This paper presents an approach for efficiently approximating the inverse of Fisher information, a key component in variational Bayes inference. A notable aspect of our approach is the avoidance of analytically computing the Fisher information matrix and its explicit inversion. Instead, we introduce an iterative procedure for generating a sequence of matrices that converge to the inverse of Fisher information. The natural gradient variational Bayes algorithm without matrix inversion is provably convergent and achieves a convergence rate of order O(log s/s), with s the number of iterations. We also obtain a central limit theorem for the iterates. Our algorithm exhibits versatility, making it applicable across a diverse array of variational Bayes domains, including Gaussian approximation and normalizing flow Variational Bayes. We offer a range of numerical examples to demonstrate the efficiency and reliability of the proposed variational Bayes method.

翻译：本文提出了一种高效近似Fisher信息逆的方法，这是变分贝叶斯推断中的关键组成部分。我们方法的一个显著特点是无需解析计算Fisher信息矩阵及其显式求逆。取而代之的是，我们引入了一种迭代过程，用于生成一系列收敛于Fisher信息逆的矩阵。无矩阵求逆的自然梯度变分贝叶斯算法可证明收敛，并达到O(log s/s)的收敛速率，其中s为迭代次数。我们还获得了迭代量的中心极限定理。我们的算法展现出广泛的适用性，可应用于多种变分贝叶斯领域，包括高斯近似和归一化流变分贝叶斯。我们提供了一系列数值算例，以证明所提出的变分贝叶斯方法的效率和可靠性。