This review examines the relevance of parameter identifiability for statistical models used in machine learning. In addition to defining main concepts, we address several issues of identifiability closely related to machine learning, showing the advantages and disadvantages of state-of-the-art research and demonstrating recent progress. First, we review criteria for determining the parameter structure of models from the literature. This has three related issues: parameter identifiability, parameter redundancy, and reparameterization. Second, we review the deep influence of identifiability on various aspects of machine learning from theoretical and application viewpoints. In addition to illustrating the utility and influence of identifiability, we emphasize the interplay among identifiability theory, machine learning, mathematical statistics, information theory, optimization theory, information geometry, Riemann geometry, symbolic computation, Bayesian inference, algebraic geometry, and others. Finally, we present a new perspective together with the associated challenges.

译文

:这篇评论探讨了参数识别性与机器学习中使用的统计模型的相关性。除了定义主要概念外,我们还将解决与机器学习密切相关的可识别性问题,这些问题展示了最新研究的优缺点,并展示了最新进展。首先,我们回顾从文献中确定模型参数结构的标准。这具有三个相关的问题:参数可识别性,参数冗余和重新参数化。其次,我们从理论和应用的角度回顾了可识别性对机器学习各个方面的深远影响。除了说明可识别性的效用和影响之外,我们还强调可识别性理论,机器学习,数学统计,信息论,优化理论,信息几何,Riemann几何,符号计算,贝叶斯推断,代数几何等之间的相互作用。最后,我们提出了一个新的观点以及相关的挑战。

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