2025/10/09 by Yifan Chen, Chen, Yifan, Sifan Liu +1 · 1 voice · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Computation (stat.CO) #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Generative Adversarial Networks and Image Synthesis #Machine Learning (stat.ML) #Model Reduction and Neural Networks #stat.CO #stat.ML
paper · pdf · doi:10.48550/arxiv.2510.07732
openalex publication_date 2025/10/09 · arxiv published 2025/10/09 · openalex created_date 2025/10/11 · arxiv updated 2026/07/09 · openalex updated_date 2026/07/28
We propose an iterative Gaussianization method for sampling from unnormalized densities by repeatedly applying mean-field variational inference (MFVI) in rotated coordinate systems. At each iteration, the method selects a rotation, solves an MFVI subproblem in the rotated coordinates, and applies the inverse coordinatewise map to transform the current target closer to the standard Gaussian. The resulting algorithm provides a computationally efficient way to construct flow-like transport maps: it requires only MFVI subproblems, avoids large-scale optimization, and produces transformations that are easy to invert and evaluate. The effectiveness of the procedure depends on selecting informative rotations. We develop an efficient PCA-type method that chooses rotations from the leading eigenvectors of a cross-covariance matrix involving the target's score function. Experiments on Bayesian posterior sampling tasks show that performing MFVI in the proposed PCA-rotated coordinate systems substantially improves over standard MFVI, and that the resulting iterative Gaussianization procedure provides accurate flow-like approximations at lower computational cost than conventional normalizing-flow variational approximations.