Differentiable annealed importance sampling (DAIS), proposed by Geffner & Domke (2021) and Zhang et al. (2021), allows optimizing, among others, over the initial distribution of AIS. In this paper, we show that, in the limit of many transitions, DAIS minimizes the symmetrized KL divergence (Jensen-Shannon divergence) between the initial and target distribution. Thus, DAIS can be seen as a form of variational inference (VI) in that 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 standard VI (optimizing the reverse KL divergence), importance weighted VI, and Markovian score climbing (optimizing the forward KL divergence).

翻译：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 的初始分布等进行优化。本文证明，在多次状态转移的极限情况下，DAIS 最小化初始分布与目标分布间的对称 KL 散度（Jensen-Shannon 散度）。因此，DAIS 可视为变分推断（VI）的一种形式，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，发现相较于标准 VI（优化反向 KL 散度）、重要性加权 VI 以及马尔可夫分数爬升法（优化前向 KL 散度），该分布通常能提供更准确的不确定性估计。