Hierarchical Importance Weighted Autoencoders
This work addresses variance reduction in variational inference for machine learning practitioners, presenting an incremental improvement over existing methods.
The paper tackles the problem of reducing variance in importance weighted variational inference by introducing a hierarchical structure to induce correlation among samples, which theoretically connects estimator variance convergence to lower bound convergence and empirically shows that maximizing the lower bound implicitly minimizes variance, leading to improved inference performance as sample count increases.
Importance weighted variational inference (Burda et al., 2015) uses multiple i.i.d. samples to have a tighter variational lower bound. We believe a joint proposal has the potential of reducing the number of redundant samples, and introduce a hierarchical structure to induce correlation. The hope is that the proposals would coordinate to make up for the error made by one another to reduce the variance of the importance estimator. Theoretically, we analyze the condition under which convergence of the estimator variance can be connected to convergence of the lower bound. Empirically, we confirm that maximization of the lower bound does implicitly minimize variance. Further analysis shows that this is a result of negative correlation induced by the proposed hierarchical meta sampling scheme, and performance of inference also improves when the number of samples increases.