Variational inference (VI) is a technique to approximate difficult to compute posteriors by optimization. In contrast to MCMC, VI scales to many observations. In the case of complex posteriors, however, state-of-the-art VI approaches often yield unsatisfactory posterior approximations. This paper presents Bernstein flow variational inference (BF-VI), a robust and easy-to-use method, flexible enough to approximate complex multivariate posteriors. BF-VI combines ideas from normalizing flows and Bernstein polynomial-based transformation models. In benchmark experiments, we compare BF-VI solutions with exact posteriors, MCMC solutions, and state-of-the-art VI methods including normalizing flow based VI. We show for low-dimensional models that BF-VI accurately approximates the true posterior; in higher-dimensional models, BF-VI outperforms other VI methods. Further, we develop with BF-VI a Bayesian model for the semi-structured Melanoma challenge data, combining a CNN model part for image data with an interpretable model part for tabular data, and demonstrate for the first time how the use of VI in semi-structured models.

翻译：变分推断（VI）是一种通过优化来近似难以计算的后验分布的技术。与MCMC相比，VI可扩展至大规模观测数据。然而在处理复杂后验分布时，现有先进的VI方法往往难以获得令人满意的后验近似。本文提出伯恩斯坦流变分推断（BF-VI），这是一种鲁棒且易用的方法，具有足够的灵活性来近似复杂的多元后验分布。BF-VI融合了归一化流与基于伯恩斯坦多项式的变换模型思想。在基准实验中，我们将BF-VI的求解结果与真实后验分布、MCMC求解结果以及包括基于归一化流VI在内的先进VI方法进行了对比。研究表明，在低维模型中BF-VI能精确逼近真实后验；在高维模型中，BF-VI优于其他VI方法。此外，我们利用BF-VI为半结构化黑色素瘤挑战数据开发了贝叶斯模型，该模型将处理图像数据的CNN模型部分与处理表格数据的可解释模型部分相结合，首次展示了VI在半结构化模型中的应用。