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).

翻译：由Geffner & Domke (2021) 与 Zhang 等人 (2021) 提出的可微退火重要性采样（DAIS）允许对AIS的初始分布进行优化。本文证明，在多次状态转移的极限情况下，DAIS能够最小化初始分布与目标分布之间的对称Kullback-Leibler散度。因此，DAIS可被视为变分推断（VI）的一种形式，因为其初始分布是对难处理目标分布的参数化拟合。我们在合成数据与真实数据上实证评估了该初始分布作为变分分布的有效性，发现其通常能比VI（优化反向KL散度）、重要性加权VI以及马尔可夫得分爬升（优化前向KL散度）提供更准确的不确定性估计。