  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.
