The origins of fiducial inference trace back to the 1930s when R. A. Fisher first introduced the concept as a response to what he perceived as a limitation of Bayesian inference - the requirement for a subjective prior distribution on model parameters in cases where no prior information was available. However, Fisher's initial fiducial approach fell out of favor as complications arose, particularly in multi-parameter problems. In the wake of 2000, amidst a renewed interest in contemporary adaptations of fiducial inference, generalized fiducial inference (GFI) emerged to extend Fisher's fiducial argument, providing a promising avenue for addressing numerous crucial and practical inference challenges. Nevertheless, the adoption of GFI has been limited due to its often demanding mathematical derivations and the necessity for implementing complex Markov Chain Monte Carlo algorithms. This complexity has impeded its widespread utilization and practical applicability. This paper presents a significant advancement by introducing an innovative variant of GFI designed to alleviate these challenges. Specifically, this paper proposes AutoGFI, an easily implementable algorithm that streamlines the application of GFI to a broad spectrum of inference problems involving additive noise. AutoGFI can be readily implemented as long as a fitting routine is available, making it accessible to a broader audience of researchers and practitioners. To demonstrate its effectiveness, AutoGFI is applied to three contemporary and challenging problems: tensor regression, matrix completion, and regression with network cohesion. These case studies highlight the immense potential of GFI and illustrate AutoGFI's promising performance when compared to specialized solutions for these problems. Overall, this research paves the way for a more accessible and powerful application of GFI in a range of practical domains.

翻译：信念推断的起源可追溯至20世纪30年代，R. A. Fisher首次提出这一概念，旨在回应他所认为的贝叶斯推断的局限性——即在缺乏先验信息时，需要对模型参数施加主观先验分布。然而，Fisher最初的信念方法因在多参数问题中引发复杂难题而逐渐失宠。2000年后，随着对当代信念推断新诠释的兴趣复兴，广义信念推断（GFI）应运而生，它扩展了Fisher的信念论证，为解决众多关键且实用的推断挑战提供了有前景的途径。尽管如此，GFI的采用仍受限于其通常繁琐的数学推导，以及实现复杂马尔可夫链蒙特卡洛（MCMC）算法的必要性。这种复杂性阻碍了它的广泛使用和实际应用。本文通过引入一种创新的GFI变体，专门用于缓解这些挑战，从而取得了显著进展。具体而言，本文提出AutoGFI，一种易于实现的算法，它简化了GFI在涉及加性噪声的广泛推断问题中的应用。只要存在合适的拟合程序，AutoGFI即可直接实现，从而使其面向更广泛的研究人员和实践者群体。为证明其有效性，我们将AutoGFI应用于三个当代且具有挑战性的问题：张量回归、矩阵补全以及带网络凝聚性的回归。这些案例研究凸显了GFI的巨大潜力，并展示了AutoGFI在面对这些问题的专用解决方案时表现出的优异性能。总体而言，本研究为GFI在多个实际领域中实现更易用、更强大的应用铺平了道路。