Differentiable Annealed Importance Sampling Minimizes The Symmetrized Kullback-Leibler Divergence Between Initial and Target Distribution
This work addresses the challenge of improving variational inference for intractable target distributions, offering a novel approach with better uncertainty estimation, though it builds incrementally on prior DAIS methods.
The paper tackles the problem of optimizing the initial distribution in differentiable annealed importance sampling (DAIS) and shows that it minimizes the symmetrized Kullback-Leibler divergence between initial and target distributions, enabling it to serve as a variational inference method. Empirically, it provides more accurate uncertainty estimates than existing methods on synthetic and real-world data.
Differentiable annealed importance sampling (DAIS), proposed by Geffner & Domke (2021) and Zhang et al. (2021), allows optimizing over the initial distribution of AIS. In this paper, we show that, in the limit of many transitions, DAIS minimizes the symmetrized Kullback-Leibler divergence between the initial and target distribution. Thus, DAIS can be seen as a form of variational inference (VI) as its initial distribution is a parametric fit to an intractable target distribution. We empirically evaluate the usefulness of the initial distribution as a variational distribution on synthetic and real-world data, observing that it often provides more accurate uncertainty estimates than VI (optimizing the reverse KL divergence), importance weighted VI, and Markovian score climbing (optimizing the forward KL divergence).