Models with unnormalized probability density functions are ubiquitous in statistics, artificial intelligence and many other fields. However, they face significant challenges in model selection if the normalizing constants are intractable. Existing methods to address this issue often incur high computational costs, either due to numerical approximations of normalizing constants or evaluation of bias corrections in information criteria. In this paper, we propose a novel and fast selection criterion, T-GIC, for nested models, allowing direct data sampling from a possibly unnormalized probability density function. T-GIC gives a consistent selection under mild regularity conditions and is computationally efficient, benefiting from a multiplying factor that depends only on the sample size and the model complexity. Extensive simulation studies and real-data applications demonstrate the efficacy of T-GIC in the selection of nested models with unnormalized probability densities.

翻译：具有非归一化概率密度函数的模型在统计学、人工智能及众多其他领域中普遍存在。然而，若其归一化常数难以计算，这类模型在模型选择方面将面临重大挑战。现有的解决方法通常因需对归一化常数进行数值近似或评估信息准则中的偏差校正而产生高昂的计算成本。本文针对嵌套模型提出了一种新颖且快速的选择准则——T-GIC，该准则允许直接从可能非归一化的概率密度函数中进行数据采样。在温和的正则性条件下，T-GIC能够实现一致性选择，并且计算效率高，这得益于一个仅依赖于样本量和模型复杂度的乘性因子。大量的模拟研究和实际数据应用验证了T-GIC在具有非归一化概率密度的嵌套模型选择中的有效性。