Many statistical models are given in the form of non-normalized densities with an intractable normalization constant. Since maximum likelihood estimation is computationally intensive for these models, several estimation methods have been developed which do not require explicit computation of the normalization constant, such as noise contrastive estimation (NCE) and score matching. However, model selection methods for general non-normalized models have not been proposed so far. In this study, we develop information criteria for non-normalized models estimated by NCE or score matching. They are approximately unbiased estimators of discrepancy measures for non-normalized models. Simulation results and applications to real data demonstrate that the proposed criteria enable selection of the appropriate non-normalized model in a data-driven manner.

翻译：许多统计模型以非标准化密度和难以实现正常化的常数的形式提供,由于对这些模型的最大可能性估算是计算密集的,因此已经制定了一些不要求明确计算正常化常数的估算方法,例如噪声对比估计和得分比对等,然而,迄今尚未提出一般非标准化模型的模式选择方法,在本研究中,我们为非标准化模型制定信息标准,由国家竞争性考试估算或得分比对等,它们大约是非标准化模型差异计量的公正估计。模拟结果和对真实数据的应用表明,拟议的标准使得能够以数据驱动的方式选择适当的非标准化模型。