistent. Our method interleaves stochastic gradient updates, SMC samplers, and iterative improvement to an estimate of the normalizing constant to reduce bias from self-normalization. In experiments with both simulated and real datasets, SMC-Wake fits variational distributions that approximate the posterior more accurately than existing methods.