Nonparametric Automatic Differentiation Variational Inference with Spline Approximation
This provides a more flexible and easy-to-implement method for variational inference in machine learning, addressing limitations in handling complex posterior distributions, though it appears incremental as it builds on existing ADVI and nonparametric techniques.
The paper tackled the problem of approximating complex posterior distributions in probabilistic models by developing a spline-based nonparametric approach for Automatic Differentiation Variational Inference (ADVI), which improves flexibility for structures like skewness and multimodality. Experiments showed it efficiently approximates complex posteriors and enhances generative model performance with incomplete data.
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.