标题： 与大数据中的误设模型比较：变分贝叶斯视角 显示英文标题

标题： Comparing Misspecified Models with Big Data: A Variational Bayesian Perspective

摘要： 大规模多输入多输出（MIMO）系统中的最优数据检测通常需要极高的计算复杂度。文献中提出了各种检测算法，它们在复杂度和检测性能之间提供了不同的权衡。近年来，变分贝叶斯（VB）已成为在大规模数据背景下解决统计推断问题的广泛使用的方法。本研究关注误设模型，并检验从变分后验分布得出的预测分布相关的风险函数。这些风险函数定义为真实数据生成密度与变分预测分布之间的Kullback-Leibler（KL）散度的期望，为评估预测性能提供了一个框架。我们基于这些风险函数提出了两种新的信息准则用于预测模型比较。在某些正则性条件下，我们证明了所提出的信息准则分别是其相应风险函数的渐近无偏估计量。通过大规模数据背景下的全面数值模拟和经济与金融领域的实证应用，我们展示了这些信息准则在比较误设模型方面的有效性。 显示英文摘要

摘要： Optimal data detection in massive multiple-input multiple-output (MIMO) systems often requires prohibitively high computational complexity. A variety of detection algorithms have been proposed in the literature, offering different trade-offs between complexity and detection performance. In recent years, Variational Bayes (VB) has emerged as a widely used method for addressing statistical inference in the context of massive data. This study focuses on misspecified models and examines the risk functions associated with predictive distributions derived from variational posterior distributions. These risk functions, defined as the expectation of the Kullback-Leibler (KL) divergence between the true data-generating density and the variational predictive distributions, provide a framework for assessing predictive performance. We propose two novel information criteria for predictive model comparison based on these risk functions. Under certain regularity conditions, we demonstrate that the proposed information criteria are asymptotically unbiased estimators of their respective risk functions. Through comprehensive numerical simulations and empirical applications in economics and finance, we demonstrate the effectiveness of these information criteria in comparing misspecified models in the context of massive data.