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:动因推导法(VI) 是一种技术,用最优化的方法来估计难以计算后部。与MCMC 相比,第六级比方是许多观测。但是,对于复杂的后部,六级最新方法往往会产生不令人满意的后部近似。本文展示了伯尔斯坦流变异推法(BF-VI),这是一种强大和易于使用的方法,足够灵活,足以接近复杂的多变量后部。BF-VI结合了正常流和伯恩斯坦多面形变异模型中的想法。在基准实验中,我们将BF-VI解决方案与精确的后部、MC MMC 解决方案和六级最新方法,包括以六为基础的正常流。我们展示了低维模型,即BF-VI准确接近真实的后部;在高维模型中,BF-VI优于其他六级方法。此外,我们与BF-VI开发了半结构的Bayesian模型,用于半结构的Melanama挑战数据,将CNN模型的首部分与图像模型结合起来,以六级模型展示了六制数据。