AutoGFI: Streamlined Generalized Fiducial Inference for Modern Inference Problems in Models with Additive Errors

The concept of fiducial inference was introduced by R. A. Fisher in the 1930s to address the perceived limitations of Bayesian inference, particularly the need for subjective prior distributions in cases with limited prior information. However, Fisher’s fiducial approach lost favor due to complications, especially in multi-parameter problems. With renewed interest in fiducial inference in the 2000s, generalized fiducial inference (GFI) emerged as a promising extension of Fisher’s ideas, offering new solutions for complex inference challenges. Despite its potential, GFI’s adoption has been hindered by demanding mathematical derivations and complex implementation requirements, such as Markov chain Monte Carlo (MCMC) algorithms. This article introduces AutoGFI, a streamlined variant of GFI designed to simplify its application across various inference problems with additive noise. AutoGFI’s accessibility lies in its simplicity—requiring only a fitting routine—making it a feasible option for a wider range of researchers and practitioners. To demonstrate its efficacy, AutoGFI is applied to three challenging problems: tensor regression, matrix completion, and network cohesion regression. These case studies showcase AutoGFI’s competitive performance against specialized solutions, highlighting its potential to broaden the application of GFI in practical domains, ultimately enriching the statistical inference toolkit.

信仰推断（fiducial inference）的概念由R·A·费希尔于20世纪30年代提出，旨在解决贝叶斯推断的公认局限——尤其是在先验信息有限的场景中，对主观先验分布的需求。然而，费希尔的信仰推断方法因存在复杂性问题（尤其在多参数问题中）而逐渐失宠。21世纪初，信仰推断研究再度兴起，广义信仰推断（generalized fiducial inference，GFI）作为费希尔思想的极具前景的延伸应运而生，为复杂推断难题提供了全新解决方案。尽管潜力可观，但广义信仰推断的推广仍受限于其严苛的数学推导与复杂的实现要求，例如马尔可夫链蒙特卡洛（Markov chain Monte Carlo，MCMC）算法。本文介绍了AutoGFI，一种针对带加性噪声的各类推断问题设计的简化版广义信仰推断方法。AutoGFI的易用性源于其极简性——仅需一个拟合流程即可完成部署，因此成为覆盖更广泛研究者与从业者的可行方案。为验证其有效性，本文将AutoGFI应用于三项具有挑战性的任务：张量回归、矩阵补全与网络凝聚性回归。这些案例研究表明，AutoGFI的性能可与专用解决方案相媲美，彰显了其拓宽广义信仰推断在实际领域应用的潜力，最终将丰富统计推断工具集。