Model selection is a ubiquitous problem that arises in the application of many statistical and machine learning methods. In the likelihood and related settings, it is typical to use the method of information criteria (IC) to choose the most parsimonious among competing models by penalizing the likelihood-based objective function. Theorems guaranteeing the consistency of IC can often be difficult to verify and are often specific and bespoke. We present a set of results that guarantee consistency for a class of IC, which we call PanIC (from the Greek root 'pan', meaning 'of everything'), with easily verifiable regularity conditions. The PanIC are applicable in any loss-based learning problem and are not exclusive to likelihood problems. We illustrate the verification of regularity conditions for model selection problems regarding finite mixture models, least absolute deviation and support vector regression, and principal component analysis, and we demonstrate the effectiveness of the PanIC for such problems via numerical simulations. Furthermore, we present new sufficient conditions for the consistency of BIC-like estimators and provide comparisons of the BIC to PanIC.

翻译：摘要：模型选择是众多统计与机器学习方法应用中普遍存在的问题。在似然及相关设定下，通常采用信息准则（IC）方法，通过惩罚基于似然的目标函数，从竞争模型中选出最简洁的模型。现有证明IC一致性的定理往往难以验证，且通常具有特殊性和定制化特征。我们提出了一组保证一类IC一致性的结果，这类IC被称为PanIC（源于希腊语词根'pan'，意为'全部'），其正则性条件易于验证。PanIC适用于任何基于损失的学习问题，并非似然问题所独有。我们针对有限混合模型、最小绝对偏差与支持向量回归、主成分分析等模型选择问题，展示了正则性条件的验证过程，并通过数值模拟证明了PanIC在这些问题上的有效性。此外，我们提出了BIC类估计量一致性的新充分条件，并比较了BIC与PanIC。