论文标题
Jensen-Shannon Divergence的基于模拟器模型的无似然模型选择
Likelihood-free Model Choice for Simulator-based Models with the Jensen--Shannon Divergence
论文作者
论文摘要
根据数据的选择，模型的适当结构和参数维度的选择在统计研究中具有丰富的历史，在1970年代开发了第一个开创性方法，例如Akaike's和Schwarz的模型评分标准，这些标准灵感来自信息理论，并体现了称为Occam Razor的依据。在这些开创性的作品之后，很快就将模型选择确立为自己的研究领域，并在计算机科学和统计学中引起了极大的关注。但是，迄今为止，对于缺乏可能性表达的基于模拟器的模型的评分标准的尝试有限。已经考虑了此类模型的贝叶斯因素，但是已经提出了争论和反对使用它们以及与其一致性有关的问题。在这里，我们使用Jensen--Shannon Divergence（JSD）的渐近特性来得出一个一致的模型评分标准，称为JSD-RAZOR的可能性无可能设置。分析了JSD-razor与既定的基于可能性方法的评分标准的关系，我们使用合成和实际建模示例证明了我们标准的有利属性。
Choice of appropriate structure and parametric dimension of a model in the light of data has a rich history in statistical research, where the first seminal approaches were developed in 1970s, such as the Akaike's and Schwarz's model scoring criteria that were inspired by information theory and embodied the rationale called Occam's razor. After those pioneering works, model choice was quickly established as its own field of research, gaining considerable attention in both computer science and statistics. However, to date, there have been limited attempts to derive scoring criteria for simulator-based models lacking a likelihood expression. Bayes factors have been considered for such models, but arguments have been put both for and against use of them and around issues related to their consistency. Here we use the asymptotic properties of Jensen--Shannon divergence (JSD) to derive a consistent model scoring criterion for the likelihood-free setting called JSD-Razor. Relationships of JSD-Razor with established scoring criteria for the likelihood-based approach are analyzed and we demonstrate the favorable properties of our criterion using both synthetic and real modeling examples.
