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.

我们提出了一种基于样条的非参数逼近方法，可以灵活逼近具有复杂结构的后验分布，如偏度、多峰性和有界支持。通过采用样条逼近，我们得到了重要性加权自编码器的下界，并建立了渐近一致性。实验证明了该方法在逼近复杂的后验分布和提高具有不完整数据的生成模型性能方面的高效性。

非参数自动微分变分推断与样条逼近