2019/04/15 by Marcel Hirt, Hirt, Marcel, Πέτρος Δελλαπόρτας +3
Computer Science · Physics and Astronomy · #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.1904.07153
openalex publication_date 2019/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper considers a new family of variational distributions motivated by Sklar's theorem. This family is based on new copula-like densities on the hypercube with non-uniform marginals which can be sampled efficiently, i.e. with a complexity linear in the dimension of state space. Then, the proposed variational densities that we suggest can be seen as arising from these copula-like densities used as base distributions on the hypercube with Gaussian quantile functions and sparse rotation matrices as normalizing flows. The latter correspond to a rotation of the marginals with complexity O(d log d). We provide some empirical evidence that such a variational family can also approximate non-Gaussian posteriors and can be beneficial compared to Gaussian approximations. Our method performs largely comparably to state-of-the-art variational approximations on standard regression and classification benchmarks for Bayesian Neural Networks.