Nonparametric Automatic Differentiation Variational Inference with Spline Approximation

Variational Inference (VI) is widely used in data representation (Kingma and Welling, 2013; Zhang et al., 2018), graphical models (Wainwright et al., 2008), among others. VI approximates intractable distributions by minimizing the divergence between the true posterior and a chosen distribution family, aiming to identify an optimal distribution within this family. Unlike methods like Markov chain Monte Carlo (MCMC) sampling, VI is recognized for its computational efficiency and explicit distribution form (Blei et al., 2017). Contemporary VI-based methods such as variational autoencoder (VAE) (Kingma and Welling, 2013) have garnered interest for learning representations of complex, high-dimensional data across fields like bioinformatics (Kopf et al., 2021), geoscience (Chen et al., 2022), and finance (Bergeron et al., 2022). Automatic Differentiation Variational Inference (ADVI) (Kucukelbir et al., 2017) is a popular approach to derive variational inference algorithms for complex probabilistic models.