Automatic Differentiation Variational Inference (ADVI) is efficient in learning probabilistic models. Classic ADVI relies on the parametric approach to approximate the posterior. In this paper, we develop a spline-based nonparametric approximation approach that enables flexible posterior approximation for distributions with complicated structures, such as skewness, multimodality, and bounded support. Compared with widely-used nonparametric variational inference methods, the proposed method is easy to implement and adaptive to various data structures. By adopting the spline approximation, we derive a lower bound of the importance weighted autoencoder and establish the asymptotic consistency. Experiments demonstrate the efficiency of the proposed method in approximating complex posterior distributions and improving the performance of generative models with incomplete data.

翻译：自动微分变分推断（ADVI）在学习概率模型方面具有高效性。经典ADVI依赖参数化方法近似后验分布。本文提出一种基于样条的非参数逼近方法，能够灵活逼近具有复杂结构（如偏态、多峰性和有界支撑）的分布。与广泛使用的非参数变分推断方法相比，所提方法易于实现且能自适应多种数据结构。通过采用样条逼近，我们推导出重要性加权自编码器的下界并建立了渐近一致性。实验表明，所提方法在逼近复杂后验分布以及提升含不完整数据的生成模型性能方面具有高效性。